lectures/07_linear-models.ipynb

{
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  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "![](img/330-banner.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "# Lecture 7: Linear Models\n",
    "\n",
    "\n",
    "UBC 2021-22\n",
    "\n",
    "Instructor: Giulia Toti"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "## Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "import os\n",
    "import sys\n",
    "\n",
    "sys.path.append(\"code/.\")\n",
    "\n",
    "import IPython\n",
    "import ipywidgets as widgets\n",
    "import matplotlib.pyplot as plt\n",
    "import mglearn\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from IPython.display import HTML, display\n",
    "from ipywidgets import interact, interactive\n",
    "from plotting_functions import *\n",
    "from sklearn.dummy import DummyClassifier\n",
    "from sklearn.feature_extraction.text import CountVectorizer, TfidfVectorizer\n",
    "from sklearn.impute import SimpleImputer\n",
    "from sklearn.model_selection import cross_val_score, cross_validate, train_test_split\n",
    "from sklearn.neighbors import KNeighborsClassifier, KNeighborsRegressor\n",
    "from sklearn.pipeline import Pipeline, make_pipeline\n",
    "from sklearn.preprocessing import OneHotEncoder, StandardScaler\n",
    "from sklearn.svm import SVC\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from utils import *\n",
    "\n",
    "%matplotlib inline\n",
    "pd.set_option(\"display.max_colwidth\", 200)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "## Learning outcomes\n",
    "\n",
    "From this lecture, students are expected to be able to: \n",
    "\n",
    "- Explain the general intuition behind linear models;\n",
    "- Explain how `predict` works for linear regression;\n",
    "- Use `scikit-learn`'s `Ridge` model; \n",
    "- Demonstrate how the `alpha` hyperparameter of `Ridge` is related to the fundamental tradeoff; \n",
    "- Explain the difference between linear regression and logistic regression;   \n",
    "- Use `scikit-learn`'s `LogisticRegression` model and `predict_proba` to get probability scores\n",
    "- Explain the advantages of getting probability scores instead of hard predictions during classification; \n",
    "- Broadly describe linear SVMs \n",
    "- Explain how can you interpret model predictions using coefficients learned by a linear model; \n",
    "- Explain the advantages and limitations of linear classifiers \n",
    "- Carry out multi-class classification using OVR and OVO strategies. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "<br><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Linear models [[video](https://youtu.be/HXd1U2q4VFA)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**Linear models** is a fundamental and widely used class of models. They are called **linear** because they make a prediction using a **linear function** of the input features.  \n",
    "\n",
    "We will talk about three linear models: \n",
    "- Linear regression \n",
    "- Logistic regression\n",
    "- Linear SVM (brief mention)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Linear regression \n",
    "\n",
    "- A very popular statistical model and has a long history.  \n",
    "- Imagine a hypothetical regression problem of predicting weight of a snake given its length. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>length</th>\n",
       "      <th>weight</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>73</th>\n",
       "      <td>1.489130</td>\n",
       "      <td>10.507995</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>53</th>\n",
       "      <td>1.073233</td>\n",
       "      <td>7.658047</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>80</th>\n",
       "      <td>1.622709</td>\n",
       "      <td>9.748797</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>0.984653</td>\n",
       "      <td>9.731572</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>0.484937</td>\n",
       "      <td>3.016555</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      length     weight\n",
       "73  1.489130  10.507995\n",
       "53  1.073233   7.658047\n",
       "80  1.622709   9.748797\n",
       "49  0.984653   9.731572\n",
       "23  0.484937   3.016555"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(7)\n",
    "n = 100\n",
    "X_1 = np.linspace(0, 2, n) + np.random.randn(n) * 0.01\n",
    "X = pd.DataFrame(X_1[:, None], columns=[\"length\"])\n",
    "\n",
    "y = abs(np.random.randn(n, 1)) * 3 + X_1[:, None] * 5 + 0.2\n",
    "y = pd.DataFrame(y, columns=[\"weight\"])\n",
    "snakes_df = pd.concat([X, y], axis=1)\n",
    "train_df, test_df = train_test_split(snakes_df, test_size=0.2, random_state=77)\n",
    "\n",
    "X_train = train_df[[\"length\"]]\n",
    "y_train = train_df[\"weight\"]\n",
    "X_test = test_df[[\"length\"]]\n",
    "y_test = test_df[\"weight\"]\n",
    "train_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let's visualize the hypothetical snake data. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X_train, y_train, \".\", markersize=10)\n",
    "plt.xlabel(\"length\")\n",
    "plt.ylabel(\"weight (target)\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let's plot a linear regression model on this dataset. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "grid = np.linspace(min(X_train.to_numpy())[0], max(X_train.to_numpy())[0], 1000)\n",
    "grid = grid.reshape(-1, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/gtoti/opt/anaconda3/envs/cpsc330/lib/python3.9/site-packages/sklearn/base.py:450: UserWarning: X does not have valid feature names, but Ridge was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import Ridge\n",
    "\n",
    "r = Ridge()\n",
    "r.fit(X_train, y_train)\n",
    "plt.plot(X_train, y_train, \".\", markersize=10)\n",
    "plt.plot(grid, r.predict(grid))\n",
    "plt.grid(True)\n",
    "plt.xlabel(\"length\")\n",
    "plt.ylabel(\"weight (target)\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**The orange line is the learned linear model.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Prediction of linear regression\n",
    "\n",
    "- Given a snake length, we can use the model above to predict the target (i.e., the weight of the snake). \n",
    "- The prediction will be the corresponding weight on the orange line. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/gtoti/opt/anaconda3/envs/cpsc330/lib/python3.9/site-packages/sklearn/base.py:450: UserWarning: X does not have valid feature names, but Ridge was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([6.20683258])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "snake_length = 0.75\n",
    "r.predict([[snake_length]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### What are we exactly learning? \n",
    "\n",
    "- The model above is a line, which can be represented with a slope (i.e., coefficient or weight) and an intercept. \n",
    "- For the above model, we can access the slope (i.e., coefficient or weight) and the intercept using `coef_` and `intercept_`, respectively. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5.26370005])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r.coef_  # r is our linear regression object"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.259057547817185"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r.intercept_  # r is our linear regression object"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### How are we making predictions? \n",
    "- Given a feature value $x_1$ and learned coefficient $w_1$ and intercept $b$, we can get the prediction $\\hat{y}$ with the following formula:\n",
    "$$\\hat{y} = w_1x_1 + b$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([6.20683258])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prediction = snake_length * r.coef_ + r.intercept_\n",
    "prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/gtoti/opt/anaconda3/envs/cpsc330/lib/python3.9/site-packages/sklearn/base.py:450: UserWarning: X does not have valid feature names, but Ridge was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([6.20683258])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r.predict([[snake_length]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Great! Now we exactly know how the model is making the prediction. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Generalizing to more features\n",
    "For more features, the model is a higher dimensional hyperplane and the general prediction formula looks as follows: \n",
    "\n",
    "$\\hat{y} =$ <font color=\"red\">$w_1$</font> <font color=\"blue\">$x_1$ </font> $+ \\dots +$ <font color=\"red\">$w_d$</font> <font color=\"blue\">$x_d$</font> + <font  color=\"green\"> $b$</font>\n",
    "\n",
    "where, \n",
    "- <font  color=\"blue\"> ($x_1, \\dots, x_d$) are input features </font>\n",
    "- <font  color=\"red\"> ($w_1, \\dots, w_d$) are coefficients or weights </font> (learned from the data)\n",
    "- <font  color=\"green\"> $b$ is the bias which can be used to offset your hyperplane </font> (learned from the data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Example \n",
    "\n",
    "- Suppose these are the coefficients learned by a linear regression model on a hypothetical housing price prediction dataset. \n",
    "\n",
    "| Feature | Learned coefficient |\n",
    "|--------------------|---------------------:|\n",
    "| Bedrooms | 0.20 |\n",
    "| Bathrooms| 0.11 |\n",
    "| Square Footage | 0.002 |\n",
    "| Age | -0.02 |\n",
    "\n",
    "- Now given a new example, the target will be predicted as follows: \n",
    "| Bedrooms | Bathrooms | Square Footage | Age |\n",
    "|--------------------|---------------------|----------------|-----| \n",
    "| 3                  | 2                   | 1875           | 66  |"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\hat{y} = w_1x_1 + w_2x_2 + w_3x_3 + w_4x_4 + b$$\n",
    "\n",
    "$$\\text{predicted price}=  0.20 \\times 3 + 0.11 \\times 2 + 0.002 \\times 1875 + (-0.02) \\times 66 + b$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "When we call `fit`, a coefficient or weight is learned for each feature which tells us the role of that feature in prediction. These coefficients are learned from the training data.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "```{important}\n",
    "In linear models for regression, the model is a line for a single feature, a plane for two features, and a hyperplane for higher dimensions. We are not yet ready to discuss how does linear regression learn these coefficients and intercept.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### `Ridge`\n",
    "\n",
    "- `scikit-learn` has a model called `LinearRegression` for linear regression. \n",
    "- But if we use this \"vanilla\" version of linear regression, it may result in large coefficients and unexpected results. \n",
    "- So instead of using `LinearRegression`, we will always use another linear model called `Ridge`, which is a linear regression model with a complexity hyperparameter `alpha`.\n",
    "- If you want to know more about how Ridge regularization works, I recommend this tutorial: https://www.analyticsvidhya.com/blog/2016/01/ridge-lasso-regression-python-complete-tutorial/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression  # DO NOT USE IT\n",
    "from sklearn.linear_model import Ridge  # USE THIS INSTEAD"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's use `sklearn`'s built in regression dataset, the Boston Housing dataset. The task associated with this dataset is to predict the median value of homes in several Boston neighborhoods in the 1970s, using information such as crime rate in the neighbourhood, average number of rooms, proximity to the Charles River, highway accessibility, and so on."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/gtoti/opt/anaconda3/envs/cpsc330/lib/python3.9/site-packages/sklearn/utils/deprecation.py:87: FutureWarning: Function load_boston is deprecated; `load_boston` is deprecated in 1.0 and will be removed in 1.2.\n",
      "\n",
      "    The Boston housing prices dataset has an ethical problem. You can refer to\n",
      "    the documentation of this function for further details.\n",
      "\n",
      "    The scikit-learn maintainers therefore strongly discourage the use of this\n",
      "    dataset unless the purpose of the code is to study and educate about\n",
      "    ethical issues in data science and machine learning.\n",
      "\n",
      "    In this special case, you can fetch the dataset from the original\n",
      "    source::\n",
      "\n",
      "        import pandas as pd\n",
      "        import numpy as np\n",
      "\n",
      "\n",
      "        data_url = \"http://lib.stat.cmu.edu/datasets/boston\"\n",
      "        raw_df = pd.read_csv(data_url, sep=\"\\s+\", skiprows=22, header=None)\n",
      "        data = np.hstack([raw_df.values[::2, :], raw_df.values[1::2, :2]])\n",
      "        target = raw_df.values[1::2, 2]\n",
      "\n",
      "    Alternative datasets include the California housing dataset (i.e.\n",
      "    :func:`~sklearn.datasets.fetch_california_housing`) and the Ames housing\n",
      "    dataset. You can load the datasets as follows::\n",
      "\n",
      "        from sklearn.datasets import fetch_california_housing\n",
      "        housing = fetch_california_housing()\n",
      "\n",
      "    for the California housing dataset and::\n",
      "\n",
      "        from sklearn.datasets import fetch_openml\n",
      "        housing = fetch_openml(name=\"house_prices\", as_frame=True)\n",
      "\n",
      "    for the Ames housing dataset.\n",
      "    \n",
      "  warnings.warn(msg, category=FutureWarning)\n"
     ]
    },
    {
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       "      <th></th>\n",
       "      <th>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NOX</th>\n",
       "      <th>RM</th>\n",
       "      <th>AGE</th>\n",
       "      <th>DIS</th>\n",
       "      <th>RAD</th>\n",
       "      <th>TAX</th>\n",
       "      <th>PTRATIO</th>\n",
       "      <th>B</th>\n",
       "      <th>LSTAT</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
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       "      <td>5.1004</td>\n",
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       "      <td>17.9</td>\n",
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       "    <tr>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.524</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.01432</td>\n",
       "      <td>100.0</td>\n",
       "      <td>1.32</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.411</td>\n",
       "      <td>6.816</td>\n",
       "      <td>40.5</td>\n",
       "      <td>8.3248</td>\n",
       "      <td>5.0</td>\n",
       "      <td>256.0</td>\n",
       "      <td>15.1</td>\n",
       "      <td>392.90</td>\n",
       "      <td>3.95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.507</td>\n",
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       "      <td>71.6</td>\n",
       "      <td>4.1480</td>\n",
       "      <td>8.0</td>\n",
       "      <td>307.0</td>\n",
       "      <td>17.4</td>\n",
       "      <td>390.07</td>\n",
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       "    <tr>\n",
       "      <th>400</th>\n",
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       "      <td>0.0</td>\n",
       "      <td>18.10</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.671</td>\n",
       "      <td>6.380</td>\n",
       "      <td>96.2</td>\n",
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       "      <td>24.0</td>\n",
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       "      <td>0.605</td>\n",
       "      <td>6.250</td>\n",
       "      <td>92.6</td>\n",
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       "      <td>5.0</td>\n",
       "      <td>403.0</td>\n",
       "      <td>14.7</td>\n",
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       "      <td>6.301</td>\n",
       "      <td>83.7</td>\n",
       "      <td>2.7831</td>\n",
       "      <td>24.0</td>\n",
       "      <td>666.0</td>\n",
       "      <td>20.2</td>\n",
       "      <td>272.21</td>\n",
       "      <td>16.23</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>404 rows × 13 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         CRIM     ZN  INDUS  CHAS    NOX     RM   AGE     DIS   RAD    TAX  \\\n",
       "0     5.20177    0.0  18.10   1.0  0.770  6.127  83.4  2.7227  24.0  666.0   \n",
       "1     0.17142    0.0   6.91   0.0  0.448  5.682  33.8  5.1004   3.0  233.0   \n",
       "2     0.09378   12.5   7.87   0.0  0.524  5.889  39.0  5.4509   5.0  311.0   \n",
       "3     0.09252   30.0   4.93   0.0  0.428  6.606  42.2  6.1899   6.0  300.0   \n",
       "4     0.01432  100.0   1.32   0.0  0.411  6.816  40.5  8.3248   5.0  256.0   \n",
       "..        ...    ...    ...   ...    ...    ...   ...     ...   ...    ...   \n",
       "399   0.51183    0.0   6.20   0.0  0.507  7.358  71.6  4.1480   8.0  307.0   \n",
       "400  23.64820    0.0  18.10   0.0  0.671  6.380  96.2  1.3861  24.0  666.0   \n",
       "401   0.04819   80.0   3.64   0.0  0.392  6.108  32.0  9.2203   1.0  315.0   \n",
       "402   1.27346    0.0  19.58   1.0  0.605  6.250  92.6  1.7984   5.0  403.0   \n",
       "403   7.75223    0.0  18.10   0.0  0.713  6.301  83.7  2.7831  24.0  666.0   \n",
       "\n",
       "     PTRATIO       B  LSTAT  \n",
       "0       20.2  395.43  11.48  \n",
       "1       17.9  396.90  10.21  \n",
       "2       15.2  390.50  15.71  \n",
       "3       16.6  383.78   7.37  \n",
       "4       15.1  392.90   3.95  \n",
       "..       ...     ...    ...  \n",
       "399     17.4  390.07   4.73  \n",
       "400     20.2  396.90  23.69  \n",
       "401     16.4  392.89   6.57  \n",
       "402     14.7  338.92   5.50  \n",
       "403     20.2  272.21  16.23  \n",
       "\n",
       "[404 rows x 13 columns]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import load_boston\n",
    "\n",
    "boston = load_boston()\n",
    "X_train, X_test, y_train, y_test = train_test_split(\n",
    "    boston.data, boston.target, test_size=0.2\n",
    ")\n",
    "pd.DataFrame(X_train, columns=boston.feature_names)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ".. _boston_dataset:\n",
      "\n",
      "Boston house prices dataset\n",
      "---------------------------\n",
      "\n",
      "**Data Set Characteristics:**  \n",
      "\n",
      "    :Number of Instances: 506 \n",
      "\n",
      "    :Number of Attributes: 13 numeric/categorical predictive. Median Value (attribute 14) is usually the target.\n",
      "\n",
      "    :Attribute Information (in order):\n",
      "        - CRIM     per capita crime rate by town\n",
      "        - ZN       proportion of residential land zoned for lots over 25,000 sq.ft.\n",
      "        - INDUS    proportion of non-retail business acres per town\n",
      "        - CHAS     Charles River dummy variable (= 1 if tract bounds river; 0 otherwise)\n",
      "        - NOX      nitric oxides concentration (parts per 10 million)\n",
      "        - RM       average number of rooms per dwelling\n",
      "        - AGE      proportion of owner-occupied units built prior to 1940\n",
      "        - DIS      weighted distances to five Boston employment centres\n",
      "        - RAD      index of accessibility to radial highways\n",
      "        - TAX      full-value property-tax rate per $10,000\n",
      "        - PTRATIO  pupil-teacher ratio by town\n",
      "        - B        1000(Bk - 0.63)^2 where Bk is the proportion of black people by town\n",
      "        - LSTAT    % lower status of the population\n",
      "        - MEDV     Median value of owner-occupied homes in $1000's\n",
      "\n",
      "    :Missing Attribute Values: None\n",
      "\n",
      "    :Creator: Harrison, D. and Rubinfeld, D.L.\n",
      "\n",
      "This is a copy of UCI ML housing dataset.\n",
      "https://archive.ics.uci.edu/ml/machine-learning-databases/housing/\n",
      "\n",
      "\n",
      "This dataset was taken from the StatLib library which is maintained at Carnegie Mellon University.\n",
      "\n",
      "The Boston house-price data of Harrison, D. and Rubinfeld, D.L. 'Hedonic\n",
      "prices and the demand for clean air', J. Environ. Economics & Management,\n",
      "vol.5, 81-102, 1978.   Used in Belsley, Kuh & Welsch, 'Regression diagnostics\n",
      "...', Wiley, 1980.   N.B. Various transformations are used in the table on\n",
      "pages 244-261 of the latter.\n",
      "\n",
      "The Boston house-price data has been used in many machine learning papers that address regression\n",
      "problems.   \n",
      "     \n",
      ".. topic:: References\n",
      "\n",
      "   - Belsley, Kuh & Welsch, 'Regression diagnostics: Identifying Influential Data and Sources of Collinearity', Wiley, 1980. 244-261.\n",
      "   - Quinlan,R. (1993). Combining Instance-Based and Model-Based Learning. In Proceedings on the Tenth International Conference of Machine Learning, 236-243, University of Massachusetts, Amherst. Morgan Kaufmann.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(boston.DESCR)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### `Ridge` on the Boston housing dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
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       "   fit_time  score_time  test_score  train_score\n",
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     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pipe = make_pipeline(StandardScaler(), Ridge())\n",
    "scores = cross_validate(pipe, X_train, y_train, return_train_score=True)\n",
    "pd.DataFrame(scores)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Hyperparameter `alpha` of `Ridge`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Ridge has hyperparameters just like the rest of the models we learned.\n",
    "- The alpha hyperparameter is what makes `Ridge` different from vanilla `LinearRegression`. \n",
    "- Similar to the other hyperparameters that we saw, `alpha` controls the fundamental tradeoff. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "```{note}\n",
    "If we set alpha=0 that is the same as using LinearRegression.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let's examine the effect of `alpha` on the fundamental tradeoff. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "scores_dict = {\n",
    "    \"alpha\": 10.0 ** np.arange(-2, 6, 1),\n",
    "    \"mean_train_scores\": list(),\n",
    "    \"mean_cv_scores\": list(),\n",
    "}\n",
    "for alpha in scores_dict[\"alpha\"]:\n",
    "    pipe_ridge = make_pipeline(StandardScaler(), Ridge(alpha=alpha))\n",
    "    scores = cross_validate(pipe_ridge, X_train, y_train, return_train_score=True)\n",
    "    scores_dict[\"mean_train_scores\"].append(scores[\"train_score\"].mean())\n",
    "    scores_dict[\"mean_cv_scores\"].append(scores[\"test_score\"].mean())\n",
    "\n",
    "results_df = pd.DataFrame(scores_dict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>alpha</th>\n",
       "      <th>mean_train_scores</th>\n",
       "      <th>mean_cv_scores</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.01</td>\n",
       "      <td>0.765604</td>\n",
       "      <td>0.741829</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.10</td>\n",
       "      <td>0.765603</td>\n",
       "      <td>0.741851</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.00</td>\n",
       "      <td>0.765572</td>\n",
       "      <td>0.742040</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>10.00</td>\n",
       "      <td>0.763671</td>\n",
       "      <td>0.741906</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>100.00</td>\n",
       "      <td>0.731996</td>\n",
       "      <td>0.718132</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1000.00</td>\n",
       "      <td>0.527530</td>\n",
       "      <td>0.522510</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>10000.00</td>\n",
       "      <td>0.155124</td>\n",
       "      <td>0.148313</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>100000.00</td>\n",
       "      <td>0.019292</td>\n",
       "      <td>0.010749</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       alpha  mean_train_scores  mean_cv_scores\n",
       "0       0.01           0.765604        0.741829\n",
       "1       0.10           0.765603        0.741851\n",
       "2       1.00           0.765572        0.742040\n",
       "3      10.00           0.763671        0.741906\n",
       "4     100.00           0.731996        0.718132\n",
       "5    1000.00           0.527530        0.522510\n",
       "6   10000.00           0.155124        0.148313\n",
       "7  100000.00           0.019292        0.010749"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "Here we do not really see overfitting but in general, \n",
    "- larger `alpha` $\\rightarrow$ likely to underfit\n",
    "- smaller `alpha` $\\rightarrow$ likely to overfit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Coefficients and intercept\n",
    "\n",
    "The model learns \n",
    "- coefficients associated with each feature\n",
    "- the intercept or bias"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's examine the coefficients learned by the model. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "pipe_ridge = make_pipeline(StandardScaler(), Ridge(alpha=1.0))\n",
    "pipe_ridge.fit(X_train, y_train)\n",
    "coeffs = pipe_ridge.named_steps[\"ridge\"].coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Coefficients</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>CRIM</th>\n",
       "      <td>-0.923517</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ZN</th>\n",
       "      <td>1.431294</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>INDUS</th>\n",
       "      <td>0.239976</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CHAS</th>\n",
       "      <td>0.546769</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NOX</th>\n",
       "      <td>-2.048052</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RM</th>\n",
       "      <td>2.668174</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AGE</th>\n",
       "      <td>0.035459</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DIS</th>\n",
       "      <td>-3.084434</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RAD</th>\n",
       "      <td>2.407602</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TAX</th>\n",
       "      <td>-2.269648</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PTRATIO</th>\n",
       "      <td>-1.883905</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B</th>\n",
       "      <td>0.897462</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LSTAT</th>\n",
       "      <td>-3.394533</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         Coefficients\n",
       "CRIM        -0.923517\n",
       "ZN           1.431294\n",
       "INDUS        0.239976\n",
       "CHAS         0.546769\n",
       "NOX         -2.048052\n",
       "RM           2.668174\n",
       "AGE          0.035459\n",
       "DIS         -3.084434\n",
       "RAD          2.407602\n",
       "TAX         -2.269648\n",
       "PTRATIO     -1.883905\n",
       "B            0.897462\n",
       "LSTAT       -3.394533"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(data=coeffs, index=boston.feature_names, columns=[\"Coefficients\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- The model also learns an intercept (bias). \n",
    "- For each prediction, we are adding this amount irrespective of the feature values.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "22.446534653465363"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pipe_ridge.named_steps[\"ridge\"].intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Can we use this information to interpret model predictions? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### ❓❓ Questions for you"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "#### True/False: `Ridge`\n",
    "\n",
    "1. Increasing the hyperparameter `alpha` of `Ridge` is likely to decrease model complexity.\n",
    "2. `Ridge` can be used with datasets that have multiple features.\n",
    "3. With Ridge, we learn one coefficient per training example.\n",
    "4. If you train a linear regression model on a 2-dimensional problem (2 features), the model will be a two dimensional plane. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "<br><br><br><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Interpretation of coefficients "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- One of the main advantages of linear models is that they are relatively easy to interpret. \n",
    "- We have one coefficient per feature which kind of describes the role of the feature in the prediction according to the model. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are two pieces of information in the coefficients based on\n",
    "\n",
    "- Sign\n",
    "- Magnitude"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Sign of the coefficients\n",
    "\n",
    "In the example below, for instance: \n",
    "- RM (average number of rooms) has a **positive coefficient**\n",
    "    - the prediction will be proportional to the feature value; as RM gets **bigger**, the median house value gets **bigger** \n",
    "- CRIM (criminal rate in the neighbourhood) has a **negative coefficient**\n",
    "    - the prediction will be inversely proportional to the feature value; as CRIM gets **bigger**, the median house value gets **smaller**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Coefficients</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>CRIM</th>\n",
       "      <td>-0.923517</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ZN</th>\n",
       "      <td>1.431294</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>INDUS</th>\n",
       "      <td>0.239976</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CHAS</th>\n",
       "      <td>0.546769</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NOX</th>\n",
       "      <td>-2.048052</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RM</th>\n",
       "      <td>2.668174</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AGE</th>\n",
       "      <td>0.035459</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DIS</th>\n",
       "      <td>-3.084434</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RAD</th>\n",
       "      <td>2.407602</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TAX</th>\n",
       "      <td>-2.269648</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PTRATIO</th>\n",
       "      <td>-1.883905</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B</th>\n",
       "      <td>0.897462</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LSTAT</th>\n",
       "      <td>-3.394533</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         Coefficients\n",
       "CRIM        -0.923517\n",
       "ZN           1.431294\n",
       "INDUS        0.239976\n",
       "CHAS         0.546769\n",
       "NOX         -2.048052\n",
       "RM           2.668174\n",
       "AGE          0.035459\n",
       "DIS         -3.084434\n",
       "RAD          2.407602\n",
       "TAX         -2.269648\n",
       "PTRATIO     -1.883905\n",
       "B            0.897462\n",
       "LSTAT       -3.394533"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(data=coeffs, index=boston.feature_names, columns=[\"Coefficients\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Magnitude of the coefficients\n",
    "\n",
    "- Bigger magnitude $\\rightarrow$ bigger impact on the prediction \n",
    "- In the example below, both RM and AGE have a positive impact on the prediction but RM would have a bigger positive impact because it's feature value is going to be multiplied by a number with a bigger magnitude. \n",
    "- Similarly both LSAT and NOX have a negative impact on the prediction but LSAT would have a bigger negative impact because it's going to be multiplied by a number with a bigger magnitude. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>coefficient</th>\n",
       "      <th>magnitude</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>LSTAT</th>\n",
       "      <td>-3.394533</td>\n",
       "      <td>3.394533</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DIS</th>\n",
       "      <td>-3.084434</td>\n",
       "      <td>3.084434</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RM</th>\n",
       "      <td>2.668174</td>\n",
       "      <td>2.668174</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RAD</th>\n",
       "      <td>2.407602</td>\n",
       "      <td>2.407602</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TAX</th>\n",
       "      <td>-2.269648</td>\n",
       "      <td>2.269648</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NOX</th>\n",
       "      <td>-2.048052</td>\n",
       "      <td>2.048052</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PTRATIO</th>\n",
       "      <td>-1.883905</td>\n",
       "      <td>1.883905</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ZN</th>\n",
       "      <td>1.431294</td>\n",
       "      <td>1.431294</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CRIM</th>\n",
       "      <td>-0.923517</td>\n",
       "      <td>0.923517</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B</th>\n",
       "      <td>0.897462</td>\n",
       "      <td>0.897462</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CHAS</th>\n",
       "      <td>0.546769</td>\n",
       "      <td>0.546769</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>INDUS</th>\n",
       "      <td>0.239976</td>\n",
       "      <td>0.239976</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AGE</th>\n",
       "      <td>0.035459</td>\n",
       "      <td>0.035459</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         coefficient  magnitude\n",
       "LSTAT      -3.394533   3.394533\n",
       "DIS        -3.084434   3.084434\n",
       "RM          2.668174   2.668174\n",
       "RAD         2.407602   2.407602\n",
       "TAX        -2.269648   2.269648\n",
       "NOX        -2.048052   2.048052\n",
       "PTRATIO    -1.883905   1.883905\n",
       "ZN          1.431294   1.431294\n",
       "CRIM       -0.923517   0.923517\n",
       "B           0.897462   0.897462\n",
       "CHAS        0.546769   0.546769\n",
       "INDUS       0.239976   0.239976\n",
       "AGE         0.035459   0.035459"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = {\n",
    "    \"coefficient\": pipe_ridge.named_steps[\"ridge\"].coef_.tolist(),\n",
    "    \"magnitude\": np.absolute(pipe_ridge.named_steps[\"ridge\"].coef_.tolist()),\n",
    "}\n",
    "coef_df = pd.DataFrame(data, index=boston.feature_names).sort_values(\n",
    "    \"magnitude\", ascending=False\n",
    ")\n",
    "coef_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Importance of scaling \n",
    "- When you are interpreting the model coefficients, scaling is crucial. \n",
    "- If you do not scale the data, features with smaller magnitude are going to get coefficients with bigger magnitude whereas features with bigger scale are going to get coefficients with smaller magnitude.\n",
    "- That said, when you scale the data, feature values become hard to interpret for humans!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{Important}\n",
    "Take these coefficients with a grain of salt. They might not always match your intuitions.  \n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### ❓❓ Questions for you"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### True/False\n",
    "\n",
    "1. Suppose you have trained a linear model on an unscaled data. The coefficients of the linear model have the following interpretation: if coefficient $j$ is large, that means a change in feature $j$ has a large impact on the prediction.\n",
    "2. Suppose the scaled feature value of NOX feature above is negative. The prediction will still be inversely proportional to NOX; as NOX gets **bigger**, the median house value gets **smaller**. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Questions for breakout room discussion \n",
    "\n",
    "- Discuss the importance of scaling when interpreting linear regression coefficients. \n",
    "- What might be the meaning of complex vs simpler model in case of linear regression? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br><br><br><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Logistic regression [[video](https://youtu.be/56L5z_t22qE)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### Logistic regression intuition \n",
    "\n",
    "- A linear model for **classification**. \n",
    "- Similar to linear regression, it learns weights associated with each feature and the bias. \n",
    "- It applies a **threshold** on the raw output to decide whether the class is positive or negative. \n",
    "- In this lecture we will focus on the following aspects of logistic regression.  \n",
    "    - `predict`, `predict_proba` \n",
    "    - how to use learned coefficients to interpret the model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Motivating example \n",
    "\n",
    "- Consider the problem of predicting sentiment expressed in movie reviews. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Training data for the motivating example\n",
    "\n",
    "\n",
    "<blockquote> \n",
    "    <p>Review 1: This movie was <b>excellent</b>! The performances were oscar-worthy!  👍 </p> \n",
    "    <p>Review 2: What a <b>boring</b> movie! I almost fell asleep twice while watching it. 👎 </p> \n",
    "    <p>Review 3: I enjoyed the movie. <b>Excellent</b>! 👍 </p>             \n",
    "</blockquote>  \n",
    "\n",
    "- Targets: positive 👍 and negative 👎\n",
    "- Features: words (e.g., *excellent*, *flawless*, *boring*)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Learned coefficients associated with all features\n",
    "\n",
    "- Suppose our vocabulary contains only the following 7 words. \n",
    "- A linear classifier learns **weights** or **coefficients** associated with the features (words in this example).  \n",
    "- Let's ignore bias for a bit. \n",
    "\n",
    "<center>\n",
    "<img src='./img/words_coeff.png' width=\"250\" height=\"300\" />\n",
    "</center>  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Predicting with learned weights \n",
    "- Use these learned coefficients to make predictions. For example, consider the following review $x_i$. \n",
    "<blockquote> \n",
    "It got a bit <b>boring</b> at times but the direction was <b>excellent</b> and the acting was <b>flawless</b>.\n",
    "</blockquote>\n",
    "- Feature vector for $x_i$: [1, 0, 1, 1, 0, 0, 0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<center>\n",
    "<img src='./img/words_coeff.png' width=\"250\" height=\"300\" />\n",
    "</center>  \n",
    "\n",
    "- $score(x_i) = $ coefficient(*boring*) $\\times 1$ + coefficient(*excellent*) $\\times 1$ + coefficient(*flawless*) $\\times 1$ = $-1.40 + 1.93 + 1.43 = 1.96$\n",
    "\n",
    "- $1.96 > 0$ so predict the review as positive 👍. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Weighted sum of the input features = 1.960 y_hat = pos\n"
     ]
    },
    {
     "data": {
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       "</g>\n",
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       "<title>y_hat=pos</title>\n",
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       "</g>\n",
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       "</g>\n",
       "<!-- excellent=1 -->\n",
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       "<title>excellent=1</title>\n",
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       "<title>excellent=1&#45;&gt;y_hat=pos</title>\n",
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       "<title>flawless=1</title>\n",
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       "</g>\n",
       "<!-- flawless=1&#45;&gt;y_hat=pos -->\n",
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       "<title>flawless=1&#45;&gt;y_hat=pos</title>\n",
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       "<text text-anchor=\"middle\" x=\"153.09\" y=\"-140.8\" font-family=\"Times,serif\" font-size=\"14.00\">1.43</text>\n",
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       "<graphviz.graphs.Digraph at 0x152fb7c10>"
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     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = [\"boring=1\", \"excellent=1\", \"flawless=1\"]\n",
    "w = [-1.40, 1.93, 1.43]\n",
    "display(plot_logistic_regression(x, w))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- So the prediction is based on the weighted sum of the input features.\n",
    "- Some feature are pulling the prediction towards positive sentiment and some are pulling it towards negative sentiment. \n",
    "- If the coefficient of _boring_ had a bigger magnitude or _excellent_ and _flawless_ had smaller magnitudes, we would have predicted \"neg\".   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def f(w_0):\n",
    "    x = [\"boring=1\", \"excellent=1\", \"flawless=1\"]\n",
    "    w = [-1.40, 1.93, 1.43]\n",
    "    w[0] = w_0\n",
    "    print(w)\n",
    "    display(plot_logistic_regression(x, w))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "4f988a9e6aec43a9beae6160e455f9dc",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=-1.4, description='w_0', max=2.0, min=-6.0, step=0.5), Output()), _dom…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "interactive(\n",
    "    f,\n",
    "    w_0=widgets.FloatSlider(min=-6, max=2, step=0.5, value=-1.40),\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "In our case, for values for the coefficient of _boring_ < -3.36, the prediction would be negative. \n",
    "\n",
    "A linear model learns these coefficients or weights from the training data! "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "So a linear classifier is a linear function of the input `X`, followed by a threshold. \n",
    "\n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "z =& w_1x_1 + \\dots + w_dx_d + b\\\\\n",
    "=& w^Tx + b\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "\n",
    "$$\\hat{y} = \\begin{cases}\n",
    "         1, & \\text{if } z \\geq r\\\\\n",
    "         -1, & \\text{if } z < r\n",
    "\\end{cases}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Components of a linear classifier\n",
    "\n",
    "1. input features ($x_1, \\dots, x_d$)\n",
    "2. coefficients (weights) ($w_1, \\dots, w_d$)\n",
    "3. bias ($b$ or $w_0$) (can be used to offset your hyperplane)\n",
    "4. threshold ($r$)\n",
    "\n",
    "In our example before, we assumed $r=0$ and $b=0$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Logistic regression on the cities data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>longitude</th>\n",
       "      <th>latitude</th>\n",
       "      <th>country</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>160</th>\n",
       "      <td>-76.4813</td>\n",
       "      <td>44.2307</td>\n",
       "      <td>Canada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>127</th>\n",
       "      <td>-81.2496</td>\n",
       "      <td>42.9837</td>\n",
       "      <td>Canada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>169</th>\n",
       "      <td>-66.0580</td>\n",
       "      <td>45.2788</td>\n",
       "      <td>Canada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>188</th>\n",
       "      <td>-73.2533</td>\n",
       "      <td>45.3057</td>\n",
       "      <td>Canada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>187</th>\n",
       "      <td>-67.9245</td>\n",
       "      <td>47.1652</td>\n",
       "      <td>Canada</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     longitude  latitude country\n",
       "160   -76.4813   44.2307  Canada\n",
       "127   -81.2496   42.9837  Canada\n",
       "169   -66.0580   45.2788  Canada\n",
       "188   -73.2533   45.3057  Canada\n",
       "187   -67.9245   47.1652  Canada"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cities_df = pd.read_csv(\"data/canada_usa_cities.csv\")\n",
    "train_df, test_df = train_test_split(cities_df, test_size=0.2, random_state=123)\n",
    "X_train, y_train = train_df.drop(columns=[\"country\"], axis=1), train_df[\"country\"]\n",
    "X_test, y_test = test_df.drop(columns=[\"country\"], axis=1), test_df[\"country\"]\n",
    "\n",
    "train_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let's first try `DummyClassifier` on the cities data. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>fit_time</th>\n",
       "      <th>score_time</th>\n",
       "      <th>test_score</th>\n",
       "      <th>train_score</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.000613</td>\n",
       "      <td>0.000376</td>\n",
       "      <td>0.588235</td>\n",
       "      <td>0.601504</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.000359</td>\n",
       "      <td>0.000197</td>\n",
       "      <td>0.588235</td>\n",
       "      <td>0.601504</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.000335</td>\n",
       "      <td>0.000196</td>\n",
       "      <td>0.606061</td>\n",
       "      <td>0.597015</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.000326</td>\n",
       "      <td>0.000184</td>\n",
       "      <td>0.606061</td>\n",
       "      <td>0.597015</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.000281</td>\n",
       "      <td>0.000161</td>\n",
       "      <td>0.606061</td>\n",
       "      <td>0.597015</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   fit_time  score_time  test_score  train_score\n",
       "0  0.000613    0.000376    0.588235     0.601504\n",
       "1  0.000359    0.000197    0.588235     0.601504\n",
       "2  0.000335    0.000196    0.606061     0.597015\n",
       "3  0.000326    0.000184    0.606061     0.597015\n",
       "4  0.000281    0.000161    0.606061     0.597015"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dummy = DummyClassifier()\n",
    "scores = cross_validate(dummy, X_train, y_train, return_train_score=True)\n",
    "pd.DataFrame(scores)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Now let's try `LogisticRegression`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>fit_time</th>\n",
       "      <th>score_time</th>\n",
       "      <th>test_score</th>\n",
       "      <th>train_score</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.008090</td>\n",
       "      <td>0.000911</td>\n",
       "      <td>0.852941</td>\n",
       "      <td>0.827068</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.004588</td>\n",
       "      <td>0.001050</td>\n",
       "      <td>0.823529</td>\n",
       "      <td>0.827068</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.004509</td>\n",
       "      <td>0.000972</td>\n",
       "      <td>0.696970</td>\n",
       "      <td>0.858209</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.004039</td>\n",
       "      <td>0.000726</td>\n",
       "      <td>0.787879</td>\n",
       "      <td>0.843284</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.004019</td>\n",
       "      <td>0.000753</td>\n",
       "      <td>0.939394</td>\n",
       "      <td>0.805970</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   fit_time  score_time  test_score  train_score\n",
       "0  0.008090    0.000911    0.852941     0.827068\n",
       "1  0.004588    0.001050    0.823529     0.827068\n",
       "2  0.004509    0.000972    0.696970     0.858209\n",
       "3  0.004039    0.000726    0.787879     0.843284\n",
       "4  0.004019    0.000753    0.939394     0.805970"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "lr = LogisticRegression()\n",
    "scores = cross_validate(lr, X_train, y_train, return_train_score=True)\n",
    "pd.DataFrame(scores)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Logistic regression seems to be doing better than dummy classifier. But note that there is a lot of variation in the scores. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Accessing learned parameters\n",
    "\n",
    "- Recall that logistic regression learns the weights $w$ and bias or intercept $b$.\n",
    "\n",
    "- How to access these weights? \n",
    "    - Similar to `Ridge`, we can access the weights and intercept using `coef_` and `intercept_` attribute of the `LogisticRegression` object, respectively. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model weights: [[-0.04108149 -0.33683126]]\n",
      "Model intercept: [10.8869838]\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>features</th>\n",
       "      <th>coefficients</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>longitude</td>\n",
       "      <td>-0.041081</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>latitude</td>\n",
       "      <td>-0.336831</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    features  coefficients\n",
       "0  longitude     -0.041081\n",
       "1   latitude     -0.336831"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr = LogisticRegression()\n",
    "lr.fit(X_train, y_train)\n",
    "print(\"Model weights: %s\" % (lr.coef_))  # these are the learned weights\n",
    "print(\"Model intercept: %s\" % (lr.intercept_))  # this is the bias term\n",
    "data = {\"features\": X_train.columns, \"coefficients\": lr.coef_[0]}\n",
    "pd.DataFrame(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Both negative weights \n",
    "- The weight of latitude is larger in magnitude. \n",
    "- This makes sense because Canada as a country lies above the USA and so we expect latitude values to contribute more to a prediction than longitude. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Prediction with learned parameters\n",
    "\n",
    "Let's predict target of a test example. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "longitude   -64.8001\n",
       "latitude     46.0980\n",
       "Name: 172, dtype: float64"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "example = X_test.iloc[0, :]\n",
    "example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Raw scores\n",
    "\n",
    "- Calculate the raw score as: ```y_hat = np.dot(w, x) + b```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.97817876])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(\n",
    "    np.dot(\n",
    "        example.to_numpy(),\n",
    "        lr.coef_.reshape(\n",
    "            2,\n",
    "        ),\n",
    "    )\n",
    "    + lr.intercept_\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- Apply the threshold to the raw score. \n",
    "- Since the prediction is < 0, predict \"negative\". \n",
    "- What is a \"negative\" class in our context? \n",
    "- With logistic regression, the model randomly assigns one of the classes as a positive class and the other as negative. \n",
    "    - Usually it would alphabetically order the target and pick the first one as negative and second one as the positive class. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- The `classes_` attribute tells us which class is considered negative and which one is considered positive. - In this case, Canada is the negative class and USA is a positive class. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['Canada', 'USA'], dtype=object)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.classes_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- So based on the negative score above (-1.978), we would predict Canada. \n",
    "- Let's check the prediction given by the model. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/gtoti/opt/anaconda3/envs/cpsc330/lib/python3.9/site-packages/sklearn/base.py:450: UserWarning: X does not have valid feature names, but LogisticRegression was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array(['Canada'], dtype=object)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.predict([example])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Great! The predictions match! We exactly know how the model is making predictions. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Decision boundary of logistic regression\n",
    "\n",
    "- The decision boundary of logistic regression is a **hyperplane** dividing the feature space in half. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/gtoti/opt/anaconda3/envs/cpsc330/lib/python3.9/site-packages/sklearn/base.py:450: UserWarning: X does not have valid feature names, but LogisticRegression was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lr = LogisticRegression()\n",
    "lr.fit(X_train, y_train)\n",
    "mglearn.discrete_scatter(X_train.iloc[:, 0], X_train.iloc[:, 1], y_train)\n",
    "mglearn.plots.plot_2d_separator(lr, X_train.to_numpy(), fill=False, eps=0.5, alpha=0.7)\n",
    "plt.title(lr.__class__.__name__)\n",
    "plt.xlabel(\"longitude\")\n",
    "plt.ylabel(\"latitude\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- For $d=2$, the decision boundary is a line (1-dimensional)\n",
    "- For $d=3$, the decision boundary is a plane (2-dimensional)\n",
    "- For $d\\gt 3$, the decision boundary is a $d-1$-dimensional hyperplane"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/gtoti/opt/anaconda3/envs/cpsc330/lib/python3.9/site-packages/sklearn/base.py:450: UserWarning: X does not have valid feature names, but KNeighborsClassifier was fitted with feature names\n",
      "  warnings.warn(\n",
      "/Users/gtoti/opt/anaconda3/envs/cpsc330/lib/python3.9/site-packages/sklearn/base.py:450: UserWarning: X does not have valid feature names, but SVC was fitted with feature names\n",
      "  warnings.warn(\n",
      "/Users/gtoti/opt/anaconda3/envs/cpsc330/lib/python3.9/site-packages/sklearn/base.py:450: UserWarning: X does not have valid feature names, but LogisticRegression was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "image/png": 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cOOhvPSaDJ2K2IzPrPA4lD/L1UIjqeeKJ1r4eQnCYPx8AkFdYiFGfTMecp59D87g4j22OxxwichfmhHfMmnUcAHg+QUR+x505oYoCj3JAXrtyOk6d2IW1q6bjvmETfTwqUoN2ORlAapO6/+cJlzqEhtaidetKREXV+nooPnfw4EGLX4+IiMA111wDrVbr5REFtqkrliH72GFMXb4U76WP8vVwiIhIZXg+QUTBTBUFHkBfbd++bQk2Do/EnV8uRp/+z7LqTnXSUpsgM+u8r4dBBq1bV+L//u8qxMbGQwjh6+H4VEJCeL2vSSlx4cIF/P7777j++ut9MKrAlFdYiLlZmVg3PBJ9vszE2CFDPTqLh4iI/AvPJ4go2KmmB8/aldMxolMIkhNDkJ4UgrWrpvt6SERkRVRULYs7NgghcPXVV6OiosLXQwkoU1csw4ikUENOhGLq8qUe2Q6LyURE/onnE0QU7FRR4FGq7eN66k8Wx/UU2LFtMYqLC3w8MiKyhsUd27h/3EuZvTO2pz62xvbUYG5WJs4WFXlke7wdlIjIv/B8gohIJQUepdqeGKsfTmKshlV3ogDx66/H8PK4MWhzY0s0ax6FNje2xMvjxuDXX4+5vO5z587iiSeGo1u39rj99s546KF7cOzYETeM2rLrrrvaY+sm25TZO6Y54blZPERE5F94PkFEpIICT15enkm1XcGqO5H/W7duFXr3vR3LD55H7LB/4//GLEXssH9j+cHz6N33dqxbt8rpdUspMXLkA+jZMw07dx7E5s178Oqr/0JBwTk3vgNSg7y8PJPZOwpPzOLh7VlERP6H5xNERHo+L/BMfXuSSbVdwao7kX/79ddjeOzJkYgd8ipiUodDG58IoQmBNj4RManDETvkVTz25EinZ/Js3rwRWm0oRo58vO5rHTt2QocOnXHffQPwxz/ehl69uuLHH1cAAE6dOoGUlE548cWnkZqajD//+W6Ul5cDAL744n/o1y8Fd9zRDaNGPYiysjIAwMmTv2LgwF7o1y8F//73G3XbKSkpqdtGx44d8d133zm5l8geU9+eZDJ7R+GpWTy8PYuIyL/wfIKISM+nBZ68vDzMnTunXrVdwao7kf/6ZNYMRHToh/CW7S2+Ht6yPcI79MWnn810av2HDv2MTp261Pt6REQE5sxZhHXrtuPbb1fh9ddfhpQSAHD8+FGMGvUUsrJy0LhxHDIy9IWBu+/+E1av3oKNG3fixhtvwvz5cwAAr732EkaOfByrV29BQkJzi9vYsGEDxowZU7cNci8lJ8xn7yg83YuHiIjUjecTRERX+LTAo78qW7/armDVnch/LV6yAOEd+thcJqJDXyxessCt25VS4q23/olevW7F/fffhbNnzyA/X3/b1rXXXoeOHTsBAJKSkvHbbycBAIcOHcDgwb3Rq1dXLFmyAIcO/QwAyM7ehnvvfQAAMGzYwxa30adPH5w+fRrnzvHWME+wLyfcM4uHt2cREfkfnk8QEV0R6suN79yxDVt2lmDaFtvLtWu92zsDIiK3KblUiPjGTW0uE9ooASXFhU6t/6ab2mPFim/rfX3Jkq9x4cJ5rF27DVqtFl273ojKSv3jysPDw+uWCwkJQUWF/hat559/HHPmfIMOHZKwYME8bNmSWbecpadhGW+jRYsYXHfddXwkuofYmxMpbd3TXJu3ZxER+ReeTxARXeHTAs/m7BwAwKxZx305DPITaalNgKwMnoD5iZhG8dAV50Mbn2h1Gd2lAsQ0jndq/ampd+Ltt1/HF1/8D8OHPwoAyMnZhd9+O4UmTRKg1WqxefNG/PbbqQbXVVJSgmbNmqO6uhqLFy9AYmILAED37n/A0qWL8Oc/P4zFi6/MNLp06VLdNjZs2ICTJ0869R6oYUpOYP583w6EiIhUiecTRERX+LzJMhEFpvvvexCVuWttLlORuwb33/egU+sXQmDOnIXYtGk9unVrj9TUZPznP2+iT58B2LNnN/r27YklSxbghhtuanBdL7/8OgYOTMWf/3yXyfJvvvkOZs/+FP36peDy5eK6r99334N12/jqq6/Qrl07p94DERERERGRu/h0Bg8RBa6nnvgrFvW9HdrWt1pstFx5+iAqc9fgyfc3O72N5s1b4L///are13/8cZPF5TMzr0zPfuaZv9f9/6hRT2DUqCfqLd+q1fUm63r++X8AAK6+uknd1xMSwut9H/mfzKzznB1IRERERH6NBR4i8ojrr2+D/346B489ORJVHfoiokNfhDZKgO5SASpy16Aydw3+++kcXH99G18PlYiIiIiIyO+xwENEHvPHP/bH+jWb8elnM7H4m3EoKS5ETON43H/fg3jy/c0s7hAREREREbkJCzxE5FHXX98G/377Hfz77Xd8PRQii/h4dCIiIiIKBGyyTEREQY/9d4iIiIjI37HAQ36nXU6Gr4dAREREREREpCos8JBfSUtt4ushEFEA4e1ZRERERBQoAqIHT0HBSaxZPw87ti8DqoqAsDj0uO1P6Ns7HQkJrXw9PCICcO5cHl74azo+mPEFmjVr7vL6Tp06gUceudfk0edTp05CdHQMevToiddeewmVlZWoqqrEPffcj7FjJ9QtN378GKxYsRR79hyFRsM6dzA4du4c3lu1Gl9s3oLqysvQhsdi+O0puP2qbrh8x0hfD4+IiHyM5xNEFAj8/swmN3cjJk2+F/vKyxDZpjPCQzWIbNMZ+8rLMGnyvcjN3ejrIRIRgOnTJiNn11Z8/MFkj2/ruecewzvvfIwNG7KRmbkb99xzf91rtbW1+OGH79Cy5TXYti3L42Mh3/txzx50nvAGFl6KRWjrrggP1SC0dVcsvBSLR5dNY04QEQU5nk8QUaDw6wJPQcFJzJo9BvFDxyOqyyBUHtmKDemRqDy6DdFdBiN+6HjMmj0GBQUnfT1UoqB27lweFi38AuuGR2DRwnk4d+6sR7d3/nxB3SyhkJAQ3HRT+7rXNm/eiHbtbsGIEY/j228XeXQc5HvHzp3DsBmfImboBER0GWySE5FdhqDxff9kThARBTGeTxBRIPHrAs+a9fMQldQP4S3bo2LHAozsFIrkxBCMTApB+Y4FCG/ZHpEd+2Lthnm+HipRUJs+bTLSk0KQnBiC4R1DPD6L58knn0PPnkkYMWIY5s79DBUVFXWvLV26CEOHDsPdd9+DNWt+RHV1tUfHQr713qrVCE/qz5wgIiKLeD5BRIHErws82dnLEdmxL3QlF1GeuxavpejfzmspGpQfWIuakkJEJfXDjh0rfDxSouClzN55+Tb931++DW6ZxSOEsPr1l14aj9Wrt+COO/rg228X4sEHBwMAqqqqsHbtKtx11xDExjZCly7dsHHjWpfGQer21dZtCO/YjzlBREQW8XyCiAKJXxd4KkqLENq4aV21PTFW/3YSYzV1VffQRgmoKCvy7UDJ7fiodP+hzN4x/v10xyye+PirUVRUZPK1oqJCXHXV1QCA669vg1GjnsCSJStx4MB+XLx4AevXr8bly8Xo1asruna9EdnZW/HttwtdGgep26WSy8wJIiKyiucTRBRI/LrAExEdh8q8wybVdoVSda88exQRUXG+GSB5BB+V7j/MZ+8o3DGLJyYmBs2aNUdm5noAQGHhRaxfvxo9evTEmjU/QkoJADh+/ChCQkLQuHEcli5diPfem4mffjqMn346jJ07D2HTpnUoKytzehykbo1iYpkTRERkFc8niCiQ+HWBp3v3IShb/4lJtV2hVN3L1s9Ejx6DfTRCcgVn6fg/89k7CnfN4pk+/X94//1/4847u+PeewfgpZfG4/rr2+Cbb+bjD3/oiDvv7I5nnhmNGTPmoLKyEhs2rEXfvgPrvj86Ohrdu/fE6tXfuzQOUq+/9PwDypkTRERkBc8niCiQhPp6AK64rdvdyM6cg9cejLH4+mspGnz+0XH0GD7FyyMjd+FsHf+lzN458ESIxddfvg3o8Nk8PPPCuLonXjnqppvaY+nS1fW+PmvWFxaXP3w4r97X5szhLVqB7JE/3IbP161kThARkUU8nyCiQOLXM3hydi7D6K6R9artisRYDUZ3iUDOrmXeHRgRWZ29o3DXLB4iWxZt24zHu0YwJ4iIyCKeTxBRIPHrGTynTuRg9fFyfLyj3OZy7Vrv9tKIiEixZ/cO7MgpwQdbbS/Xo3y7dwZEQWnnsSPYcrQCH+6osLkcc4KIKDjxfIKIAolfF3j+/jIfV0ikVitW7fD1EIiweeLb9b6WmXUeh5IH+WA0RESkNjyfIKJA4te3aFFwYxNm31KeUkWWcf8QEREREZE3scBDfonNl32rrEyDy5cLWcSwQkqJCxcuICIiwtdDITOcvUNEREREgcqvb9EiIt84fjwcwEVERZ339VB87vx5y4fRiIgIXHPNNV4eDRERERERBSsWeIjIYTqdBocPR/p6GKrwxBOtfT0EIiIiIiIi3qJFRETBITOLM86IiIiIKHCxwENEREGD/XeIiIiIKFCxwENERERERERE5OdY4CEiIiIiIiIi8nNssuyHCgpOYnnGdOzOWYWammpIXTVCw6PQtcsADL77GSQktPL1EImIVCXYHo/OnCAiIluYE0SBiQUeP5ObuxEzZz2PGkjEJt+FmKT+CG3cFLrifPyc8wN2v3UPnnpsGjp0uMPXQ/WKdjkZQXXSRkTUEOYEERHZwpwgCly8RcuPFBScxKf//RtqhUCzP09EfK+R0MYnQmhCoI1PxFW9H8XV9/0Tn/7vRRQUnPT1cD0uLbWJr4dARKQqzAkiIrKFOUEU2Fjg8SNr1s+DiG+JmM4DEd6yvcVlwlu2R2SHPli7YZ6XR0dEpE7B9Hh05gQREdnCnCAKbCzw+JHs7OWoLjyDmKR+NpeL7jwAO3as8NKoiIjUL1hu5WROEBGRLcwJosDGHjx+pKK0CBJAaOOmNpcLbZSAirIir4yJiIjUgzlBRES2MCeIAhtn8PiRiOg4aCJioCvOt7mc7lIBIqLivDMoIiJSDeYEERHZwpwgCmws8PiR7t2HQBvfAiX7VttcrnTPSvToMdhLoyIiUq9gezw6c4KIiGxhThAFNhZ4/Ejf3umQhadRsudHVJ4+aHGZytMHUZ67Fn3uTPfy6IiIyNeYE0REZAtzgiiwscDjRxISWuHJx6ZBIyXOffM6Cjd+jurCPMgaHaoL83Bx/f9wYcm/8OSj7yEhoZWvh0tERF7GnCAiIluYE0SBjU2W/UyHDnfgjQkrsOL76fhp90pc/mkFpK4aoRFR6NplAAaP/44HYyKiIMacICIiW5gTRIGLBR4/U1BwEmvWz8O+/RtRU1WOiOg4dO8+BH17p/NATKrTLicjqPqfkLoEW/8dBXOCiIhsYU4QBS4WePxIbu5GzJo9BlFJ/RD/8BSENm4KXXE+9u1fg+2T78UTo99Fhw53uGVbyoE/O3s5KkqLeOAnIvIDzAkiIrKFOUEU2NiDx08UFJzErNljED90PBqlpUMbnwihCYE2PhGN0tIRP3Q8Zs0eg4KCky5vKzd3IyZNvhf7yssQ//AU/N9LSxH/8BTsKy/DpMn3Ijd3o+tviIiI3Io5QUREtjAniAIfCzx+Ys36eYhK6ofwlu0tvh7esj0iO/bF2g3zXNqONw/8FNja5WT4eggUxDKzzvt6CF7HnCAiIluYE0SBjwUeP5GdvRyRHfvaXCYqqR927Fjh0na8deAnIvK0YOu/w5wgIiJbmBNEgY8FHj9RUVqE0MZNbS4T2igBFWVFLm3HWwd+IiJyL+YEERHZwpwgCnws8PiJiOg46IrzbS6ju1SAiKg4l7bjrQM/ERG5F3OCiIhsYU4QBT4WePxE9+5DUL5/jc1lyvatRo8eg13ajrcO/BTY2H+HfCkY++8AzAkiIrKNOUEU+Fjg8RN9e6ejbN9qVJ4+aPH1ytMHUb5/Dfrcme7Sdrx14KfAl5baxNdDoCAWbP13AOYEERHZxpwgCnws8PiJhIRWeGL0uyhc+haKN81FdWEeZI0O1YV5KN40F4VL38ITo99FQkIrl7bjrQM/ERG5F3OCiIhsYU4QBb5QXw+A7Nes2fXonPRH/LT7BxRtXwwRqkVISBi6dumHweO+dflgDFw58M+aPQaRHfsiKqkfQhslQHepAGX7VqN8/xq3HPiJiMj9mBNERGQLc4IosLHA4ydyczdi1uwxiErqh6YjpiG0cVPoivNRvn8N9uxbje633u22g2SHDndgwrhvsXbDPOyY/woqyooQERWHHj0Go4+bDvxERJ4QrP13AOYEERHZxpwgCnws8PiBgoKTmDV7DOKHjkd4y/Z1X9fGJ0Kblo7wNt0wa/YYTHDjwTIhoRUeGjYBDw2b4Jb1ERF5SzD232FOEBGRLcwJouDAAo+bFRScxJr185CdvRwVpUWIiI5D9+5D0Ld3utMHyzXr5yEqqZ/JwdhYeMv2iOzYF2s3zOMBlHxOeYJWZtb5oDzRJmoIc4KIiGxhThCRs9hk2Y1yczdi0uR7sa+8DPEPT8H/vbQU8Q9Pwb7yMkyafC9yczc6td7s7OWI7NjX5jJRSf2wY8cKp9ZP5G58ghaRZcwJIiKyhTlBRK7gDB43aWjaY0jT6zFj1vPQhmpRWXbJoUp8RWkRQhs3tblMaKMEVJQVueOt2MUTVxaIiAIZc4I5QURkC3OCOUHkKhZ43MTWtMfyY7twcfVMxHQegJhOA+oamu3bvwbbJ9+LJ0a/iw4d7rC67ojoOOiK86GNT7S6jO5SASKi4tzwThpm3KAt/uEpDr8fIiJPUPttgcwJ5gQRkS3MCeYEkat4i5abWJv2WF2Yh/Pfv4em901A/B2joI1PhNCEQBufiEZp6YgfOh6zZo9BQcFJq+vu3n0Iyvevsbn9sn2r0aPHYJffR0OMryw0Skt36v0QEQUj5gRzgojIFuYEc4LIVSzwuIm1aY+Xd2cgplN/uxqaWdO3dzrK9q1G5emDFl+vPH0Q5fvXoM+d6fVeKyg4ifkLJ+FvY7rhqaduwN/GdMP8hZOcPmA60qCNgk+7nAz23yGygjlh//shIgpGaswJd2cEwJwg8iQWeNxEmfZorLowDyX716Jk7yqcnDoEv330CC6u+wzVhXkmyzXU0CwhoRWeGP0uCpe+heJNc1FdmAdZo0N1YR6KN81F4dK38MTod+vdq+qJJm2+aNB27Nw5PDPvC8Q99VdoHhmOuKf+imfmfYFj5865bRtERJ7GnLD//TjKEycgRETepracCKSGz8wJChbsweMm3bsPwb79a6BN01e9y4/twvnv30NMUj/EJt9Vd19pyb7VOPvFGDS5+0VEtrkVgH0NzTp0uAMTxn2LtRvmYcf8V1BRVoSIqDj06DEYfcZ9W+9De0NN2sLbdMOs2WMwwcL32uLtBm0/7tmDYTM+RXhSf0Q/9A4aG/bjwv2rMW/CG5jQ6yHEqbjnRrDKzDrv6yFQkPGHnznmxBXuzAn2cSCiQKGmnPBURgDMCSJPYoHHTfr2Tsf2yfcivE03aKLi6u6TNT8gxvcagai23ZG/ZBKaD38X2vhEuxuaJSS0wkPDJuChYRMaXNaRqY/2rE/hzQZtp4vP44kvPkXM0Pr7UZs2Ato23fHGkn9hfM8H2GlfhdTc7JYCk9p/5pgTV7grJzx5AkJE5G1qyglPZQTAnCDyJN6i5SbG0x4vrHgHMZ1sHxBjOvXD5d0ZADzT0MxTUx+92aBtUW4WwpNs328ckdSP9+eqRLucDF8PgUjVmBNXuOv9sI8DEQUSNeWEJ2+jYk4QeQ4LPG6kTHusufg7YpL621w2Jqk/Sg9ustn40hWemvroSiNPR605uhvhHfvZXCay0wC33p9LrmGDZSLbmBPuzQlf9HEgIvIkteSEJ2+jYk4QeQ5v0XLAoUNbsXDJFOSdOQKpq4IIDUNiixvwwH0vo127ngD0lfeaqnK7Doi1ZZesNr50laemPipXFmbNHoPIjn0RldQPoY0SoLtUgLJ9q1G+f43b3k9ZxWVc7cX7c4mIXMWc8G5OeLuPAxGRq/wlJzx5GxVzgshzOIPHTp9//g+8P20Uzpw5AkAavipx5swRvD9tFBYunFS3rKUO+OZ0lwoQGh6JCeO+9UhTL09OfVSuLHSOjkbh/Ffw23v3oXD+K+gcHW33+2mXk9HgLT1REbF27Ud33J9LRP5LLQ2WmRNXuCMn7GHvfmROEJEa+FNOePo2KuYEkWdwBo8d5sz5B7ZvXwoRGobYLoMQ03nAlS72e1bi8u4MrF8/F5WVpUhP/3e9DviWlO1bjdtT/uyxZl7GTdos3XNaN/Vx3LdOrd+RRp62GBd5zBuk9m3bBVn7V0ObNsLq95fvXen2vhRE5H983WCZOVGfu3LCFnv3I3OCiHzN33LC0xkBMCeIPIEFngYcOrQV27bpD8bNHnwTIY2bofSHqYjo9QQqNs1Co7teRtSNt+HcgtewZetSREREe+WAaElBwUmsWT8PO7YvA6qKUBsShYJv3kBs8kBEJfX32NTHhsaBsDj0uO1P6Ns73WR7xv1aLF2BH9YhFWuXfwDRtDUqTx9CyYENCK++hEptI8TccifCW7ZDxb7V6DP+O7e/ByIie1nKiZIVb0NKiUZDXkP8naOYEw2Mw1pONETZjyFNr7eaE57Yj0REjvDXnBBVRTi7YDwadxmM6M4DvJYR5uNgThDZj7doNeCrBf8CQsMQ23UQwlu2R8WOBZB5P6Ns5buQeT+jfMcChLdsj9gud0MTGYP1m77GhQun6zrgF2+ai+rCPMgaHaoL81C8aa5H7pPNzd2ISZPvxb7yMkS26YzwUA1ibuyO6Jt74XLOj7jw5Usem/rY0Dgi23TGvvIyTJp8L3JzN9q9rpaNm+AfA/riwg/TIEJCEde2C8JDNYhr2wUiJBQXfpiGB2+5nY80VAE+QYuCmaWcQP4vkOd+QfmOBQDAnGhgHM7mREJCK/TrPdJmTvTrPZI5QUQ+5c850bhNMip+P4C82c/it3fv9XhGWBsHc4LIPizwNCC/4BQEJGI6DYCu5CLKc9diQ3okqs+fxDf3h6P8wFrUlBQipvNAyKoyxCTfhUVLpnjtvlJAX+GeNXsM4oeOR1SXQag8shUb0iNReXQbGvV8CAl/fgMQApP+tQbT3s3GQ8MmeOyKrLVxRHcZjPih4zFr9hgUFJy0a32ni8/jPyvXoNkDbyKqfS9U/bIJ39wfrn9ft/4JzR54EwsObK5bX0HBScxfOAkv/L0rXnimDV74e1fMXzjJ7u2Ra5QZWWrph0LkLeY5UZa7FhvSoxCqAcpy16CmpBAAmBMNjMOZnCgoOInV6+fYzInV6+eY5MTn88bh78/fhCefbIu/jenGnCAij/PnnKg+tQcJQ8ej2YNvIiyqEca/8o3HMsLWOFzNiSaDx0LkHUDF4S1X8s8sJ3guQYGABZ4GCEhIXTVCGzdFxY4FGNkpFMmJIRidrMWPR2swMikE5TsWILRRAqSuGrHJdxkap125r3Tau9n4ZOZhj31oXrN+HqKS+tVdEVDGqIwtvGV7RHbsi7Ub5rl1u54ex6LcLIQn9Ud4y/YoW/kOtBppss/DW7ZHRFI/rN0wz2qlf0/pZUyYOJAf5L3M1/1QiLypXk50FEhODMGITmG4+arauquzzAn3j8N4fdZyQlmfkhMHfv0JWlGLq7sOQPzDU5gTRORxzAnfjUNZX+2pn4D8X3Dz1dLi+hYt/rfFc4m9ZaV4fdJgPPdCJzz11A3MCVI9FngaIHXVEKFaVOYdRnnuWryWot9l41PDMXdvNZ7oDJQfWIvKs0chQrWGA3OVV8eYnb0ckR371s0wUsb4WoqmboZRVFI/7Nixwq/GseboboR37IfKc8dRff4U1qdHm+zzmpJCRHYagO3bv7Na6Y81VOY1kbGIHTTGqamdZB/O3CFfyMw67/OConFOlOWuxYRULQBgbEoYjl/U1V2d1V0qYE64eRzK+mzlRFRSv7qcaNT/OdRc/A0b0iNR/vN6aLQRiLtjFHOCiDyKOeG7cWRnL0dYm251s6aOX9ThbEltvfXtz91k8VwipusQJPz5Degg0PzRGYh/eApzglSNBZ4GiFAtRHg0StfNxMhOoUiM1e+yxFgN0pO0mLtXh5FJIShdNwMiItZwYA7z6hgrSotMZhgZj9F4hlFFWZE6xlFaaNJg2ZqyissIbdwUZSvfwehkLZITQ0z2+ZX3VdxgpT+mUz+UH81Go7R0u6Z2KlM0/zamW1BX6wsKTmL2nLF45vkkPPlkWzz1THs883wS/vf5P0z2ha9PsIl8ySQnOgqTY5/x1dmSPT8yJ9w8DmV99uZE7amf6mUEAOaEC+zNCaJgxpzw3TgqSougO7jeZNbU1C1V9dYna6ptn0t07o+SPT9CG5/InHDQoUNbMfGte/DUMzcbcuJmTHzrHhw6tNXXQwtILPA0QEAgNP4a6AqO11WQFWNTwuquFNYUHEejHvejZM+PaNHiBq+OMSI6rt4MI4VSna48exQRUXGqGEd0ZEyD62qXk4GoiFiUHduF6vOnMD41HIDpPq+bORWibbDSH5PUH6UHNwFAg1M7jW/3in94Cv7vpaVBWa3Pzd2IiW/dg591tWg6Yhqu/ccyJI7+GFHJA7EzZyXemDQ4aPYFkS3GOaFclVXUXZ3dvwqXfspAXK8RzAk3jiMiOs7unAhr081qRgBgTjiBOUFq0i4nQ7UPfWBO+G4c4ZGN6s2amru32mQWT+XZo9BExtp9LgEwJ+yVkfERpk1/DCWJNyFx9HRDTkxHSeJNmDb9MWRkfOTrIQYcFnhsKCg4CWg0EPmHMCo5vK6CrDCZxZMcDpzZj8s532PYfS97dZzduw9B2fpPTKrcxmMcmRSCsvUz0aPHYFWMo2/bLnatb0RaT1Ss/QCjk7VWZ06Vb5gJKWvsqvTXll2qW7e1qZ3Gjd0apaVDG58IoQlxqFofCAoKTuLT/72Iq+/7J67q/ajJfojvNRLN/jwRtULg0//+LeD3BZEtJjnROczisW9EpzC0j69FdHwThMUnMifcOI7u3Yc0mBNl6/U5oTu43mpGAGBOOIg5QWqjzA5XCj1qKfgwJ3w7jsQmzerNmkpP0prM4ild9zGi2/dy6FwCYE405NChrchYORPNHngT8XeMMs0Jw+3RGStnciaPm7HAY8Oa9fMQ0+GP0AhZr9quUKrAT3YJQeWRrehzRzratevp1XHe1u1u6PKP1atyK15L0UBXcBw9bvXsbTT2jqNv62S71jegwy2oKbtUd1VWYXx1tjr/OKLCwuyq9GuiGtV93drUTuPGbpZ4q8Gcr61ZPw+RHfvY3A8xnQdAxLcw2Rfsw0PBxiQn0ixPpx+bEoZfi2pRU3wWZxeMx6ABTzMn3DSODu17NpgTuoLj0GrDUWYjI5TeF8wJ+zmbE0SelJbaxOQPAJ8Xe5gTvhtHcXE+zuf/Wm+/m8/iqSn4FaFNrnXoXAJgTjRk4ZIpiO0yyOZ+iE2+G4uWTPHyyAIbCzw2ZGcvR0h1icVqu8L4SuGjXaMgasu9PEogZ+cyjO4aaXOMo7tEIGfXMlWMY9PxnXat719LFppclTVej7LPH+8SjvbNmqB8/Uyblf7S9TMR3b5X3dd1lwosTu1UGrvZ4o0Gc76Wnb0c0Z0G2FwmJqk/qovO1tsX7MdDwUTJiZFJITaPfSM6heHmq4FuSakYNOg5L4/S/3LC3nGsXPGfBnNidJcINA7XYmSSxmpGlO9YgJJ9q5gTDnAlJ4i8xbzg44vZPcwJ341j7crpSE8SVjNCmcUzKjkc1dvmOXQuATAnGpJ35ghiGsqJzgPrnhhH7hHq6wGoWUVpEcIvnsKM/WWYscP2slFaoKy6Cu1a7/bO4IycOpGD1cfL8fEO28UlT4/N3nF0Sjxh8evtcjLqigMXSovx8+nTWH5vtMVlx6aEoc2HJSjXAUnXVKE6/xRee9Byb5/XUjT4/KPjaNT76bqvle1bbXFqp9LYzRZvNJjzNXv3Q235ZVQI4aVREZlSw4wxJSdmnq7EzJ2VNpeN0gLXRuV5aWSm/C0n7BlHcXE+8vKOYvz9DedElLYCE1ItL/daigZzZqxGOcKRmP5+3deZE7YxJ8gfGT/kIzPrfL0ijycuUjEnfDOO4uJ8bN+2BHOetn4XRpsPS/D+dv3TyiJDK/Faiv3nEgBzoiFSV2XXfvD2E+MCHQs8NkRExyHq7nFoHJ9o8XVdyUWULH8TlRcK8P77u7w8uiv+/rI6qr/2jsPSFZO01CYmJ2sL9q7CEw1U75+8NQqicU9IAGktimwuOzI5AosObQBatkPl6YMo378GfcZ9W2/ZiOg46IrzobXybw5Yr9YHEnv3gyYyFuEaHkbId3w9Y4w54Rh3jmPtyul4tGuUzWP/Y7dG44czLXFXi9O2r5x3EJh/qX3dMY850TDmBPk78ye6mhd83JUvzAnHuGsca1dOx4hOtmdNPXZrNH6JHgpIiRtKv7X7XAJgTthDhIbZtR+8/cS4QMfEtaF79yHYt38NtGnpFl+v2LEAKDiCxGY3enlkgUuZxfNLwUksyivDtO22l09pq5/St+VoBaZnV9hcNq75PhRvmovy/WvwxOh3kZDQqt4yDf2bA9ar9YGke/ch2LN3JeLuGGV1mZK9KyFCtKiuKsdTT92AiOg49L8+CcOKz+PyHSO9N1gvKig4iTXr5yE7ezkqSosQER2HvfsfwYt/ex5t2rTx9fDIB5gTvqO/yluKjxrIiauiT+GjUxUNLhfX8jyqC/NQtm81c8IOzuZE9+5D0Ld3usV9GwiYE/7LU7N7mBO+YW9GKDOB7Jk1FNfyZ+aEAxJb3ICSvSsRbysn9vyIqOjG+NuYbnXHTOaEa1jgsaFv73Rsn3wvwtt0q9ccSldyEWX712DLiCjc8cUJFBcXoHHjBB+NNDAos3ja5WTgw3v+Ue/Kii2ZWedNgrddTgZa3liD91etwZdbt+JSyWVUlpShR3Q0+oz71uoBw9a/OWC7Wh9I+vZOx7a3hyLyhtus7ofLP2Ugqn0aYjr1Q+WWOQhJGowfs5fiu2+mQC54E5HR8QF1gM7N3YhZs8cgKqkf4h+egtDGTaErzsfCnLWY17UbFn39FQYOHOjrYZKXMSd8xx1XeQsKTmLthnnYsWMFivNOoXL+K+jRYzBzwg7O5sT2ncuQmfk1ZE0Vc4JUy52ze5gTvuGumUDMCec9cN/LmDb9MUTZyond3yOmQ2/EdOgN7cZZqI5ujswti7Bp/VyERcXiD7fdGzAZAXgnJ4SU0k3DveLWW2+Vu3bZP8Vw1qzjbh+Duyj/CJEd+yIqqR9CGyVAd6kAl1dMxiMtf8eMuyPw/Koa/BI9FPcNm+jr4fqFdjkZDRZvMrPOu1zgMb8SY28YW/s3N67Wd+hwh91j81e5uRvxyX//hogOfRCbfFfdfijZuxKXf8pAXOojaNR9KErWzYAu90dU1ISgUmgRUVsOCA1E6xRoo2JReXir3++zgoKTmDT5XsQPHW81oEpWvI09P+1ssPIuhPhJSnmrp8bqLxzNCcyfX+9Ljvxee5LVnMj4Nx5p8RtzIgAxJ/SYE1cwJ9zPHTnhKeY94BrKIuZE8GFO6GVkfISMlTMRm3w3YjoPvJITe37E5d3f1+VE4aJxEGf2o0KGorJKhyitQO213aGNvQpVR7YFxP7yVk6wwGMH48ptRWkhYqKiUVtdiiPP6u/9z7tci/af6DD+jY2sujdAufrhSPHGHsYnepa24eiJoMm/eVkRIqLi9NX6OwOngmyPgoKTWPHDx/hp90roKsogQrUQIgRRN6fh6gHPQVdyERc/G40tI8ORMqcCYa27Aye2Q1cjAW0EympDEfeHB1CyfRFeH/+d3+67+QsnYV95GRrZmGpbkjUPD3ZNxPQPp9lcFz+46wVSgQeof8wIj2iEEN0lHHk2kjkRoJgTeswJPeaE+6m5wGPM3mIPcyL4MCf0Dh3aikVLpuDMmSOQuiqI0DBERTeG5vquuKr/MyjesRQVm/+HraOjcfu8amhiExBy6TSqtDFAVTnCbh2GyzuXYsQjb+K224b6+u04zVs5wQKPg9rlZGDpryuA4q14v/+VO9xYdbePPbN3nGFe4LE0tVYtJ4L+7m9juiH+4SnQxifi0g/v4MHwLZhxdyT+ulKHuTkV2DwyEr3mlEIjAFx7Ky7/fhiRbXsgoewixo1d5OvhO8X4PVtTXZiH0sWvouhCvs118YO7XqAVeMwtWfhP3FS2DB/2D6n7GnOCggVzwjLmhGP8pcBjzt6CD3OCgplyzASAC58/jdHJWswYqMVfV1Zj7k/l2Dw6Grd/XgptiECF1EJ70x0o+XkTBg98GoMGPefj0TvHWznBHjwOulBajLlZmTjwlGm373E9Bdp/shh9+j/LqrsPWXpCFznHUgOw7t2HoLy0CAmNm0JXchEVv2RhwrORAIAJKRp8mVMLjZCQADaMiMbtc3IQ1WEgZHUlTp7cj0OHtqJdu56+fWNOsPdxl5eLLnppRKRmVx7NahqxzAkKNMyJK5gTpLCnWTNzgoJFQzlxYdUMaITEhNv1hc4JKSH4MgfQCAmNADakRyFlTgVqqiqg0YYjY+VMtG3blTlhg+VnwZFVC/auwoik0HqP0UuM1WBER4GfvnwJ7XIyWGjwIU/MEAo2ubkbMWnyvcgpzIfmui4QkbEoLy1E5pZFQIgWFb/lomLHAoxMuvL4ycRYDUYna/H4igo8mqxFcmIIRiRpEFp+EeXHdkLW6LBoyRQfvzPnKI+7tEV3qQCxcVd5aUSkZtYezZoYq0F6UgjWrpruo5ERuQ9zwhRzgixJS21i8gfQX4zc9eVLGJkkmBMU0OzJCd0vGzAyOcxmTozsrEXtr9tRW1GC2OS7mRMNYIHHTu1yMpCw+SusOpyNsT0t77ZXUkKw5mg2buzIiVG+wKKaexQUnNR3d+9+H0oObUZITDyaP/IOrn1pGRJHfIBGXe5G/pI3UbZ/NSakmc5kezklHAfyazGqsxYAMCEtHFXHdqC2rBiayFicOXPEF2/JZd27D0H5/jU2l6nMXYNH/vKwl0ZEaqVclR3XU1h8fVxPgR3bFqO4uMDLIyNyH+ZEfcwJskdaahPc0CEEa47uxCspIRaXYU5QILA3J0RNFSaY/S7Uy4nbQ6GpqYKIiEFM54HMiQawwGOFMgvHeDZOZn4mRnXW1qu2K/RV91BMXb7Um0MlI2qdveNPs7rWrJ+H8Bt7onj7N2h63wTE9xoBbXwihCYE2vhExN85GnFtO2NkR8tXnkYnazF3r67u7yOSNAjTahDdvhekrsoXb8llfXuno2zfalSePmjx9crTB1F5YA3+/oJ/3hNM7mNt9o6CV2cpEDAn6mNOkL2mrlhm8W4AhXJXAHOC/Jm9OWHp3NpSTozsrEV046sQ2iiBOdEATjUxY3wSbl4seHXtEWw5WoZp222vI6XtEfzpek+Mjpxh3uzOmw4d2oqFS6Yg78xhSF01ROhYJLa4AQ/c97Jq7x3Nzl4OzXVdENOpv8VH+OlKLqLq158w4a/hFr//1dRwdJhZirEpYWgeo8GEtHDM2VOCsGtuhti7ytPD94iEhFZ4YvS7Fh93WZm7BpUH1mDR1181+EhDCnynTuRg9fFSfNRATrRrvds7AyIAjs3w9Hbj7is5ceXpIswJ/8OcIHvtPGbf+USnxI0mxy61PlSAPI85oc+JuTPOoPLsUYjQMIvfo3beygkWeIw09AjvzRPfrvc1m09vysrgwdiLbM3e8cW/Q0bGR8hYOROxXQYhccALCG3cFLrifJTsXYlp0x/DoAH2d4G31qCsb2/3PWZR2UZ5SSE0x3ei+SPvWFyuYscCjOxk+8pTepIWU7dU4b3+EXVV93nbv0aLFje4Zay+0KHDHZgw7lv94y7nv1L3uMvRox7B3+ft5Id2L1PrE7T+/vIKXw+BDMyLOvbM8DRviOrpnzHmBHOCgo+l84mGWGvWTIGPOXElJ0Z0CsEX62YwJxrAAo9BQ8UdCj7Kz4QzAXro0FZkrJyJZg+8aVK11sYnIv6OUYi64TZkLHzNri7wubkb9fewJvVD/MNT6g7s+/avwfbJ9+KJ0e+iQ4c7HB6jtW1oImNRW37Japf32rOHMOP3MszYYXudKf935X7aCWnhmPPhSdw9+iOXxulrCQmt8NCwCXho2IS6rz3xRGsfjoiIjNmahWsPa0+/8cSJFHOCOUFkL/PjmbeL0eQbzAmznEgJwZyfjjMnGsACD9xX3DmUPAjIymCRyApP9qBR2z5fuGQKYrsMsjglEQDCW7av6wL/z/HfWV2P0qAsfuj4egd2bVo6wtt0w6zZYzBh3LdOV97Nt6GrrkTJ/jXQFedDG59Yb/lGf/kQjQBUF+bh0tynUVKpQ1gI8GiyFjPujrS4Df3V2TAcO7YDXbve5dQ4iYiscbWwY4myHuVEyt0nUMwJU8wJIvvVO85lcXZPIAqWnLg85wlcrpJ25cToLhE4wpywiQUeA7UVCAKVv+xn5XY7Zz/Y5505gsQBL9hcJqbzQJyZ/b3NZdasn4eopH42D+yRHfti7YZ5JlVgR5hvI7bLIJTsW4OSvasQf8dIq99Xtm8Vbr39EUy8IRmvrn0PM3edxMxd1Ta3FaX9Elk7fnD7dFAiCk6eKOyYM84CwH0nTsGUEw8Nm4D3pwzGzF0/MyeIPMDa7EOAxR5/Fiw50TV1BHPCjYK+wOOJWSWZWef9ppDhLfX6E/kJ5YO9o6SuyuqURIU9XeCzs5cj/uEpNpeJSuqHHfNfcfqAbL4NbXwi4ns/hsK1nyLqhh4Ww6Dy9EGU71+LJ4bo7/ndPPFtHDt3Dh3Hv47G9/3T6vfkL5mEJoPGYN/JvW6bDkpEwccbhR1jnpjNEyw50WfctwD0/akKCk5i0uR7611FNv4e5gSRazi7J3AwJ5gTzgjqAo8n+u4cSh7kN4/D9gRLVzj9bX9YbMzpYMNsERpmdUqiQnepoMEu8BWlRXYd2CvKiuweG6CfRrni+4/x0+6V0FWWoWL2M0CIFlE3/AGNez6A2E79AADnFr2OmE79EZt8V12X97J9q/TFndHvomV1Sd06X/p8OSKtdMoH9FcHYjr1Q/nRbFz1x8fdMh2Ugpczv5fk/7xd2DHnysxOc8GSE8bHd3uuIjMniNzL1uwegAUfNWNO1MecaJjlttVBgE2VPUvZv/66n10db2KLG1Cyd6XNZUr2/NhgF/iI6DjoivNtLqO7VICIqDi7x5abuxET37oHuSWXEH7DH6CJagSpq4KsrUHZoUycmfUEfvvgIVSfP4mEe8cDshZnv3wJp94ZisL5r6BzdAwmjPsWHTrcYfKhYM3R3YhI6m9z2zFJ/VF6cBMA0+mgRES2tMvJMMkTX2aKsm1XL14ES04Yy85ejsiOfW1umzlB5DnK8dP4OKocX/3tgmwwYE5YxpywLShn8Lij6JBXWIhRn0zHnKefAyxcyVNu6/FEY0a1M+9X4E/FHXeF2z+SeuHFlf9F1A23WZ1eeDnnezz67H9trqd79yHYt38NtGnpVpcp27caPXoMtmtcBQUn8en/XkTMbcNQtHUhtFe1hNRVQYSGI6bzQH1lXXn84r5VOP/dFDS5+0WEhIahc3S01WmbmVnnUVZxGVcbrg5UF+bh8u4MlBzYgPDqS6jUNkLMLXcipvMA1JZdqvs+V6eDEqlZcXE+vvz8BTwy6kM0bpzg6+H4LTVmiTtm8jxw38uYNv2xoMkJwPQqMnOCyPR8onlcnNe3z9u51I05wZxwRtAVeNz1QXHqimXIPnYYU5cvxZ+uN/1lUG7TcrR/iycfx+oNloojavpAbi93jLnLNTfijXsG4Y2FryE2+W7EdB5YNyWxZM+PuLz7ewwa+HSDjzTs2zsd2yffi/A23Wzcu7qm7t5Vc4cObcXCJVOQd+aI4cCrRehVLVG4+UtoQrQIa9YausIzaDrsn/W66sf3Gomotj1wbsFrkFKivPtgFBSctDr9MSoiFrrifOgunsb5799DTKf+iGvbBbVHMhHZtgtqQsNw7suxEGFXOuM7Mx2UyF+sXTkdp07swtpV03HfsIm+Ho7fUWNhx5izPdoU7dr1xKABTyPDWk7kfI9BAwIrJ5SryMwJIj3j84n30kf5ejhs1qwyasiJgoKTWJ4xHbtzVqGmphpSVw2NNhwh8YkO54TQaJD8zCybY2VOuC6oCjzu+rCYV1iIuVmZWDc8En2+zERqs14Wl3Plg5+/UvatWj+Qe4Pyc/bPe+/F7TfdhL/NX4Dc2d8bPjiHocM1LTF6wGOIGvRcg+tKSGiFJ0a/i1mzxyCyY19EJfUzund1Ncr3r6l376pi0aJJWL/pa8Qk34XEAS/UVdIv7/kRuotn0PgPD0B3+TxiOg+w/fjFroNRU1aMwwjBJBuNzO5p3goZO5ei5NBmNL1vAkIaN0Ph/x7D5vRI3P7FNlw1+r+Iatsd5xa9jurCPGjjE6G7VIDwyEaO7WAiP1BcnI/t25Zg4/BI3PnlYvTp/yxn8djJ1312HOFqL6hBg55D27ZdsWjJFJwxyokWLW7Ao8/+t8EP7YB/5UT37kOQw5wgAlD/fGLskKE+mcVjDWf3qIMvcyI3dyNmfvosaqSsNzPH8ZwYhMrfcjFj1nM2myIzJ1wXVAUewD0fFqeuWIYRSaFITgxBepLEwj2r0DvlYZNlgqXZciC9R3c+6UtZT+9bbsG+tybVez0z67zFW/ss6dDhDkwY9y3WbpiHHfNfQUVZESKi4tCjx2D0sdJQbOXKmVi/6Ws0e/DNepX0q+4cjegb/4D8JZMgpURi+ns2tx/TqT/OfvUPNHn2S4uNzA4lD8Idy9/GzY9+gIWTBiOm80CEt2yPknUzMLKT/vdkRIdqLNw8B7ED/o7Y5IG4vDsDV/3xcZTs+RHVuirk5m5k93sKKGtXTseITiGGnABn8djBnwo75ly5Vatdu5745/jvXNq+2nNC0bd3Ojab5cQIJSeSJBbtWICYPz7NnKCgYH4+oZZZPNawWbPv+CInCgpOYsanz6K2ttZNOTEAJbnr0HToeJtNkZkTrlNtk2V3N/ty18m7Um0f21O/68b21GDV4R0oLi5wed3+wrwZm3mzNrW5UFqMz9/s55V/I3t/Zh3dVwkJrfDQsAmY9m42Ppl5GNPezcZDwyZYPDAWFJzEsozpiO062ORgXF2Yh4vrPsNvHz2Cs1+9DFmrg6yuhKytsbnt0EYJqC0rRnVhnsVGZsp7TkhohZCQEMR06g9dyUWU567Fayn635MJqWGoOLgRNSWFiOk0AKUHN6Hy9EGU7F+L+AHPYtbsMSgoOOnQPiFSK2X2zrieAgAwrqfAjm2LgyonHOXrBsp5hYUYMHkSzhYVOfy97mq67Co154TxGM1zYoKSEykalB9Yy5ygoGDpfGJuVqZTxyBfCMZmzcXF+fh42kN+neWO5MTyjOmokdLtOaGJikNkxz5WmyIzJ1ynugKP8YHBXZVgdx5olGp7Yqx+1yXGapDeKRRrV02vt2wgVrL9pahjLDM/E78U/Grx30jhzp8RX++TNevnARoNYjpdeaJV+bFdOPvFGIjQMDR/5D+49qWlSBzxAWK73I1zX/4D5cd2WV2f7lIBRFgUzn4xBuXHdukbme1YUfd689/2YeOQVwEA1eUlCG3cFBU7FmBkJ9PfkxFJGuR/NgqXf1qO2tIi5C/+F5rc/SKi26Wy+z0FFGX2jklOJIXYPAYFKyXzfZ0nxn0wnOHr476jvJ0TxqqMcmKEeU7cUouC/z5qyIli5C+ZxJyggGTxfCIp1OljkK+ZF3yMiz2BUvAx7qsXDHbnrILwUE5o4lpg2zbrP+vMCdeoqsDjiYaK7lynebVd8UpKSFBcnVXDh3BH1d3fnB6J7C0Lbf4bNfS+/CWgsrOXQ1aVm3SgP//9e2h63wTE9xoBbXwihCZEP72y96Noev8/cf7791BdmGdxfSX7ViGmYx80vW8Czn//HmStDhWlhXWvn/2/pLr/j4iOQ2XeYZPZO4oJaeEIkTpIKSFCw6Ft1gaRbW4FAJsnA0TWKB8i1cR89o6Cs3hMmc8C9SXjPhiuXEFX48+jNd7OCWOhYZF1OTHBZk6EIa7XSOYEBRxr5xP+NovHlkCb3aNk+/rhkUGT5TU11R7LiaJNc1BZVmx1tk2DOSHAnLBBNQUe4w967mpO7O4Pj+bVdoWtq7OBMovHXw/IJvc3W5lpZc97s+dnyJ09fFxRUVoETWQj6IrzAQCXd2cgplN/hDRuhuJFr6CmxPRDd3jL9ohJ6ovLu+vvh8rTB1GydzViuwzSL9epHy7t+BYh4Vc61xv/jHfvPgSl62aYzF5QJMZqMLKTFiGlBWj24JuoOnOwLgSU7veHDm3FxLfuwVPP3Iwnn2yLp565GRPfugeHDm112/4h8iTz2TsKzuLRs3R7r6+Z9sFw/Qq6P+SlpZyIap+Gii1z62UE4HpOmCtdPxMjkiz/noxICkFYTTmaPfgmijbNYU5QwLF9PuG/s3isCYTZPaZ99YIjy6Wu2nM5kdQX0EbYnG3TUE6EayRzwgq7CjxCiBuFEOuEELmGvycJIV5z1yAszQxxtTDi7uKOtWq7IpCvzqrlKqujzP/NXkkJsTqLx9/emy0R0XGIbN0NJXtXAQBKf96EmKR+qNixADLvZ5TvWFDve2I6DUDJ/rWoLsyDrNGhujAPhRs/r5v2qI1P1C+X1B9lh7cC0vK2b+t2N3QFv2JCSojF1yekhaPq+A6ENm6OmM4D60JAd6kAISFhmDb9MZQk3oTE0dNx7T+WIXH0dJQk3oRp0x9DRsZHbtg75Cmezgl/YG32jiKQc6IhaizsAO7vg6GW99UQSzmhrS6xmhGA+3JCV1kKXf5xTLjdek5UHNyoz4lO/ZgTAYQ50fD5RCDN4rHG1uweNRZ8grWvXmh4lOdyotMACKGxOtumwZy4PQTlB9YyJ6ywdwbPZwDGAagGACnlPgAPumsQ5l3ZXeWJgoS1arvC1auzajygAf5b3AHs65fkrv3uzHrsnc5fUHAS8xdOwt/GdMNTT92Av43phvkLJ1md1ti9+xCgpgqXf1qBytMHUVt+CSIkFOW5a7EhPbKuOZmx0EYJkFVlyJv7N5x6ZyjOfvEiZI0OzYe/WzftsW65yjLoqsotbvvXH6dhVGetzd+TkZ20uLx2OmKT70bpwU0AgOKsL1Aja9HsgTcRf8cok2mf8XeMQrMH3kTGyplBU3n3Ux7NCVvUcvy0NntHEYyzeNRa2FF4og+GL27VcjknyopRcWSr1YwA3JcTURHhGNUlwubvyYgkDco2z0FMUn/mRGDxWU6ohX3nE4E3i8caf2jWHCh99RzNia5dBqC2qtxzOVFdgYqyIovbtisnOmpQvmMBc8ICex+THiWlzBbC5KqkzgPjAeCe25rc/SFy57Ej2HK0DNO2216uXevdTm/DnbenuYM/F3eUKyQHngoz+forKSFo/8liPNXyJhQYHm3v7kejK5R/S3t7+1j6uc/N3YhZs8cgKqkf4h+egtDGTaErzkfOzqXYPGkwQkJCUF1egojoOHTvPgR9e6fXPV4wos2tyF8yCSIsAmWb59Y9snxkksRCwyMGFbpLBRAhWkTd2BON/zCsrsJuTnepAJqIaISHhlt8HzMKTmJvXjVm7qq2+Z5jw3cidPA41JZdQuXpgyg7mo3YroNMuvQbC2/ZHrHJd2PRkikuPyaSPMarOaFQ03Hz1IkcrD5eio88mBP+wF8ed24tJ8b21KDDJ5kYO2QomsfFOb1+Vx6d7gh35ER4WAhGGm4/sJQRgHtyAgBiI6MxM/siZmZX2HxfjRrvRGjf55gTgcUnOaEm9p5PpLQ94p0BqYzaHsWuzN6Z87TpKfO4ngLtP1mMPv2fRePGCV4dkzOcyYnBdz+Dnf+623M5ERmLcI3lUoS9ORF/zUGENnqcOWHG3gLPeSFEGxgm3Aoh7gdguYOSC9w1e8cTHyg3T3zb6muZWef9qteOIxVxNX84t8XW/c0jOgos3LMKvQ0FHld56gpDQcFJzJo9BvFDx5scqHQXT6Pk0GbEdB6ImE796w7S+/avwfbJ9+KB+/SPLNRo9f0PZFUlKn7JwmvP6v/+WooGc2auRWSPBxESEw8AKNnzI0IaN4UmMtbqwRgASvauhPaqlujR/g8WX9/zzhRsO3IEvd98A8sfjMQ9C8px7PkYk3+HvMu1aPNhCUoOZkKERaJw6VuArEVMpwE290dM54E4M/t7+3Ye+YJXcsIab51M2/L3l4O3sZ/5cdAfssOePhjvpY9yat3eKjw6mxN39XsMtbU1qDy1Xz/LMxSYkBIBwHJGAO7LiZFPfIoP3/0zto6Owp3zyvDzX+tnxC0zSlBRUY7Ks0eZE4HFpzmhBrbOJ8iUpQunxlnjjcy3p6/efcMmenwcrnAlJ6SUjuXE3pXQRMRCExFjOyf2rYI2rnmDOfFdA+cS2p6PGp7OxZwwZm+B5xkAswC0E0KcBvArgEc8MSBXflnVMpXPH/jDh29nWbsqq3glJQQ3z9iBB7bMR1r/1m7Zpq39mZl13urrytctnQisWT8PUUn9TA7Gxh3sjb+ujU+ENi0d4W26Yd5X4yBECERYBGKbNAeirsLDsT+ZTC0dmRRSV3mvPH0QpXtXIURoULL7e0Tf+AeLlW99g7RVCBUCfe5Mr/u6+UyvRds249HkcLy6rhKPJte/XSsxVoPRyVrMWfcRWjS7CU8/8SFee+2PdV36rQltlACpq7K5DPmU13LCnJpm8QQTfyzqKBrKCX+ZxeNMTiAiFstWfISY5LsQdVNPlGVMxr3XlVnNCAAu54SxnJ3LMLprJObu1eGRjpYzYkSnMGSeqsHhdR+jRbPrmROBw2c5Qf6vXsZkeXZ2j7XZOwp/mcXjzZy4vDsDsroKJXt+QPRNPa3nxJ6VduVEQ+cSc3+cDNGuL3PCjF0FHinlcQB9hBDRADRSysueHZbj/Pl2Im8KhiKYXfc3dwrFwj2rMLT/0xaXcZdDyYOc3ufZ2csR//AUk68pT8SyNvVQExUHERKGZsMmovrQBugKjkJXC0x4NspkuddSNJgzYw0qdLXQHdmGvz7xITp0uAO5uRvxyX//hogOfRCbfBdCGyVAd6kAJXtX4vKeHxECgScf/wAJCa1M1mf8e6efflyJyFBg+UOm21WMTw3H7JwS/GnwC0hIaAURGgZdcb7Nar/uUgFEqOWTMfI9NeSEGmbxuJOjxw5PvndrY/HXzHWkD4aaZ/E4mhPVhXko3v4Nmj34JsJbtsflle9BU34R4RqtyXJKRoS2uxNlv2xB1c8bXM4Jhf5WxnJEhALHn4+xuMzYlDDM3VsCne5XPDJmMXMiQKghJyhwePp2Lkf66ql5Fo83c+LZp2a4NSfsOZfQ7V+Dl19bzpwwYrPAI4R40crXAQBSyvfcNRBXbnMKtOKOp09SAmU/WWPv/c2dEk+4vC17bwm0NYvHmorSoroq9OXc9SjeNBe1FZeROPpjq99zeXcGYrvchZDGzXApdy02p0ei15xSCLOH+iTGajCig8TCIzswbty3dQfYDh3uwOvjv8OKHz7GT/P+Bl1FGUSoFiEhWnTvMgCD737W5GBs6aRv88S30W38y+iRcM5mKI5O1mLjN/9EUlJvJLa4ASV7VyL+DusnUiV7fkSLFjdYfZ18w5s5YYtyMu0vRR57ijeOHDMsfbh1t0DKDm/1wUhLbQJkee5n0jwnijZ+DllZajUnjD/U60ouovzgJmwZGY0+X5Rh4p21aB5z5ersiA4Ssxe9gibN2+FpF3LC3N9fXoElC/+JG0oW226g2SkMWb/VIGfXMrRuncyc8GNqyQkKXJ64nStQ+uopOVFdmIfCDZ+j/MRuCFmr+pyY+tYADGh2osFzie9ONa5bF3NCr6EZPLGG/94EoBuA5Ya/DwaQ6alBOSLQijuevOIXDLN3AO/d32zv/nR2Fk9EdBx0xfk4v2o6qk4fgggJgdRV25x6WPrzJjR/5D+o2LEAIwxNlUcnazF1SxXe6x9hsuyEtHB8daAUYWGmlfGEhFYYPWIqRo+Y6vCYFafO52PXiWp8vNN2s+UmUfqf9QfuexnTpj+GqBtuszqd83LO93j02f86PSbyGNXkhFqLPN6Y/RIoGegt3u6D4amfSUdzQskIACjfPAcjkzRITgxBelL9nJiQFo45e0vxyENv1Psg7mpO6E+cKvFxdqXN5aK0wLUR+pMn5oRfU01OUHBwx+yeQOmrFxEdh5L963BxzSeARgOh0UBWVqo+Jwov/IaPTzV8LnFV9IW6/2dO6Nks8EgpJwKAEGI1gC7KVEohxBsAvnHXIFwtaPjbB1tfFFoCrRDma+7en5au8nbvPgRbvnkdNZcvIOaWOyFrdCg7lIlT7/wJmsjGiL65F2K7DDKZhmj8SPQJf9VPP3w5JRwdZpZibEpYXdUdUK6Qhro8tdTSPjj36ecNfp/ye38IQLt2PTFowNPIWPgaYpPvRkzngVemc+75EZdzvsegAU+jXbueTo+TPMNbOWEvXxd5LB3fedwNbp68cKPkhO7SeYQ1vR66ojxIAL9PH47oW+60mBGhjZvWXZWdYGi+PzYlrF5OJMZqMLpLRN0MGndy5sSJOeG/1JYTFFzU0KzZlzp2uAPZa2YA0CCsSSu/yYnJ7x1w+HuYE3r2Nlm+FoBxN6IqANe5axCu3pqlBtZOJtTUt4AnGa5z5vG/zjzZraDgJM6dOw7dpQJA1qD0wAbEJN+FxNEf13W5L9m3Gme/GIMmd7+IyDa3AgA0kY3qHolu3AjtgVtC0WpaCapqLIzPh1NLjX9nBg16Dm3bdsWiJVNwZvb3kLoqiNAwtGhxAx599r8BfzAOAB7NCUfU/b4ZGjB66sMbiznkCHcXHetyovgchCYU4dfcjCaDXzLKiFUWM0JXnI/K3UsxMinErpxQ0+0HzAm/p5qcoODl7WbNvlRQcBJHju4EpITQCOZEkOSEvQWeLwBkCyGWQv9ow6EA5nlsVHZQ04wU4yvGll7zNTUVwvyZ8ROvPFncyc3diFmzx0DT8maIkDBASDT788R6Xe7je41AVNvuyF8yCc2HvwttfCLCW9xk8kh0xYS0cMw9oEHT0f/F5Z3LkBwbi4eGTXBoXNY401/ImnbteuKf479zy7rI61SXE5aOzc58cFNToZ78k7tn8Sg5gYTWEJrQumaYCn1GjERU2x4mGRF9cy9c2rkMtQevzPJUKDkRdtMf0fjiKdUei5kTfk11OUFk63Yufy721OVEk+shivKZE0HE3qdovSWE+BFAquFLo6SUOZ4blm1qKu4o1DQWS9Q+Pn9i77505gN9QcFJzJo9BrF9nsTF1TMR2borQuOaWX1qVnjL9ohJ6ofibYsQEtUYNSd24tHO9Tv+K48znL9+JspPHkCfV5c6NC5rXHlKGAUWteWEoqErdU6tg8hJ7pjFY5wTF378CLFdBzeQEX1x+acViO06GLWVZdAdXI/RXcIsP568owazc1Zh2LNzXBojkSVqzQkiRaDM7mFOBDe7CjxCiGsBnAew1PhrUspTnhqYNWos7niC8iFQeb+BcBtbMHL053TN+nmI7NgXlacPIaZTf5TsW4Pmaf8xWUZXchElK96GlBKNhryGmE79kTf7GUS0vQ0hqMWENMuPE3wtRYPPP9qKR4a/Z7NzPZEz1JQTtgR6dpB6uWsWj3FOQAAxnfrXW6by3HGULB6H2Pv/jZhOA5A3+xmU7F0JjSYEERpgwu0hFtc94fYQfLFXIDExsJ8wQr7hLzlBpPD0o9g9hTkR3Cw/d6y+7wFkGP6sA3AcwI+eGpQ1wVLcUd6fu4ozgb6/vC2vsBADJk/C2aIit67vwNkT2LLlG0Ql9UPpz5sQk9SvrtGZsYodC4D8XyDP/YLyHQsQ2ihB/9SUS6cxukuEzccJPtolCr+fVM99shRQVJETRGpgKyecyfbi4nx8PO0hHD+eY5ITsqrc4pNQyla+g5DqUpSufKcuI2SNDtc2v7bBnBiVHI61q6Y7PEYiOzAnyG+lpTYx+QPoj+fKH0cpx/Xi4gK3jI85QQp7b9HqaPx3IUQXAE96ZERWBEtxR2GpYmxvldiZRsBkv6krliH72GFMXb4U76WPcs/6jv6CrCPHoKvSIbRx07rCjtLoTOluryu5iLLctdiSHoXUz0tRun81QtvdCRGqhTx/HB+fkfg4u8Lm9tTUCI0ChxpygkgtrOWEs7N41q6cjlO/7sKH0x6Grqq6LifMMwLQX5WtPn8KW0ZHI2X2SZQczIQIDYOsrUFleRE+2l6Kj7bb3h5zgjyBOUGBxNXbudaunI5TJ3a5/DRbk/W5kBOa8GjImmrmRACwt8myCSnlbiFEN3cPpiHBWqxw5rG/wbqvPC2vsBBzszKxbngk+nyZibFDhqJ5XJxL65uTuQnr06Nw+7wqiIhY6Irz6w7G0Tf3Qsm+1YjvNQKAfvbOyI4CyYkhSO+kxfLDOhSvnwEpNKhCBD79NNdN75TINb7KCSJfaygn0lKbAFn253lxcT62bVuMTemR9XIisvWtJhkB6K/Kjk7WIjkxBCM7azFv3UeIvOEPKD+2C+dLKvDpp8fc/ZaJnMKcoEDiSLPm4uJ8bN+2BBuHR+LOLxejT/9n0bhxgtPbdkdOSKlF9M29cPHYLuaEn7PrFi0hxItGf14SQswH4J75ZHZgHxnHHslNnjN1xTKMSArVF1iSQjF1uWvNiqeuWIa/dNToD7CdtIhufBUu5/xQV9iJ7TIIJXtXofL0wbrZOxNStQD0newLyySqzx1H1A23oaq2BrEb57jhXRI5ztc5QaQW9uaEvXm9duV0pBsK++Y5IUK1dRkBXLkqOz41HIA+J2p11YhofStikweiqrocBQUn3fNGiRzEnKBgYX47l/GtXO1yMrB25XSM6BRiyIkQl293ckdOhF9zM6SUqKwsYU74OXt78MQa/QmH/h7aezw1KGPBdmtWQ2x9IOS+8izlquzYnvpfm7E9NZiblel0Lx5lfeNv1xdsXkvRoLboDC7v/h7hLduhZO8q1JYVocndLyJ/ySQUL30DIzuKuntiE2M1GJ2sRZMogfAQQAD45kCWO94qkTN8lhNEamFvTtib08pV3vG36ydcm+dE2S9b0Pi2PyN/ySQUbpqD0h/+jdHJ2no5UZU5CzGdBkAAWLuBT6Umn2FOUFAyLvZcKC3Gjq2LMK6nAACM6ymwY9tip3vxuCsnQvMPovzYTkhdNXPCz9lb4PlZSjnR8OctKeVXAAZ7cmAACxbm7Gm+zH3lOcpVWeMDoiuzeCytb2SnUIRpanDh+2kIv7Yj8hf/C+Un9yC+39OoOX+ibvaO4tXUcBSWS5T/shlSV4U1Rz13P6y7m8FRwPFJThCpiaM50dAsHuUqr62cKN62CJFte6Dq/G/QXTxTd1VWMT41HDXlJaguyoPUVWPHjhVueKeWMSeoAcwJCnqZ+ZkY1dm0wDKio8BPX77k1J0Y9uREUdaXiLqxp+2cqChFbVkRRKjWYznBjPAOews84+z8mlsYdyNnwcKUu5+wRfYxvyqrcGYWz/oDB9Du5XH4ZN3aeut7LUWDEAFoE29Exa85qK3V4XLODyhZ+T5GJoXU62ivVN2vjqhBeGgISstL6l5z98+IcTM4423wd5QMvJoTRGrjaE7YOnYeOrQV//zXXcjM/KruKq/CUk6UHtwEcWqnyVVZhZIT5T9MgQgNQ0WZ6TjcyVJOEBlhTlBQs5YTr6SEYM3RbNzYMbTe7VzW2J8TuyFlLWRtTYM5EaUFRESsx3KCGeEdNgs8QoiBQoiPALQUQnxo9GcOAJ27BmHpB9n4EXRkylKRhyfanmV+VVbh6Cyef337Lfr8512crgnFqM5hFtc3MjkMIv8XXD3wOcQm9QMgoJE1mJAWbnGdr6bqe/FA1iAyIsojxT9l+uf64ZEuTSOlwOOtnCBSO2dzwvyYnZHxEaZNfwyltdX254QEUFtb76qsQrk6q4lLRERUnNPv0RbmBFnDnCDSsycn7HkUu2M58Ty0V12D2hpdgzkhJRDe+laP5AQzwnsamsFzBsAuABUAfjL6sxxAf3cNwrwRFQsVDTP/pSfPsVZtV9g7i2f9gQN4Y3kGmgwei5qLv2FCWpjF5SakhCAEEhdWfQwREorGbTpjZJKm3sFbYdyLp32zqxx6b/b+/Li7GRwFFK/kBJGaOZsT5p93Dh3aioyVMx3Oidi4OItXZRVKTkSUnEaPHp65I4Y5QTYwJyjoOZMTlpo1l614Dxk/OpYT4S1uBI5ssisnNEc2eCQnmBHeY/Mx6VLKvQD2CiG+klKywq4yyuPTlf8nz7BWbVcYV93fSx9ldT0vzF+A2C6DUHvqJ5NmyZbWN6KzFvOLbkHFb7kIPX8YM6skZu6qtjnOmDCgia7K5Gvtcuo/itdSQcfScgql4j7naf3hYlxPgfaf6B/p6Czl55b8H3OCyLWcMH5s+sIlU5zKibDL+fh4J/DxzoZzoset9j2e3RG2csKVR/9SYGBOELnnfCIttQmeGf8BYrs6mBMFJxAmavHxzlqf5AQzwrtsFniEEIuklMMA5AghpPnrUsokj42M7MLCjuftPHYEW46WYdp228ultD1i8/UDv/+OxH7jUPrdRMw8V4WZu6psLh8T/hP+cPsj6HPnTGSu/x9uKPkW0wdqrS7/wsoqhMR1qPv7oeRBVmfomP/c2Cq4WGreplTee9zQzeZ7sMVaQYn8C3OCyD050S4nA3lnjiBxwAsey4lnV1YjZ9cytG6dbHugDrKVE/cNm+jWbZH/YU4QqeN8YtX309BRtwof32X5Ni3AMznBjPAumwUeAC8Y/sszMQpamye+bfL3vMJC3DL2Rax7RIs+X1bjwH/eR/O4uAbXI3XVCG3cFFJo8Ew3LabfFVn32rM/lOOL31og7pEPcOqdofj006Mm33vqRA5WHy/Hx9nlNreR0vYI/nS96ddcKQKaV9wVSuX9QsubALDIGOSYExT0XM0JZUau1FV5PCfatXbv0xYbygleoSUwJ4h8cj6x6alpda8dSmiFgnNHMeN4JWbsrLS5DXfmBDPC+xq6RSvP8L9/lVK+bPyaEGIKgJfrfxdRYFOmWOrvIZUN3pqlEKFalB3bherzpzD+4RiT18anhmP2RydR9utuiND699L+/WXrjys0b7CtzMZxR+Nt84q7Qqm8L9yzCkP7P+3SNsi/MSeI6lNbTnhSQznBK7TEnCCqzxs5oZwHZGadR7ucDHza70kA3p1Fz4zwPnsfk97XwtcGunMgRP7AvEGaI49Jv+Waa1C+5gPrjyfsrEX56mlo0eIGh8Z0KHlQvVus3NF4W6m4mz96UTGup8CqwzscekQ8BTTmBBGcz4m01Ca4Lr65R3LCU+zJCT4thYwwJ4jgnfOJDte0rPu6pWbN9jyK3VXMCN9o6DHpTwsh9gO4SQixz+jPrwD2eWeIRNblFRZiwORJXisymDdIc+Qx6c/98U7Ull+y+XjC2vJLuDPtIZfG6K6+TNYq7orEWA3SO9n/iHgKTMwJUjt/yolXhvT1Sk64i105waelBD3mBKmZtzMC8M75xHN/vNPqOmw9it2dBR9mhG801INnPoAfAUwG8IrR1y9LKS96bFREdpq6Yhmyjx22e1qjK5Rq+4GnTKfGj+2pQYdPMjF2yFCb985+tm6VXY8nXJk1F6mpDzo8vsys8ybFHVcLPfp+DqX4yMVmcBTwmBOkaswJz7E3J9zd94f8DnOCVMubGQF4Lyc+W7cKj/fu3eB4LD14xbjI48rtXMwI32ioB08xgGIADwGAEKIpgAgAMUKIGCnlKc8Pkcgy5QC5bngk+nzZ8AHRVdYeb2jvY9JPnc/HrhPVDT6e8Kpox3+tlCdmKdwxi8eefg7u6PND/o05QWrGnPAsX/X9If/CnCC18nZGAN7LiaYx+U6Nr97n+izTGT2OFHyYEb7R0AweAIAQYjCA9wC0AJAPoBWAgwBu8dzQiGxztjmZM6xV2xX2VN3Pffp5g9vJzDrvs8eHt8vJ4KPLyWnMCVIjf84JX+YBkScwJ0htvJkRgPfOJ9zJ/EEu7prdQ55jb5PlNwHcBuCwlPJ6AH8EsMVjoyJqgCvNyZxhrdqucOTeWTXiLBxyA+YEqYq/54TSCJMogDAnSDW8nRGA/59P+KpZMznGrhk8AKqllBeEEBohhEZKucHwWEMin7DVnMwTlfedx45gy9EyTFNpPxp3HVQ5i4dcwJwgVQmUnOBxmQIIc4JUw9sZAaj/fMJRtmb3AJzh4yv2FniKhBAxADIBfCWEyAeg89ywiKxztTmZMzZPfNut67PF2Q/zrs7CSUttUndw5gGZnMCcINUIlJzgcZkCDHOCVMEXGQF493zC2zzZrJkcY+8tWvcAKAfwdwArARwDMNhTgyKyxZ7mZP7KmSKNOxsdGz8u0ZvbpYDAnCDVCKSccOS4TKRyzAlShUDKCLXy1qPYqT67ZvBIKUuN/jrXQ2MhapA7mpMFEk8cIJUrxkSOYE6QWgRiTvh6Jo+jWcMrtWQJc4LUIBAzQu04u8e7bBZ4hBCXAUhLLwGQUspGHhkVkRWONCfzZBd8NVAOjJ6YRZOW2gTI8syJBItHgYU5QWoTqDnhzSKPeUHHkZwx/uDOD+0EMCdIXQI1I/yJOx/FTvXZLPBIKWO9NRAiewRaczJXefoWKU+dSPDAHTiYE6Q2gZwTdcf8LM8UUIwLO87mi/J9LPSQgjlBahLIGeGv2KzZvextskykCoHUnCyvsBCjPpmOOU8/V28KaEOFFWf739japjneqkVE/igYcsJ4Ng/g2odf86KOss0bOzacE7aYF3r4AZ2I1CCQMgJw7LO9P2yPt3O5zt4my0TkZlNXLEP2scP1Grk1VLhxpe+OtW1ak5bahI3QiIh8xNYx21LzSnuYN7o0b4TpaE40hE2iiYg8x93HbLVtj82aHccCDzktr7AQAyZPwtmiIl8PRRUc2R9Kg7d1wyMxNyvT7n3oSt8dZ7dJROQMZkR9nsgJ4w+/5h98Lf0x/x5ntukoFnmIyBLmRH3eOJ9wZWy+PJcwzi5LBR/SY4GHnObtCq7aObI/lAZvyYkhdj+O0dWmys5sU9keD5pE5ChmRH2ezgnzD7/W/rhzm/ZikYeIzDEn6vN0Trg6Nm9uryHm2cbZPXos8JBTfF3BVRtH9oey7Nie+l+/sT01du9DZ4s7rmxTEcwHSiJyDDOiPm/lhKvj8+Q2WeQhIgVzoj4154QvcslRnN2jxwIPOUVtFVxfc2R/mD+e0fhxjNa4emByZpvGPP20LiIKLMyI+jydE+4an6e3ySIPEQHMCUvUnBO+yCVXBPPsHhZ4yGH+UMH1Jkf2h/myCkvfY37wcaTIYnz/riPbbEigHxCJyHXMiPo8lROujskTOWEPFnmIghtzoj4158Tekye9mhGeEEzNmlngIYf5WwXX0xzZH+bLKsy/x9UZM8b379q7zYZwFg8R2YMZUZ8ncsIdY3J3TjiCmUIUvJgT9ak5Jx6fNcPrGeFJgd6smQUecoi3r/I5w5sd+R3ZH9aWtfU9roxp3fBIzMnahM8zN7l1m4Fw4CMiz/CHjACYE57OCXuxiT9R8PGHnPD2073UnhMHTv+OkZ0sL6emfzdnBdrtXCzwkEN8cZXPUd7syO/I/rC2rK3vARwvqLy+eCEevgVITgzBXzpocGO8dHib1rhrWr0/HiyJqGH+kBFA4OWEozyZE85gJhAFD3/ICW8/3UvtOTG6sxZz9+o8uj018ffZPaG+HgD5D6WSe+CpMIuvj+2pQYdPMjF2yFA0j4vz7uAMjKvNfb707Fgc3R87jx3BlqNlmLbd9npT2h6p9zV7p7LnFRbi661bcPjZKADAq7dr0ebDSoiJlxzepjVpqU2QmXXe7uXd/f1EpE7+kBFA4OaEI2PydE44gplAFDz8ISe8mRHG21N1TqSGo82HJXh/e5VHtqdm9c7BskyLPIeSB3lxNPZhgYfs5kjF+L30UV4enZ5p93np0bE4uj82T3zb4W20y8lwqE/B64sXYnhSiMn9u0/eGgXRuKdb9wN7JxCROX/ICCDwcsJR3soJR6SlNgGyMlT5QZmI3McfcsKbGWG8PeaEfzA+B8rMOl9vVo8acowFHjfJKyzEqE+mY87Tz/n0yqQneaNi7ArzCrinrwKobX+YV9sVargaQkSBnxNqOyZawpxQd060y2GRh4Ibc0IvWM4lAPXtE7XnhJqYX/A2L/j4Ks9Y4HET43s1A7WyaVwx/vu8z4HirXi/fyj+vkqnioqure7znhibpyvojs6SMa+2K9RwNYSIAj8nzI+JzAnP54Sj1JwTvFWLiDnh65zwdkYAzIlAopbbudhk2Q2M79X09y7i9jDv3q6G7un+0JHfk5Rq+4S0cIuvB8t+IFIr5oTvj0HMCf/ICX9pYknkbswJ3x6Dgj0jAP/JCX/hq2bNLPC4gem9moHVRdwSW9VttYxJ4YuxefvRioD1artCDf9GRMGMOeH7YxBzQv05wf5uFMyYE749BqkpIwDmRKDx5qPYeYuWi3xxr6YvWev07sv3rbaO/L6YXrtm3x6cuFiNmbuqbS6npg737LVAwYI5ocecuII5YRvzgYINc0LPV+9bbRkBMCcCnScvaHAGj4vUVn32NLVVt22NSeHNsfliem1eYSGKKypx5sUYyNcb1ftz5sUYXBUVhryPP1bNfb68SkvBhDmhx5zQY07YxnygYMSc0PPV+1ZTRgDMCXINCzwu2HPiBD5bvy5o7tW0dm+qwlfve+exI5i2vQxi4iWrf6ZtL0P2Mc9Xm30xvVZtoUREVzAnTDEnmBP2UKavEwUD5oQpX7xvNWUEwJwg1/AWLReM+mQ60jvZrj4HUpdxR37xvfm+1VJF9tX0WrU9XpGIrmBOmGJOMCeI6Iq8wkL0e3sic8KIL963WjICYE6Q61jgcdKeEyfwS14efvhzjMXXA/HeWf7i2+aLRysC6golIrqCOWEdc4I50ZC01CZAFnvxUGD7x1dfoKSyChPSmBPmmBPMCXIOCzxOGvXJdIxO1qqq+uxp/MW3Tm3N4ojI95gTZIw5QUTG8goL8d1PO5gTVIc5Qe7AAo8T8goLcexcHvb8Bny8k13Gyb5mcYESzETUMOYEmWNOOI6zeCiQvb54IQT0GcGcIIA5Qe7BAo8TXl+8EI8kaTHj7si6r/31+3JsP9cEu//9jg9HRr6gxkcrEpFvMSfIGHOCiIzlFRZiwbYtGJ2sxbQBV3Li2R8rERafypP4IMScIHfhU7QclFdYiK+3bsGEtHCTr09IC8ehvDzsO3nSRyMjX2HXeSIyxpwgc8wJ5/GJWhSIXl+8EFLW4uUU05wYf7sWc7I2BdyTs6hhzAlyF87gcdDrixdieFKIxalzIztrMXLmR7w6G2TYLI6IjDEnyBxzgogUyuydRy303kmM1eDhDhreihOEmBPkLizwOEC5Knv42SiLr09IC0ebD/VXZ5NatfLy6MhX1N4sLq+wEKM+mY45Tz/HKZ1EHsacIEuYE65rl8NePBQYrszesZwT42/X4pZPNvFWnCCj5pzwh4ygK3iLlgOsXZVVGF+dVeQVFmLA5Emcakk+M3XFMmQfO8wpnURewJwgf6T2nEhLbeLrIRC5ha3ZOwrjWTzG38ecIF9Re0aQKc7gccCafXtw4mI1Zu6y3ek+NiwPZ4uK0DwuzuQXglMtyduUhm3rhkeiz5dszEbkacwJ8jf+lBOcxUP+buqKZbg6EvhgRzU+2GE7J7pff8jk+5gT5Av+lBGkxxk8Dmh51VV2LXd1lL7qbvwLMTcrk1V38jqlYVtyYoiqGrNlZp339RCIPII5Qf5GrTlhjrN4KBDsPHYEJ4pqG1zuujgNUm5sBwDMCfIpf8kIuoIzeByg3BuZV1iIW8a+iANPhVmcXpl3uRYdPslEaWWl0S+EZNWdvMr8cYtqe7wir8JSIGJOkD9Re05Ywlk85M8czYixQ4aanWAzJ8h7/DEjiDN4nGLPY+zuaxeC+Vu3YGxP/TJje2pYdSevMv855eMVibyHOUH+wN9ygrN4KFDY+0jsf36zAHOzMpkT5BP+lhGkxwKPE3YeO4Jp28sgJl6y+mfu3nKkd3LPLwQbq1nG/WKdUnFXPhAo+MGAyDuYE+rA/WIdc4LId+zJiGnby7B6X47bTrB5PLSM+8UyZoT/4i1aTmjoMXbKtMvXUsNMvu7stDY2VrOM+8U6a1eGjD8YcJ8ReQ5zQh24X6zz15xIS20CZPE2LfJv9jwSW8mJsT2ZE57E/WKZv2YEcQaPR9jzC2EvNlazjPvFOmsVdwUr70S+x5zwPO4X65gTROrHnPA87hfLmBH+jQUeN3P3LwQ7l1vG/WKdvfd1c58R+QZzwju4X6wLhJxol5Ph6yEQeQxzwju4XywLhIwIZrxFy80c+YVoaFobO5dbxv1i285jR7DlaBmmbbe9XErbI94ZEBGZYE54HveLbf6eE2mpTZCZdd7XwyDyGOaE53G/WOfvGRHsWOBxM3f+QtjqXB7M9zxyv9hmz33dROQ7zAnP436xLVBygo9Mp0DFnPA87hfrAiUjghULPG7mrl8I86qyIliry3mFhRj1yXRMeTid+4WI/BpzwjOYE8GFs3gokDEnPIM5QcGAPXhUyp2N1QKB0uH+8VkzuF+IiMCcMMecICIyxZwwxZygYMACjwqxc7kp4w73B07/jpGdLC8XaPslr7AQAyZPCpj3Q0Tuw5wwxZwo8vVQfIbNloksY06YYk4U+Xoo5CUs8KiQmjqXq+GgYNzhfnRnLebu1Vlczl37RQ3vGbhylYFXEYjIHHPCFHMiOHMiLbWJr4dApFrMCVPMieDMiWDEHjwqpKbO5cYHBV80HDO/d/jV1HC0+bAE72+vsvo9ru4XX79nwPQqQ58veS8wEZliTlzBnGBOsNkyUX3MiSuYE8yJYMICjwqppXO5Gg4KljrcP3lrFETjnh45WKrhPQOmVxnSkyQ7+hORCebEFcyJ4M4JNlsmsow5cQVzIrhzItjwFi2yyvSg4P2GY9buHfbkvbG+fs9A/fcdaPcCE1Hg8PUxkznBnCAidfP1MZM5wZwINizwkEVqOCh4u/O/Gt4zYPkqAzv6E5HaqOGYyZxgTijYbJlIfdRwzGROMCeCDQs8ZJGvDwq+6Pzv6/cM+OYqAxGRM3x9zGROMCcUbLZMpE6+PmYyJ5gTwYgFHqpHDQcFb3f+V8N7Brx/lYGIyBlqOGYyJ5gT5jiLh0g91HDMZE4wJ4IRmyxTPfYcFDzdoMvbnf/V8J7NO/ybG9tTgw6fsAM+EfmeGo6ZzIn6gjkn2GyZSF3UcMxkTtQXzDkRLFjgIRNqOSh4s/O/Wt6zI1cZ2AGfiHxFLcdM5kR9zAkiUgO1HDOZE/UxJwIfCzw+kldYiFGfTMecp59TVfU0GA8KannP3r7KQETqxpxQD7W8Z+ZEw9rlZOBQ8iBfD4PIK5gT6qGW98ycIBZ4fGTqimXIPnZYdQe2YDwoqOU9e/Mqg6+lpTYBsvghnMgW5oR6qOU9B1NOOIO3aVGwYU6oh1reM3OCWODxgbzCQnyeuQkdmgh8nrlJVfdABuNBwRvvWa1XWIhInZgT6sKc8C+cxUPBgDmhLswJUgs+RcsHpq5YhhviJX4uqMEN8ZKdzIOA8RUWuoJPPCGyjDkRfJgT7sFHplOwYE4EH+YE2YMFHi9Tqu1HL+qwLj0aRy/q8HnmJq89No+8T2m6tm54pFcfkah2/BBOZBlzIvgwJ4jIEcyJ4MOcIHuxwONlSrV9ZKcwJCeGYESnMLdX3fecOIGWf30c+06edNs6yXlK07XkxJC65mpERNZ4OifyCgtx579eR+9Jb/ADokowJ9yPM0QpkDEngg9zguzFAo8XGVfbx6boH6E3NiXM7VX3xz+bidKKMjw2a4Zb1kfOU6rtY3vqf9XG9tSw6m6GH8KJrvBGTkxdsQw/nTiKnBNH+QFRBZgT7scZohTImBPBhzlBjmCBx4uMq+3KI/QSYzVurbrvOXECB37/HRtGROPA6d85i8fHzB+ZaPyIROKHcCJzns4J5cQgBMD69CjMyeKUfl9jTngOLyBQIGJOBB/mBDmCBR4vsVRtV7iz6v74ZzPxaLIWyYkhGN1Zy1k8PmRebVew6l4fP4QTeScn6k4MOuun9f+lg4YfEH2IOeE5vIBAgYg5EXyYE+QoFni8xFK1XeGuqrsye+fV1HAAwKup4ZzF40Pm1XYFq+6m+CGcSM/TOWHpxODV27W8OutDzAkicgRzIvgwJ8hRLPB4yZZfDiI3v361XTE2JQy5+Tps/uWQ09tQZu8YT98LtFk8eYWFGDB5kupDxlq1XcGqOxGZ83ROWJvWH2hXZ5kTZIwzRCmQMCfcgzlBgYwFHi9Juak9nro1ql71VZEYq8Ho5DB0ub61U+s3n72jCKRZPHtOnMAt//gbso/+ovqQsVZtV7DqbiottQk/hFPQ82RO2JrWHyhXZ/MKC9F70utIef1VZB87rPrjK3PC8zhDlAINc8I1zAkKBqG+HkCw2HnsCLYcLcO07baXu+6qHKfWbz57R2E8iyf7rSlOrVstRsycjopqHbaMjkafLzMxdshQNI+L8/WwLLL33zul7RHvDIiIVM+TOaFclb39/yxP61euzr6XPsrhdavF1BXL8NOvR1FdA+YEmWiXk4FDyYN8PQwilzEnXMOcoGDAAo+XbJ74ttXX8goLccvYF7HuES36fFmJs0VFDh1olNk7y++Nsfj6q6nhaPuRfhZPUqtWjg5dFfacOIGjZ/PweFd9A+lHOtaqOmRs/XsTEVniqZxQrsoKqcPyB63kxO1a3PLJJlV/0LUlr7AQczI3YciNoYgNF0hODMHwJOYE6WfxZGad9/UwiNyCOeE85gQFC96ipQLK9LvkxBCnptlZm72jCIRePCNmTodGA7ySor8F7ZWUEN5zGmB4mxaRda7khK2mnAp/77EwdcUyDL1J4PsjOkxI0+fEyz2ZE0QUPJgTtjEnKFhwBo+PKc2zDjylv9d1bE8NOnzi2HTBU+fzsetENabvrLa5XEL0OVeH6xPGs3eMG7490jFE1VV3IiJ3cDUndh47gp8LdNh1Bpi2o8rmsv44zVu5Kvvn9sAIs8agw5OYE2ToxZPF27QocDEnbGNOUDBhgcfHzJtnGTfLsvdAc+7Tz22+/vd5n2Nu5no8cnsvl8frC8rsnZdTTBtIv5IS4nAxjNSPvRKITLmaEw1N8VYyYmRab7/8gKtclV38cxUO/NX01oKXezIniCjwMSdsY05QMOEtWj5k7dF37nzknbKNdcMj/XIKojJ7x1oDaWUWDwUGPvGEyJSnc8LfM0K5KhuqkSZXZRXGV2eJeBswBSLmhG3MCQo2LPD4kLVH37nzkXeu9vfxNWuzdxTsxROY+CGcSM/TOeHvGXHlqmx1vcf6KthjgQBeQKDAxZywjTlBwYYFHh+xVm1XuKPqbr4Nd84M8gZbs3cUnMUTePghnEjP0znh7xnR0FVZBa/OkjFeQKBAwpywjTlBwYg9eHzEWrVd4Uwvnoa24Y51etPjn81EQrTABzuq8cEO2w2k/bHhGxGRLZ7OCX/PiKkrluGRjhrk5Omw5beagGwMSu7FR6ZToGFO2MacoGDEAo+P7Dx2BFuOlmHadtvLOXugMe+mr3DmKV2+cup8PvJLZIPLNY0Ja7A5HPkfNlumYOfJnAiEjNDvn8oGl4vSAsmtWjEnqA7zhQIFc8I25gQFIxZ4fMTTBxB77sdVe+W9oaeDUeDiVVYiz+ZEIGQEP4iTM5gvFEiYE7YxJygYsQdPAPJGfx8iIvJPzAgi9uIhsoU5QeS/WOAJQI7cj0ukZvwATuR+zAgKdmzmT2Qbc4LIf/EWrQDk6f4+RN7AafREnsGMINJjLx4iy5gTRP6LBZ4AxPtNKZDwAziRezEjiHgRgcgW5gSR/+ItWkSkWpxGT0REnsRbgYmIKJCwwENEREREQYcXEYiIKNCwwENEqscrrERE5CnMGCIiChQs8BCRqvEKKxEReQozhoiIAgkLPKR6eYWFGDB5Es4WFfl6KEREpELMCXJFWmoTzuIhCnDMCQoWLPCQ6k1dsQzZxw5j6vKlvh4K+Qg/fBORLcwJcgfmDFHgYk5QsGCBh1Qtr7AQc7MysW54JOZmZbLqTkREJpgT5A68VYsocDEnKJiwwEOqNnXFMoxICkVyYgjSk0JZdQ9yvLpKROaYE+QunC1KFJiYExRMWOAh1VKq7WN76n9Mx/bUsOoexHh1lYjMMSfIE1jkIQoczAkKNizwkGop1fbEWP2PaWKsxmrVnY3Tggc/eBORgjlB7qZcTGDWEAUGe3OCGUGBggUeUiXzarvCWtWdjdOCA2fxEJGCOUGewiIPUWBwJCeYERQoWOAhVXp98UI8fAvqqu0KS1V3Nk4jIgo+zAnyJBZ5iPyfvTnBjKBAwgIPqU5eYSG+3roF41PDLL5uXnVn47Tgww/cRMGNOUHewCIPkf9yJCeYERRIWOAh1Xl98UIMTwqpV21XGFfd2Tgt+PA2LSJiTpC3pKU2qXu6Fgs9RP7D3pz45zcLmBEUUEJ9PQAic2v27cGJi9WYuava5nIpbY/YbJz2XvoobwyXiIi8jDlB3paW2gSZWefrijyHkgf5eEREZIu9OdHqqhxmBAUUFnhIVfIKC1FcUYkzL8YgMVaDvMu16PBJFQ785300j4urt+wtY1/EgadMp16O7alBh08yMXbI0HrfQ4GjXU4GP2ATBSHmBPmKyQzSLEdm8zzv9rEQkXX25oSSEWN7MiMocPAWLVIVRx55a76swtb3UGDgbVpEwYs5QWqg3Lplzx8i8i57c4IZQYGIBR5SDUceZWhtWVvfQ4GH/RCIggtzgoiIbLE3J5gRFKhY4CHVcKSKbm1ZW99DgYVXRYmCD3OCiIhssTcnmBEUqNiDh1RBqaKb90lQmN8Lu/PYEWw5WoZp222vN6XtEQ+MloiIvI05QUREtjiSE8wIClQs8JAqOFJFfy99FDZPfNvLIyQ1SkttAmSx2TJRMGBOEBGRLY7kBDOCAhULPKQKrKITEZEtzAkiIrKFOUHEAg+pBKvoRERkC3OCiIhsYU4QsckyEfm5tNQmfJoWEREREREFPRZ4iHwsr7AQAyZP4mMYiYjIIuYEERHZwpwgBQs8RD42dcUyZB87zMcwuoizeIgoUDEniIjIFuYEKVjgIfIh5XGO64ZHYm5WJqvuTkpLbeLrIRAReQRzgoiIbGFOkDEWeIh8SHmcY3JiSN1jG8l5nMVDRIGGOUFERLYwJ8gYCzxEPqJU28f21P8aju2pYdXdBZzFQ0SBhjlBRES2MCfIHAs8RD6iVNsTY/W/homxGlbdiYioDnOCiIhsYU6QORZ4iHzAvNquYNXddbxNi4gCAXOCiIhsYU6QJSzwEPmAebVdwaq7a3ibFhEFCuYEERHZwpwgS1jgIfIya9V2BavuRETBjTlBRES2MCfImlBfDwAA8PDDvh4BkddMfe6vGJEcVq/arkiM1SA9OQxTDx3Aex9+7OXR+b+0h4E0Xw+C3I85QUGEOUHkBOYEBRHmBFmjjgIPURDZuWMbtuwswbQttpdLqdrqnQEREZGqMCeIiMgW5gRZwwIPkZdtzs7x9RCIiEjFmBNERGQLc4KsYQ8eIiIiIiIiIiI/xwIPEREREREREZGfE1JK969UiAIAJ92+YiIi/9dKSpng60H4GnOCiMgq5gSYE0RENljNCY8UeIiIiIiIiIiIyHt4ixYRERERERERkZ9jgYeIiIiIiIiIyM+xwEOqIYQo8cA6hwghXjH8/5+EEDc7sY6NQohb3T02IiJyDHOCiIisYUYQscBDAU5KuVxK+W/DX/8EwOGDMhERBS7mBBERWcOMIH/DAg+pjtD7jxAiVwixXwjxgOHrdxgq4IuFEIeEEF8JIYThtbsMX9sshPhQCJFh+PpIIcR0IURPAEMA/EcIsUcI0ca4mi6EaCKEOGH4/0ghxAIhxD4hxEIAkUZj6yeE2CaE2C2E+EYIEePdvUNERMwJIiKyhhlBwSzU1wMgsuBeAJ0BdALQBMBOIUSm4bVkALcAOANgC4AUIcQuAJ8CSJNS/iqE+Np8hVLKrUKI5QAypJSLAcBwPLfkaQBlUsokIUQSgN2G5ZsAeA1AHyllqRDiZQAvAviXG94zERHZjzlBRETWMCMoaLHAQ2p0O4CvpZQ1AM4JITYB6AbgEoBsKeXvACCE2APgOgAlAI5LKX81fP/XAJ5wYftpAD4EACnlPiHEPsPXb4N+WuYWwwE9DMA2F7ZDRETOYU4QEZE1zAgKWizwkBpZLYcDqDT6/xrof4ZtLW+LDlduU4wwe01aGdcaKeVDTm6PiIjcgzlBRETWMCMoaLEHD6lRJoAHhBAhQogE6Kvg2TaWPwSgtRDiOsPfH7Cy3GUAsUZ/PwGgq+H/7zfb/l8AQAjRAUCS4evboZ/G2dbwWpQQ4kZ73hAREbkVc4KIiKxhRlDQYoGH1GgpgH0A9gJYD2CslPKstYWllOUA/gpgpRBiM4BzAIotLLoAwD+EEDlCiDYA3gHwtBBiK/T35ypmAogxTKccC0MgSCkLAIwE8LXhte0A2rnyRomIyCnMCSIisoYZQUFLSGlp9hiRfxFCxEgpSwyd8D8GcERK+b6vx0VEROrAnCAiImuYERQoOIOHAsXjhkZpBwA0hr4TPhERkYI5QURE1jAjKCBwBg8RERERERERkZ/jDB4iIiIiIiIiIj/HAg8RERERERERkZ9jgYeIiIiIiIiIyM+xwENERERERERE5OdY4CEiIiIiIiIi8nMs8BARERERERER+bn/B5ZLmTURR1dSAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1440x360 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 3, figsize=(20, 5))\n",
    "for model, ax in zip(\n",
    "    [KNeighborsClassifier(), SVC(gamma=0.01), LogisticRegression()], axes\n",
    "):\n",
    "    clf = model.fit(X_train, y_train)\n",
    "    mglearn.plots.plot_2d_separator(\n",
    "        clf, X_train.to_numpy(), fill=True, eps=0.5, ax=ax, alpha=0.4\n",
    "    )\n",
    "    mglearn.discrete_scatter(X_train.iloc[:, 0], X_train.iloc[:, 1], y_train, ax=ax)\n",
    "    ax.set_title(clf.__class__.__name__)\n",
    "    ax.set_xlabel(\"longitude\")\n",
    "    ax.set_ylabel(\"latitude\")\n",
    "axes[0].legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- Notice a linear decision boundary (a line in our case). \n",
    "- Compare it with  KNN or SVM RBF decision boundaries. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Main hyperparameter of logistic regression \n",
    "\n",
    "- `C` is the main hyperparameter which controls the fundamental trade-off.\n",
    "- We won't really talk about the interpretation of this hyperparameter right now. \n",
    "- At a high level, the interpretation is similar to `C` of SVM RBF\n",
    "    - smaller `C` $\\rightarrow$ might lead to underfitting\n",
    "    - bigger `C` $\\rightarrow$ might lead to overfitting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>C</th>\n",
       "      <th>mean_train_scores</th>\n",
       "      <th>mean_cv_scores</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.0001</td>\n",
       "      <td>0.664707</td>\n",
       "      <td>0.658645</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.0010</td>\n",
       "      <td>0.784424</td>\n",
       "      <td>0.790731</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.0100</td>\n",
       "      <td>0.827842</td>\n",
       "      <td>0.826203</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.1000</td>\n",
       "      <td>0.832320</td>\n",
       "      <td>0.820143</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.0000</td>\n",
       "      <td>0.832320</td>\n",
       "      <td>0.820143</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>10.0000</td>\n",
       "      <td>0.832320</td>\n",
       "      <td>0.820143</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>100.0000</td>\n",
       "      <td>0.832320</td>\n",
       "      <td>0.820143</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1000.0000</td>\n",
       "      <td>0.832320</td>\n",
       "      <td>0.820143</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>10000.0000</td>\n",
       "      <td>0.832320</td>\n",
       "      <td>0.820143</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>100000.0000</td>\n",
       "      <td>0.832320</td>\n",
       "      <td>0.820143</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             C  mean_train_scores  mean_cv_scores\n",
       "0       0.0001           0.664707        0.658645\n",
       "1       0.0010           0.784424        0.790731\n",
       "2       0.0100           0.827842        0.826203\n",
       "3       0.1000           0.832320        0.820143\n",
       "4       1.0000           0.832320        0.820143\n",
       "5      10.0000           0.832320        0.820143\n",
       "6     100.0000           0.832320        0.820143\n",
       "7    1000.0000           0.832320        0.820143\n",
       "8   10000.0000           0.832320        0.820143\n",
       "9  100000.0000           0.832320        0.820143"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scores_dict = {\n",
    "    \"C\": 10.0 ** np.arange(-4, 6, 1),\n",
    "    \"mean_train_scores\": list(),\n",
    "    \"mean_cv_scores\": list(),\n",
    "}\n",
    "for C in scores_dict[\"C\"]:\n",
    "    lr = LogisticRegression(C=C)\n",
    "    scores = cross_validate(lr, X_train, y_train, return_train_score=True)\n",
    "    scores_dict[\"mean_train_scores\"].append(scores[\"train_score\"].mean())\n",
    "    scores_dict[\"mean_cv_scores\"].append(scores[\"test_score\"].mean())\n",
    "\n",
    "results_df = pd.DataFrame(scores_dict)\n",
    "results_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br><br><br><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Predicting probability scores [[video](https://youtu.be/_OAK5KiGLg0)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### `predict_proba`\n",
    "\n",
    "- So far in the context of classification problems, we focused on getting \"hard\" predictions. \n",
    "- Very often it's useful to know \"soft\" predictions, i.e., how confident the model is with a given prediction.  \n",
    "- For most of the `scikit-learn` classification models we can access this confidence score or probability score using a method called `predict_proba`.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let's look at probability scores of logistic regression model for our test example. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "longitude   -64.8001\n",
       "latitude     46.0980\n",
       "Name: 172, dtype: float64"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/gtoti/opt/anaconda3/envs/cpsc330/lib/python3.9/site-packages/sklearn/base.py:450: UserWarning: X does not have valid feature names, but LogisticRegression was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array(['Canada'], dtype=object)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr = LogisticRegression()\n",
    "lr.fit(X_train, y_train)\n",
    "lr.predict([example])  # hard prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/gtoti/opt/anaconda3/envs/cpsc330/lib/python3.9/site-packages/sklearn/base.py:450: UserWarning: X does not have valid feature names, but LogisticRegression was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[0.87848688, 0.12151312]])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.predict_proba([example])  # soft prediction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- The output of `predict_proba` is the probability of each class. \n",
    "- In binary classification, we get probabilities associated with both classes (even though this information is redundant). \n",
    "- The first entry is the estimated probability of the first class and the second entry is the estimated probability of the second class from `model.classes_`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['Canada', 'USA'], dtype=object)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.classes_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- Because it's a probability, the sum of the entries for both classes should always sum to 1. \n",
    "- Since the probabilities for the two classes sum to 1, exactly one of the classes will have a score >=0.5, which is going to be our predicted class.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### How does logistic regression calculate these probabilities? \n",
    "\n",
    "- The weighted sum $w_1x_1 + \\dots + w_dx_d + b$ gives us \"raw model output\".\n",
    "- For linear regression this would have been the prediction.\n",
    "- For logistic regression, you check the **sign** of this value.\n",
    "  - If positive (or 0), predict $+1$; if negative, predict $-1$.\n",
    "  - These are \"hard predictions\"."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- You can also have \"soft predictions\", aka **predicted probabilities**. \n",
    "  - To convert the raw model output into probabilities, instead of taking the sign, we apply the **sigmoid**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### The sigmoid function \n",
    "- The sigmoid function \"squashes\" the raw model output from any number to the range $[0,1]$ using the following formula, where $x$ is the raw model output. \n",
    "$$\\frac{1}{1+e^{-x}}$$\n",
    "- Then we can interpret the output as probabilities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sigmoid = lambda x: 1 / (1 + np.exp(-x))\n",
    "raw_model_output = np.linspace(-8, 8, 1000)\n",
    "plt.plot(raw_model_output, sigmoid(raw_model_output))\n",
    "plt.plot([0, 0], [0, 0.5], \"--k\")\n",
    "plt.plot([-8, 0], [0.5, 0.5], \"--k\")\n",
    "plt.xlabel(\"raw model output, $w^Tx$\")\n",
    "plt.ylabel(\"predicted probability\")\n",
    "plt.title(\"the sigmoid function\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- Recall our hard predictions that check the sign of $w^Tx$, or, in other words, whether or not it is $\\geq 0$.\n",
    "  - The threshold $w^Tx=0$ corresponds to $p=0.5$. \n",
    "  - In other words, if our predicted probability is $\\geq 0.5$ then our hard prediction is $+1$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let's get the probability score by calling sigmoid on the raw model output for our test example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.12151312])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sigmoid(\n",
    "    np.dot(\n",
    "        example.to_numpy(),\n",
    "        lr.coef_.reshape(\n",
    "            2,\n",
    "        ),\n",
    "    )\n",
    "    + lr.intercept_\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is the probability score of the positive class, which is USA. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/gtoti/opt/anaconda3/envs/cpsc330/lib/python3.9/site-packages/sklearn/base.py:450: UserWarning: X does not have valid feature names, but LogisticRegression was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[0.87848688, 0.12151312]])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.predict_proba([example])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With `predict_proba`, we get the same probability score for USA!!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- Let's visualize probability scores for some examples. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "data_dict = {\n",
    "    \"y\": y_train[:12],\n",
    "    \"y_hat\": lr.predict(X_train[:12]).tolist(),\n",
    "    \"probabilities\": lr.predict_proba(X_train[:12]).tolist(),\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>y</th>\n",
       "      <th>y_hat</th>\n",
       "      <th>probabilities</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>160</th>\n",
       "      <td>Canada</td>\n",
       "      <td>Canada</td>\n",
       "      <td>[0.7046068097086481, 0.2953931902913519]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>127</th>\n",
       "      <td>Canada</td>\n",
       "      <td>Canada</td>\n",
       "      <td>[0.5630169062040135, 0.43698309379598654]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>169</th>\n",
       "      <td>Canada</td>\n",
       "      <td>Canada</td>\n",
       "      <td>[0.8389680973255864, 0.16103190267441364]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>188</th>\n",
       "      <td>Canada</td>\n",
       "      <td>Canada</td>\n",
       "      <td>[0.7964150775404333, 0.20358492245956678]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>187</th>\n",
       "      <td>Canada</td>\n",
       "      <td>Canada</td>\n",
       "      <td>[0.9010806652340972, 0.0989193347659027]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>192</th>\n",
       "      <td>Canada</td>\n",
       "      <td>Canada</td>\n",
       "      <td>[0.7753006388010791, 0.2246993611989209]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>62</th>\n",
       "      <td>USA</td>\n",
       "      <td>USA</td>\n",
       "      <td>[0.030740704606528002, 0.969259295393472]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>141</th>\n",
       "      <td>Canada</td>\n",
       "      <td>Canada</td>\n",
       "      <td>[0.6880304799160921, 0.3119695200839079]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>183</th>\n",
       "      <td>Canada</td>\n",
       "      <td>Canada</td>\n",
       "      <td>[0.7891358587234145, 0.21086414127658554]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>USA</td>\n",
       "      <td>USA</td>\n",
       "      <td>[0.006546969753885579, 0.9934530302461144]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50</th>\n",
       "      <td>USA</td>\n",
       "      <td>USA</td>\n",
       "      <td>[0.2787419584843098, 0.7212580415156902]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>89</th>\n",
       "      <td>Canada</td>\n",
       "      <td>Canada</td>\n",
       "      <td>[0.8388877146644937, 0.1611122853355063]</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          y   y_hat                               probabilities\n",
       "160  Canada  Canada    [0.7046068097086481, 0.2953931902913519]\n",
       "127  Canada  Canada   [0.5630169062040135, 0.43698309379598654]\n",
       "169  Canada  Canada   [0.8389680973255864, 0.16103190267441364]\n",
       "188  Canada  Canada   [0.7964150775404333, 0.20358492245956678]\n",
       "187  Canada  Canada    [0.9010806652340972, 0.0989193347659027]\n",
       "192  Canada  Canada    [0.7753006388010791, 0.2246993611989209]\n",
       "62      USA     USA   [0.030740704606528002, 0.969259295393472]\n",
       "141  Canada  Canada    [0.6880304799160921, 0.3119695200839079]\n",
       "183  Canada  Canada   [0.7891358587234145, 0.21086414127658554]\n",
       "37      USA     USA  [0.006546969753885579, 0.9934530302461144]\n",
       "50      USA     USA    [0.2787419584843098, 0.7212580415156902]\n",
       "89   Canada  Canada    [0.8388877146644937, 0.1611122853355063]"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(data_dict)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "The actual `y` and `y_hat` match in most of the cases but in some cases the model is more confident about the prediction than others. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Least confident cases \n",
    "\n",
    "Let's examine some cases where the model is least confident about the prediction. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>longitude</th>\n",
       "      <th>latitude</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>127</th>\n",
       "      <td>-81.2496</td>\n",
       "      <td>42.9837</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>141</th>\n",
       "      <td>-79.6902</td>\n",
       "      <td>44.3893</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     longitude  latitude\n",
       "127   -81.2496   42.9837\n",
       "141   -79.6902   44.3893"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "least_confident_X = X_train.loc[[127, 141]]\n",
    "least_confident_X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "127    Canada\n",
       "141    Canada\n",
       "Name: country, dtype: object"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "least_confident_y = y_train.loc[[127, 141]]\n",
    "least_confident_y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>y</th>\n",
       "      <th>y_hat</th>\n",
       "      <th>probability score (Canada)</th>\n",
       "      <th>probability score (USA)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>127</th>\n",
       "      <td>Canada</td>\n",
       "      <td>Canada</td>\n",
       "      <td>0.563017</td>\n",
       "      <td>0.436983</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>141</th>\n",
       "      <td>Canada</td>\n",
       "      <td>Canada</td>\n",
       "      <td>0.688030</td>\n",
       "      <td>0.311970</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          y   y_hat  probability score (Canada)  probability score (USA)\n",
       "127  Canada  Canada                    0.563017                 0.436983\n",
       "141  Canada  Canada                    0.688030                 0.311970"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "probs = lr.predict_proba(least_confident_X)\n",
    "\n",
    "data_dict = {\n",
    "    \"y\": least_confident_y,\n",
    "    \"y_hat\": lr.predict(least_confident_X).tolist(),\n",
    "    \"probability score (Canada)\": probs[:, 0],\n",
    "    \"probability score (USA)\": probs[:, 1],\n",
    "}\n",
    "pd.DataFrame(data_dict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/gtoti/opt/anaconda3/envs/cpsc330/lib/python3.9/site-packages/sklearn/base.py:450: UserWarning: X does not have valid feature names, but LogisticRegression was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mglearn.discrete_scatter(\n",
    "    least_confident_X.iloc[:, 0],\n",
    "    least_confident_X.iloc[:, 1],\n",
    "    least_confident_y,\n",
    "    markers=\"o\",\n",
    ")\n",
    "mglearn.plots.plot_2d_separator(lr, X_train.to_numpy(), fill=True, eps=0.5, alpha=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The points are close to the decision boundary which makes sense. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Most confident cases \n",
    "\n",
    "Let's examine some cases where the model is most confident about the prediction. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>longitude</th>\n",
       "      <th>latitude</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>-98.4951</td>\n",
       "      <td>29.4246</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>165</th>\n",
       "      <td>-52.7151</td>\n",
       "      <td>47.5617</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     longitude  latitude\n",
       "37    -98.4951   29.4246\n",
       "165   -52.7151   47.5617"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "most_confident_X = X_train.loc[[37, 165]]\n",
    "most_confident_X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "37        USA\n",
       "165    Canada\n",
       "Name: country, dtype: object"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "most_confident_y = y_train.loc[[37, 165]]\n",
    "most_confident_y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>y</th>\n",
       "      <th>y_hat</th>\n",
       "      <th>probability score (Canada)</th>\n",
       "      <th>probability score (USA)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>USA</td>\n",
       "      <td>USA</td>\n",
       "      <td>0.006547</td>\n",
       "      <td>0.993453</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>165</th>\n",
       "      <td>Canada</td>\n",
       "      <td>Canada</td>\n",
       "      <td>0.951092</td>\n",
       "      <td>0.048908</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          y   y_hat  probability score (Canada)  probability score (USA)\n",
       "37      USA     USA                    0.006547                 0.993453\n",
       "165  Canada  Canada                    0.951092                 0.048908"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "probs = lr.predict_proba(most_confident_X)\n",
    "\n",
    "data_dict = {\n",
    "    \"y\": most_confident_y,\n",
    "    \"y_hat\": lr.predict(most_confident_X).tolist(),\n",
    "    \"probability score (Canada)\": probs[:, 0],\n",
    "    \"probability score (USA)\": probs[:, 1],\n",
    "}\n",
    "pd.DataFrame(data_dict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>longitude</th>\n",
       "      <th>latitude</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>-98.4951</td>\n",
       "      <td>29.4246</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>165</th>\n",
       "      <td>-52.7151</td>\n",
       "      <td>47.5617</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     longitude  latitude\n",
       "37    -98.4951   29.4246\n",
       "165   -52.7151   47.5617"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "most_confident_X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/gtoti/opt/anaconda3/envs/cpsc330/lib/python3.9/site-packages/sklearn/base.py:450: UserWarning: X does not have valid feature names, but LogisticRegression was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mglearn.discrete_scatter(\n",
    "    most_confident_X.iloc[:, 0],\n",
    "    most_confident_X.iloc[:, 1],\n",
    "    most_confident_y,\n",
    "    markers=\"o\",\n",
    ")\n",
    "mglearn.plots.plot_2d_separator(lr, X_train.to_numpy(), fill=True, eps=0.5, alpha=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The points are far away from the decision boundary which makes sense. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Over confident cases\n",
    "\n",
    "Let's examine some cases where the model is confident about the prediction but the prediction is wrong. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>longitude</th>\n",
       "      <th>latitude</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-130.0437</td>\n",
       "      <td>55.9773</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-134.4197</td>\n",
       "      <td>58.3019</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   longitude  latitude\n",
       "0  -130.0437   55.9773\n",
       "1  -134.4197   58.3019"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "over_confident_X = X_train.loc[[0, 1]]\n",
    "over_confident_X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    USA\n",
       "1    USA\n",
       "Name: country, dtype: object"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "over_confident_y = y_train.loc[[0, 1]]\n",
    "over_confident_y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>y</th>\n",
       "      <th>y_hat</th>\n",
       "      <th>probability score (Canada)</th>\n",
       "      <th>probability score (USA)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>USA</td>\n",
       "      <td>Canada</td>\n",
       "      <td>0.932487</td>\n",
       "      <td>0.067513</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>USA</td>\n",
       "      <td>Canada</td>\n",
       "      <td>0.961902</td>\n",
       "      <td>0.038098</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     y   y_hat  probability score (Canada)  probability score (USA)\n",
       "0  USA  Canada                    0.932487                 0.067513\n",
       "1  USA  Canada                    0.961902                 0.038098"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "probs = lr.predict_proba(over_confident_X)\n",
    "\n",
    "data_dict = {\n",
    "    \"y\": over_confident_y,\n",
    "    \"y_hat\": lr.predict(over_confident_X).tolist(),\n",
    "    \"probability score (Canada)\": probs[:, 0],\n",
    "    \"probability score (USA)\": probs[:, 1],\n",
    "}\n",
    "pd.DataFrame(data_dict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/gtoti/opt/anaconda3/envs/cpsc330/lib/python3.9/site-packages/sklearn/base.py:450: UserWarning: X does not have valid feature names, but LogisticRegression was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mglearn.discrete_scatter(\n",
    "    over_confident_X.iloc[:, 0],\n",
    "    over_confident_X.iloc[:, 1],\n",
    "    over_confident_y,\n",
    "    markers=\"o\",\n",
    ")\n",
    "mglearn.plots.plot_2d_separator(lr, X_train.to_numpy(), fill=True, eps=0.5, alpha=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- The cities are far away from the decision boundary. So the model is pretty confident about the prediction. \n",
    "- But the cities are likely to be from Alaska and our linear model is not able to capture that this part belong to the USA and not Canada."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Below we are using colour to represent prediction probabilities. If you are closer to the border, the model is less confident whereas the model is more confident about the mainland cities, which makes sense.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/gtoti/opt/anaconda3/envs/cpsc330/lib/python3.9/site-packages/sklearn/base.py:450: UserWarning: X does not have valid feature names, but LogisticRegression was fitted with feature names\n",
      "  warnings.warn(\n",
      "/Users/gtoti/opt/anaconda3/envs/cpsc330/lib/python3.9/site-packages/sklearn/base.py:450: UserWarning: X does not have valid feature names, but LogisticRegression was fitted with feature names\n",
      "  warnings.warn(\n",
      "/Users/gtoti/opt/anaconda3/envs/cpsc330/lib/python3.9/site-packages/sklearn/base.py:450: UserWarning: X does not have valid feature names, but LogisticRegression was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 2, figsize=(18, 5))\n",
    "from matplotlib.colors import ListedColormap\n",
    "\n",
    "for ax in axes:\n",
    "    mglearn.discrete_scatter(\n",
    "        X_train.iloc[:, 0], X_train.iloc[:, 1], y_train, markers=\"o\", ax=ax\n",
    "    )\n",
    "    ax.set_xlabel(\"longitude\")\n",
    "    ax.set_ylabel(\"latitude\")\n",
    "\n",
    "axes[0].legend([\"Train class 0\", \"Train class 1\"], ncol=2, loc=(0.1, 1.1))\n",
    "\n",
    "mglearn.plots.plot_2d_separator(\n",
    "    lr, X_train.to_numpy(), fill=True, eps=0.5, ax=axes[0], alpha=0.5\n",
    ")\n",
    "mglearn.plots.plot_2d_separator(\n",
    "    lr, X_train.to_numpy(), fill=False, eps=0.5, ax=axes[1], alpha=0.5\n",
    ")\n",
    "scores_image = mglearn.tools.plot_2d_scores(\n",
    "    lr, X_train.to_numpy(), eps=0.5, ax=axes[1], alpha=0.5, cm=plt.cm.coolwarm\n",
    ")\n",
    "cbar = plt.colorbar(scores_image, ax=axes.tolist())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Sometimes a complex model that is overfitted, tends to make more confident predictions, even if they are wrong, whereas a simpler model tends to make predictions with more uncertainty. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "To summarize, \n",
    "- With hard predictions, we only know the class. \n",
    "- With probability scores we know how confident the model is with certain predictions, which can be useful in understanding the model better. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### ❓❓ Questions for you"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### True/False (for practice)\n",
    "\n",
    "- Increasing logistic regression's `C` hyperparameter increases model complexity.\n",
    "- Unlike with `Ridge` regression, coefficients are not interpretable with logistic regression.\n",
    "- The raw output score can be used to calculate the probability score for a given prediction. \n",
    "- For linear classifier trained on $d$ features, the decision boundary is a $d-1$-dimensional hyperparlane.  \n",
    "- A linear model is likely to be uncertain about the data points close to the decision boundary. \n",
    "- Similar to decision trees, conceptually logistic regression should be able to work with categorical features.\n",
    "- Scaling might be a good idea in the context of logistic regression. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Zoom poll\n",
    "\n",
    "1. The intercept of a linear model has a meaning similar to the model's coefficients (T/F)\n",
    "2. The snake weight linear model was trained on snakes between 0 and 200 cm of length. Should we try predicting the weight of a 250 cm long snake?\n",
    "3. A positive coefficient indicates positive correlation between the feature and the target (T/F)\n",
    "4. RIDGE regression helps controlling the model complexity by limiting the number of non-zero coefficients in the model (T/F)\n",
    "5. Logistic regression only accepts binary inputs (T/F)\n",
    "6. Changing the order of the classes in logistic regression will not affect the coefficients (T/F)\n",
    "7. A larger coefficient indicates a stronger correlation (T/F)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Linear SVM \n",
    "\n",
    "- We have seen non-linear SVM with RBF kernel before. This is the default SVC model in `sklearn` because it tends to work better in many cases. \n",
    "- There is also a linear SVM. You can pass `kernel=\"linear\"` to create a linear SVM. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "cities_df = pd.read_csv(\"data/canada_usa_cities.csv\")\n",
    "train_df, test_df = train_test_split(cities_df, test_size=0.2, random_state=123)\n",
    "X_train, y_train = train_df.drop(columns=[\"country\"], axis=1), train_df[\"country\"]\n",
    "X_test, y_test = test_df.drop(columns=[\"country\"], axis=1), test_df[\"country\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/gtoti/opt/anaconda3/envs/cpsc330/lib/python3.9/site-packages/sklearn/base.py:450: UserWarning: X does not have valid feature names, but SVC was fitted with feature names\n",
      "  warnings.warn(\n",
      "/Users/gtoti/opt/anaconda3/envs/cpsc330/lib/python3.9/site-packages/sklearn/base.py:450: UserWarning: X does not have valid feature names, but SVC was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 2, figsize=(18, 5))\n",
    "from matplotlib.colors import ListedColormap\n",
    "\n",
    "for (model, ax) in zip([SVC(gamma=0.01), SVC(kernel=\"linear\")], axes):\n",
    "    mglearn.discrete_scatter(\n",
    "        X_train.iloc[:, 0], X_train.iloc[:, 1], y_train, markers=\"o\", ax=ax\n",
    "    )\n",
    "    model.fit(X_train, y_train)\n",
    "    ax.set_xlabel(\"longitude\")\n",
    "    ax.set_ylabel(\"latitude\")\n",
    "    mglearn.plots.plot_2d_separator(\n",
    "        model, X_train.to_numpy(), fill=True, eps=0.5, ax=ax, alpha=0.5\n",
    "    )\n",
    "\n",
    "axes[0].set_title(\"SVM RBF\")\n",
    "axes[1].set_title(\"Linear SVM\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- `predict` method of linear SVM and logistic regression works the same way. \n",
    "- We can get `coef_` associated with the features and `intercept_` using a Linear SVM model. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model weights: [[-0.0195598  -0.23640124]]\n",
      "Model intercept: [8.22811601]\n"
     ]
    }
   ],
   "source": [
    "linear_svc = SVC(kernel=\"linear\")\n",
    "linear_svc.fit(X_train, y_train)\n",
    "print(\"Model weights: %s\" % (linear_svc.coef_))\n",
    "print(\"Model intercept: %s\" % (linear_svc.intercept_))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model weights: [[-0.04108149 -0.33683126]]\n",
      "Model intercept: [10.8869838]\n"
     ]
    }
   ],
   "source": [
    "lr = LogisticRegression()\n",
    "lr.fit(X_train, y_train)\n",
    "print(\"Model weights: %s\" % (lr.coef_))\n",
    "print(\"Model intercept: %s\" % (lr.intercept_))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Note that the coefficients and intercept are slightly different for logistic regression. \n",
    "- This is because the `fit` for linear SVM and logistic regression are different. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br><br><br><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Model interpretation of linear classifiers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- One of the primary advantage of linear classifiers is their ability to interpret models. \n",
    "- For example, with the sign and magnitude of learned coefficients we could answer questions such as which features are driving the prediction to which direction. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- We'll demonstrate this by training `LogisticRegression` on the famous [IMDB movie review](https://www.kaggle.com/lakshmi25npathi/imdb-dataset-of-50k-movie-reviews) dataset. The dataset is a bit large for demonstration purposes. So I am going to put a big portion of it in the test split to speed things up. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>review</th>\n",
       "      <th>label</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Once again Mr. Costner has dragged out a movie for far longer than necessary. Aside from the terrific sea rescue sequences, of which there are very few I just did not care about any of the charact...</td>\n",
       "      <td>neg</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>This is an example of why the majority of action films are the same. Generic and boring, there's really nothing worth watching here. A complete waste of the then barely-tapped talents of Ice-T and...</td>\n",
       "      <td>neg</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>First of all I hate those moronic rappers, who could'nt act if they had a gun pressed against their foreheads. All they do is curse and shoot each other and acting like clichÃ©'e version of gangst...</td>\n",
       "      <td>neg</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Not even the Beatles could write songs everyone liked, and although Walter Hill is no mop-top he's second to none when it comes to thought provoking action movies. The nineties came and social pla...</td>\n",
       "      <td>neg</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Brass pictures (movies is not a fitting word for them) really are somewhat brassy. Their alluring visual qualities are reminiscent of expensive high class TV commercials. But unfortunately Brass p...</td>\n",
       "      <td>neg</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                                                                                                                                                                    review  \\\n",
       "0  Once again Mr. Costner has dragged out a movie for far longer than necessary. Aside from the terrific sea rescue sequences, of which there are very few I just did not care about any of the charact...   \n",
       "1  This is an example of why the majority of action films are the same. Generic and boring, there's really nothing worth watching here. A complete waste of the then barely-tapped talents of Ice-T and...   \n",
       "2  First of all I hate those moronic rappers, who could'nt act if they had a gun pressed against their foreheads. All they do is curse and shoot each other and acting like clichÃ©'e version of gangst...   \n",
       "3  Not even the Beatles could write songs everyone liked, and although Walter Hill is no mop-top he's second to none when it comes to thought provoking action movies. The nineties came and social pla...   \n",
       "4  Brass pictures (movies is not a fitting word for them) really are somewhat brassy. Their alluring visual qualities are reminiscent of expensive high class TV commercials. But unfortunately Brass p...   \n",
       "\n",
       "  label  \n",
       "0   neg  \n",
       "1   neg  \n",
       "2   neg  \n",
       "3   neg  \n",
       "4   neg  "
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "imdb_df = pd.read_csv(\"data/imdb_master.csv\", encoding=\"ISO-8859-1\")\n",
    "imdb_df = imdb_df[imdb_df[\"label\"].str.startswith((\"pos\", \"neg\"))]\n",
    "imdb_df.drop([\"Unnamed: 0\", \"type\", \"file\"], axis=1, inplace=True)\n",
    "imdb_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let's clean up the data a bit. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "import re\n",
    "\n",
    "\n",
    "def replace_tags(doc):\n",
    "    doc = doc.replace(\"<br />\", \" \")\n",
    "    doc = re.sub(\"https://\\S*\", \"\", doc)\n",
    "    return doc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "imdb_df[\"review_pp\"] = imdb_df[\"review\"].apply(replace_tags)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Are we breaking the Golden rule here? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let's split the data and create bag of words representation. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5000, 3)"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_df, test_df = train_test_split(imdb_df, test_size=0.9, random_state=123)\n",
    "X_train, y_train = train_df[\"review_pp\"], train_df[\"label\"]\n",
    "X_test, y_test = test_df[\"review_pp\"], test_df[\"label\"]\n",
    "train_df.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<5000x10000 sparse matrix of type '<class 'numpy.int64'>'\n",
       "\twith 383702 stored elements in Compressed Sparse Row format>"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vec = CountVectorizer(stop_words=\"english\", max_features=10000)\n",
    "bow = vec.fit_transform(X_train)\n",
    "bow"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Examining the vocabulary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- The vocabulary (mapping from feature indices to actual words) can be obtained using `get_feature_names()` on the `CountVectorizer` object. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "vocab = vec.get_feature_names_out()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['00', '000', '01', '10', '100', '1000', '101', '11', '12', '13'],\n",
       "      dtype=object)"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vocab[0:10]  # first few words"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['conrad', 'cons', 'conscience', 'conscious', 'consciously',\n",
       "       'consciousness', 'consequence', 'consequences', 'conservative',\n",
       "       'conservatory'], dtype=object)"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vocab[2000:2010]  # some middle words"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['00', 'announcement', 'bird', 'cell', 'conrad', 'depth', 'elite',\n",
       "       'finnish', 'grimy', 'illusions', 'kerr', 'maltin', 'narrates',\n",
       "       'patients', 'publicity', 'reynolds', 'sfx', 'starting', 'thats',\n",
       "       'vance'], dtype=object)"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vocab[::500]  # words with a step of 500"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Model building on the dataset "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "First let's try `DummyClassifier` on the dataset. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>fit_time</th>\n",
       "      <th>score_time</th>\n",
       "      <th>test_score</th>\n",
       "      <th>train_score</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.001969</td>\n",
       "      <td>0.001606</td>\n",
       "      <td>0.505</td>\n",
       "      <td>0.505</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.001631</td>\n",
       "      <td>0.001257</td>\n",
       "      <td>0.505</td>\n",
       "      <td>0.505</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.001744</td>\n",
       "      <td>0.001285</td>\n",
       "      <td>0.505</td>\n",
       "      <td>0.505</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.001428</td>\n",
       "      <td>0.001229</td>\n",
       "      <td>0.505</td>\n",
       "      <td>0.505</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.001473</td>\n",
       "      <td>0.001143</td>\n",
       "      <td>0.505</td>\n",
       "      <td>0.505</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   fit_time  score_time  test_score  train_score\n",
       "0  0.001969    0.001606       0.505        0.505\n",
       "1  0.001631    0.001257       0.505        0.505\n",
       "2  0.001744    0.001285       0.505        0.505\n",
       "3  0.001428    0.001229       0.505        0.505\n",
       "4  0.001473    0.001143       0.505        0.505"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dummy = DummyClassifier()\n",
    "scores = cross_validate(dummy, X_train, y_train, return_train_score=True)\n",
    "pd.DataFrame(scores)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have a balanced dataset. So the `DummyClassifier` score is around 0.5. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Now let's try logistic regression. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>fit_time</th>\n",
       "      <th>score_time</th>\n",
       "      <th>test_score</th>\n",
       "      <th>train_score</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.583542</td>\n",
       "      <td>0.122627</td>\n",
       "      <td>0.847</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.661934</td>\n",
       "      <td>0.124442</td>\n",
       "      <td>0.832</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.588559</td>\n",
       "      <td>0.122931</td>\n",
       "      <td>0.842</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.575748</td>\n",
       "      <td>0.124213</td>\n",
       "      <td>0.853</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.595037</td>\n",
       "      <td>0.121719</td>\n",
       "      <td>0.839</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   fit_time  score_time  test_score  train_score\n",
       "0  0.583542    0.122627       0.847          1.0\n",
       "1  0.661934    0.124442       0.832          1.0\n",
       "2  0.588559    0.122931       0.842          1.0\n",
       "3  0.575748    0.124213       0.853          1.0\n",
       "4  0.595037    0.121719       0.839          1.0"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pipe_lr = make_pipeline(\n",
    "    CountVectorizer(stop_words=\"english\", max_features=10000),\n",
    "    LogisticRegression(max_iter=1000),\n",
    ")\n",
    "scores = cross_validate(pipe_lr, X_train, y_train, return_train_score=True)\n",
    "pd.DataFrame(scores)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Seems like we are overfitting. Let's optimize the hyperparameter `C`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>C</th>\n",
       "      <th>mean_train_scores</th>\n",
       "      <th>mean_cv_scores</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.001</td>\n",
       "      <td>0.83470</td>\n",
       "      <td>0.7964</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.010</td>\n",
       "      <td>0.92265</td>\n",
       "      <td>0.8456</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.100</td>\n",
       "      <td>0.98585</td>\n",
       "      <td>0.8520</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.000</td>\n",
       "      <td>1.00000</td>\n",
       "      <td>0.8426</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>10.000</td>\n",
       "      <td>1.00000</td>\n",
       "      <td>0.8376</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>100.000</td>\n",
       "      <td>1.00000</td>\n",
       "      <td>0.8350</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         C  mean_train_scores  mean_cv_scores\n",
       "0    0.001            0.83470          0.7964\n",
       "1    0.010            0.92265          0.8456\n",
       "2    0.100            0.98585          0.8520\n",
       "3    1.000            1.00000          0.8426\n",
       "4   10.000            1.00000          0.8376\n",
       "5  100.000            1.00000          0.8350"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scores_dict = {\n",
    "    \"C\": 10.0 ** np.arange(-3, 3, 1),\n",
    "    \"mean_train_scores\": list(),\n",
    "    \"mean_cv_scores\": list(),\n",
    "}\n",
    "for C in scores_dict[\"C\"]:\n",
    "    pipe_lr = make_pipeline(\n",
    "        CountVectorizer(stop_words=\"english\", max_features=10000),\n",
    "        LogisticRegression(max_iter=1000, C=C),\n",
    "    )\n",
    "    scores = cross_validate(pipe_lr, X_train, y_train, return_train_score=True)\n",
    "    scores_dict[\"mean_train_scores\"].append(scores[\"train_score\"].mean())\n",
    "    scores_dict[\"mean_cv_scores\"].append(scores[\"test_score\"].mean())\n",
    "\n",
    "results_df = pd.DataFrame(scores_dict)\n",
    "results_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The maximum validation score is 0.852 at C = 0.10 \n"
     ]
    }
   ],
   "source": [
    "optimized_C = results_df[\"C\"].iloc[np.argmax(results_df[\"mean_cv_scores\"])]\n",
    "print(\n",
    "    \"The maximum validation score is %0.3f at C = %0.2f \"\n",
    "    % (\n",
    "        np.max(results_df[\"mean_cv_scores\"]),\n",
    "        optimized_C,\n",
    "    )\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let's train a model on the full training set with the optimized hyperparameter values. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(steps=[('countvectorizer',\n",
       "                 CountVectorizer(max_features=10000, stop_words='english')),\n",
       "                ('logisticregression',\n",
       "                 LogisticRegression(C=0.1, max_iter=1000))])"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pipe_lr = make_pipeline(\n",
    "    CountVectorizer(stop_words=\"english\", max_features=10000),\n",
    "    LogisticRegression(max_iter=1000, C=optimized_C),\n",
    ")\n",
    "pipe_lr.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Examining learned coefficients "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "- The learned coefficients are exposed by the `coef_` attribute of [LogisticRegression](http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LogisticRegression.html) object. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [],
   "source": [
    "feature_names = np.array(pipe_lr.named_steps[\"countvectorizer\"].get_feature_names_out())\n",
    "coeffs = pipe_lr.named_steps[\"logisticregression\"].coef_.flatten()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Coefficient</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>00</th>\n",
       "      <td>-0.074949</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>000</th>\n",
       "      <td>-0.083893</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>01</th>\n",
       "      <td>-0.034402</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.056493</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>100</th>\n",
       "      <td>0.041633</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>zoom</th>\n",
       "      <td>-0.013299</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>zooms</th>\n",
       "      <td>-0.022139</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>zorak</th>\n",
       "      <td>0.021878</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>zorro</th>\n",
       "      <td>0.130075</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>â½</th>\n",
       "      <td>0.012649</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>10000 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       Coefficient\n",
       "00       -0.074949\n",
       "000      -0.083893\n",
       "01       -0.034402\n",
       "10        0.056493\n",
       "100       0.041633\n",
       "...            ...\n",
       "zoom     -0.013299\n",
       "zooms    -0.022139\n",
       "zorak     0.021878\n",
       "zorro     0.130075\n",
       "â½        0.012649\n",
       "\n",
       "[10000 rows x 1 columns]"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "word_coeff_df = pd.DataFrame(coeffs, index=feature_names, columns=[\"Coefficient\"])\n",
    "word_coeff_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- Let's sort the coefficients in descending order. \n",
    "- Interpretation\n",
    "    - if $w_j > 0$ then increasing $x_{ij}$ moves us toward predicting $+1$. \n",
    "    - if $w_j < 0$ then increasing $x_{ij}$ moves us toward predicting $-1$. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Coefficient</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>excellent</th>\n",
       "      <td>0.903484</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>great</th>\n",
       "      <td>0.659922</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>amazing</th>\n",
       "      <td>0.653301</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>wonderful</th>\n",
       "      <td>0.651763</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>favorite</th>\n",
       "      <td>0.607887</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>terrible</th>\n",
       "      <td>-0.621695</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>boring</th>\n",
       "      <td>-0.701030</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bad</th>\n",
       "      <td>-0.736608</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>waste</th>\n",
       "      <td>-0.799353</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>worst</th>\n",
       "      <td>-0.986970</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>10000 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           Coefficient\n",
       "excellent     0.903484\n",
       "great         0.659922\n",
       "amazing       0.653301\n",
       "wonderful     0.651763\n",
       "favorite      0.607887\n",
       "...                ...\n",
       "terrible     -0.621695\n",
       "boring       -0.701030\n",
       "bad          -0.736608\n",
       "waste        -0.799353\n",
       "worst        -0.986970\n",
       "\n",
       "[10000 rows x 1 columns]"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "word_coeff_df.sort_values(by=\"Coefficient\", ascending=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- The coefficients make sense!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let's visualize the top 10 features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mglearn.tools.visualize_coefficients(coeffs, feature_names, n_top_features=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let's explore prediction of the following new review. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [],
   "source": [
    "fake_review = \"It got a bit boring at times but the direction was excellent and the acting was flawless. Overall I enjoyed the movie and I highly recomment it!\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "feat_vec = pipe_lr.named_steps[\"countvectorizer\"].transform([fake_review])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<1x10000 sparse matrix of type '<class 'numpy.int64'>'\n",
       "\twith 12 stored elements in Compressed Sparse Row format>"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "feat_vec"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let's get prediction probability scores of the fake review. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.1718113, 0.8281887]])"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pipe_lr.predict_proba([fake_review])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model is 82% confident that it's a positive review. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'pos'"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pipe_lr.predict([fake_review])[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "We can find which of the vocabulary words are present in this review:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False, False, False, ..., False, False, False])"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "feat_vec.toarray().ravel().astype(bool)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False, False, False, ..., False, False, False])"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "words_in_ex = feat_vec.toarray().ravel().astype(bool)\n",
    "words_in_ex"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How many of the words are in this review?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(words_in_ex)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['acting', 'bit', 'boring', 'direction', 'enjoyed', 'excellent',\n",
       "       'flawless', 'got', 'highly', 'movie', 'overall', 'times'],\n",
       "      dtype=object)"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array(feature_names)[words_in_ex]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Coefficient</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>acting</th>\n",
       "      <td>-0.126498</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bit</th>\n",
       "      <td>0.390053</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>boring</th>\n",
       "      <td>-0.701030</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>direction</th>\n",
       "      <td>-0.268316</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>enjoyed</th>\n",
       "      <td>0.578879</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>excellent</th>\n",
       "      <td>0.903484</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>flawless</th>\n",
       "      <td>0.113743</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>got</th>\n",
       "      <td>-0.122759</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>highly</th>\n",
       "      <td>0.582012</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>movie</th>\n",
       "      <td>-0.037942</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>overall</th>\n",
       "      <td>0.136288</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>times</th>\n",
       "      <td>0.133895</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           Coefficient\n",
       "acting       -0.126498\n",
       "bit           0.390053\n",
       "boring       -0.701030\n",
       "direction    -0.268316\n",
       "enjoyed       0.578879\n",
       "excellent     0.903484\n",
       "flawless      0.113743\n",
       "got          -0.122759\n",
       "highly        0.582012\n",
       "movie        -0.037942\n",
       "overall       0.136288\n",
       "times         0.133895"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ex_df = pd.DataFrame(\n",
    "    data=coeffs[words_in_ex],\n",
    "    index=np.array(feature_names)[words_in_ex],\n",
    "    columns=[\"Coefficient\"],\n",
    ")\n",
    "ex_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let's visualize how the words with positive and negative coefficients are driving the hard prediction. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mglearn.tools.visualize_coefficients(\n",
    "    coeffs[words_in_ex], np.array(feature_names)[words_in_ex], n_top_features=6\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def plot_coeff_example(feat_vect, coeffs, feature_names):\n",
    "    words_in_ex = feat_vec.toarray().ravel().astype(bool)\n",
    "\n",
    "    ex_df = pd.DataFrame(\n",
    "        data=coeffs[words_in_ex],\n",
    "        index=np.array(feature_names)[words_in_ex],\n",
    "        columns=[\"Coefficient\"],\n",
    "    )\n",
    "    return ex_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Most positive review "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Remember that you can look at the probabilities (confidence) of the classifier's prediction using the `model.predict_proba` method.\n",
    "- Can we find the messages where our classifier is most confident or least confident?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.95205899, 0.83301769, 0.9093526 , ..., 0.89247531, 0.05736279,\n",
       "       0.79360853])"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pos_probs = pipe_lr.predict_proba(X_train)[\n",
    "    :, 1\n",
    "]  # only get probabilities associated with pos class\n",
    "pos_probs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let's get the index of the example where the classifier is most confident (highest `predict_proba` score for positive). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [],
   "source": [
    "most_positive = np.argmax(pos_probs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Moving beyond words is this heart breaking story of a divorce which results in a tragic custody battle over a seven year old boy.  One of \"Kramer v. Kramer\\'s\" great strengths is its screenwriter director Robert Benton, who has marvellously adapted Avery Corman\\'s novel to the big screen. He keeps things beautifully simple and most realistic, while delivering all the drama straight from the heart. His talent for telling emotional tales like this was to prove itself again with \"Places in the Heart\", where he showed, as in \"Kramer v. Kramer\", that he has a natural ability for working with children.  The picture\\'s other strong point is the splendid acting which deservedly received four of the film\\'s nine Academy Award nominations, two of them walking away winners. One of those was Dustin Hoffman (Best Actor), who is superb as frustrated business man Ted Kramer, a man who has forgotten that his wife is a person. As said wife Joanne, Meryl Streep claimed the supporting actress Oscar for a strong, sensitive portrayal of a woman who had lost herself in eight years of marriage. Also nominated was Jane Alexander for her fantastic turn as the Kramer\\'s good friend Margaret. Final word in the acting stakes must go to young Justin Henry, whose incredibly moving performance will find you choking back tears again and again, and a thoroughly deserved Oscar nomination came his way.  Brilliant also is Nestor Almendros\\' cinematography and Jerry Greenberg\\'s timely editing, while musically Henry Purcell\\'s classical piece is used to effect.  Truly this is a touching story of how a father and son come to depend on each other when their wife and mother leaves. They grow together, come to know each other and form an entirely new and wonderful relationship. Ted finds himself with new responsibilities and a new outlook on life, and slowly comes to realise why Joanne had to go.  Certainly if nothing else, \"Kramer v. Kramer\" demonstrates that nobody wins when it comes to a custody battle over a young child, especially not the child himself.  Saturday, June 10, 1995 - T.V.  Strong drama from Avery Corman\\'s novel about the heartache of a custody battle between estranged parents who both feel they have the child\\'s best interests at heart. Aside from a superb screenplay and amazingly controlled direction, both from Robert Benton, it\\'s the superlative cast that make this picture such a winner.  Hoffman is brilliant as Ted Kramer, the man torn between his toppling career and the son whom he desperately wants to keep. Excellent too is Streep as the woman lost in eight years of marriage who had to get out before she faded to nothing as a person. In support of these two is a very strong Jane Alexander as mutual friend Margaret, an outstanding Justin Henry as the boy caught in the middle, and a top cast of extras.  This highly emotional, heart rending drama more than deserved it\\'s 1979 Academy Awards for best film, best actor (Hoffman) and best supporting actress (Streep).  Wednesday, February 28, 1996 - T.V.'"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train.iloc[most_positive]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True target: pos\n",
      "\n",
      "Predicted target: pos\n",
      "\n",
      "Prediction probability: 1.0000\n"
     ]
    }
   ],
   "source": [
    "print(\"True target: %s\\n\" % (y_train.iloc[most_positive]))\n",
    "print(\"Predicted target: %s\\n\" % (pipe_lr.predict(X_train.iloc[[most_positive]])[0]))\n",
    "print(\"Prediction probability: %0.4f\" % (pos_probs[most_positive]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let's examine the features associated with the review. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "feat_vec = pipe_lr.named_steps[\"countvectorizer\"].transform(\n",
    "    X_train.iloc[[most_positive]]\n",
    ")\n",
    "words_in_ex = feat_vec.toarray().ravel().astype(bool)\n",
    "mglearn.tools.visualize_coefficients(\n",
    "    coeffs[words_in_ex], np.array(feature_names)[words_in_ex], n_top_features=20\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The review has both positive and negative words but the words with **positive** coefficients win in this case! "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Most negative review "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.04794101, 0.16698231, 0.0906474 , ..., 0.10752469, 0.94263721,\n",
       "       0.20639147])"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "neg_probs = pipe_lr.predict_proba(X_train)[\n",
    "    :, 0\n",
    "]  # only get probabilities associated with pos class\n",
    "neg_probs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [],
   "source": [
    "most_negative = np.argmax(neg_probs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Review: 36555    I made the big mistake of actually watching this whole movie a few nights ago. God I'm still trying to recover. This movie does not even deserve a 1.4 average. IMDb needs to have 0 vote ratings po...\n",
      "Name: review_pp, dtype: object\n",
      "\n",
      "True target: neg\n",
      "\n",
      "Predicted target: neg\n",
      "\n",
      "Prediction probability: 0.0000\n"
     ]
    }
   ],
   "source": [
    "print(\"Review: %s\\n\" % (X_train.iloc[[most_negative]]))\n",
    "print(\"True target: %s\\n\" % (y_train.iloc[most_negative]))\n",
    "print(\"Predicted target: %s\\n\" % (pipe_lr.predict(X_train.iloc[[most_negative]])[0]))\n",
    "print(\"Prediction probability: %0.4f\" % (pos_probs[most_negative]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "feat_vec = pipe_lr.named_steps[\"countvectorizer\"].transform(\n",
    "    X_train.iloc[[most_negative]]\n",
    ")\n",
    "words_in_ex = feat_vec.toarray().ravel().astype(bool)\n",
    "mglearn.tools.visualize_coefficients(\n",
    "    coeffs[words_in_ex], np.array(feature_names)[words_in_ex], n_top_features=20\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The review has both positive and negative words but the words with negative coefficients win in this case! "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### ❓❓ Questions for you"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "#### Question for you to ponder on \n",
    "\n",
    "- Is it possible to identify most important features using $k$-NNs? What about decision trees?  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "<br><br><br><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Summary of linear models \n",
    "\n",
    "- Linear regression is a linear model for regression whereas logistic regression is a linear model for classification. \n",
    "- Both these models learn one coefficient per feature, plus an intercept. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "### Main hyperparameters \n",
    "- The main hyperparameter is the \"regularization\" hyperparameter controlling the fundamental tradeoff. \n",
    "    - Logistic Regression: `C`\n",
    "    - Linear SVM: `C` \n",
    "    - Ridge: `alpha`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Interpretation of coefficients in linear models \n",
    "- the $j$th coefficient tells us how feature $j$ affects the prediction\n",
    "- if $w_j > 0$ then increasing $x_{ij}$ moves us toward predicting $+1$\n",
    "- if $w_j < 0$ then increasing $x_{ij}$ moves us toward prediction $-1$\n",
    "- if $w_j == 0$ then the feature is not used in making a prediction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Strengths of linear models \n",
    "\n",
    "- Fast to train and predict\n",
    "- Scale to large datasets and work well with sparse data \n",
    "- Relatively easy to understand and interpret the predictions\n",
    "- Perform well when there is a large number of features "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Limitations of linear models \n",
    "\n",
    "- Is your data \"linearly separable\"? Can you draw a hyperplane between these datapoints that separates them with 0 error. \n",
    "    - If the training examples can be separated by a linear decision rule, they are **linearly separable**.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "A few questions you might be thinking about\n",
    "- How often the real-life data is linearly separable?\n",
    "- Is the following XOR function linearly separable?  \n",
    "\n",
    "| $$x_1$$ | $$x_2$$ | target|\n",
    "|---------|---------|---------|\n",
    "| 0 | 0  | 0|\n",
    "| 0 | 1  | 1|\n",
    "| 1 | 0  | 1|\n",
    "| 1 | 1  | 0|    \n",
    "\n",
    "- Are linear classifiers very limiting because of this?     "
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