Week2_권지수_예습과제.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3. 분류\n",
    "## 3.1 MNIST"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['data', 'target', 'frame', 'categories', 'feature_names', 'target_names', 'DESCR', 'details', 'url'])"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import fetch_openml\n",
    "mnist = fetch_openml('mnist_784', version=1)\n",
    "mnist.keys()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "배열 탐색"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, y = mnist['data'], mnist['target']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(70000, 784)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(70000,)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "이미지가 28x28 pixel이고 특성은 0~255의 픽셀 강도를 나타냄  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**이미지 확인**  \n",
    "특성 벡터를 추출하여 28x28 배열로 크기를 바꾸고, 맷플롯립의 imshow()로 그려봄"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "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": [
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "some_digit = X[0]\n",
    "some_digit_image = some_digit.reshape(28, 28)\n",
    "\n",
    "plt.imshow(some_digit_image, cmap='binary')\n",
    "plt.axis('off')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'5'"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "레이블이 문자로 정의되어있기 때문에 target(y)을 정수로 변환"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = y.astype(np.uint8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "train, test set split  \n",
    "- mnist 자료는 훈련 세트가 앞 60,000, 테스트 세트가 뒤 60,000로 나뉘어 있음"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = X[:60000], X[60000:], y[:60000], y[60000:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.2 이진 분류기 훈련\n",
    "문제를 단순화하여 5인 것, 5가 아닌 것으로만 분류하는 **이진 분류기**를 만들어보자."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_train_5 = (y_train == 5)\n",
    "y_test_5 = (y_test == 5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`SGDClassifier`를 사용해 **확률적 경사 하강법** 분류기로 시작  \n",
    "SGD는 훈련 샘플을 한 번에 하나씩 독립적으로 처리함(온라인 학습에 잘 쓰임)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SGDClassifier(random_state=42)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import SGDClassifier\n",
    "\n",
    "sgd_clf = SGDClassifier(random_state = 42) #SGD는 훈련하는데 무작위성을 사용하여 random_state 지정\n",
    "sgd_clf.fit(X_train, y_train_5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sgd_clf.predict([some_digit])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.3 성능 측정"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.95035, 0.96035, 0.9604 ])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.model_selection import cross_val_score\n",
    "cross_val_score(sgd_clf, X_train, y_train_5, cv=3, scoring='accuracy')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "모든 이미지를 5가 아니라고 출력하는 더미 분류기와 비교"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.base import BaseEstimator\n",
    "\n",
    "class Never5Classifier(BaseEstimator):\n",
    "    def fit(self, X, y=None):\n",
    "        return self\n",
    "    \n",
    "    def predict(self, X):\n",
    "        return np.zeros((len(X),1), dtype=bool)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.91125, 0.90855, 0.90915])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "never_5_clf = Never5Classifier()\n",
    "cross_val_score(never_5_clf, X_train, y_train_5, cv=3, scoring='accuracy')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**정확도(accuracy)는 특히 불균형한 데이터셋을 다룰 때 분류기의 성능 측정 지표로 선호하지 않음**  \n",
    "위 더미 측정기가 정확도 90대가 나왔음.. 이미지의 10% 정도만 5이기 때문"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.3.2 오차 행렬\n",
    "<img src='https://blog.kakaocdn.net/dn/S1z2M/btqvWpQKfvo/O2gB015AN6589ZBDuTBv71/img.png' width=50%>\n",
    "\n",
    "먼저 실제 타깃과 비교할 수 있도록 예측값을 만들어야 함.(test set는 분류기 작업이 끝난 후 마지막에 사용)  \n",
    "`cross_val_predict()`: 평가 점수를 반환하지 않은 **깨끗한 예측**을 얻을 수 있음"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import cross_val_predict\n",
    "\n",
    "y_train_pred = cross_val_predict(sgd_clf, X_train, y_train_5, cv=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`confusion_matrix(target class, predict class)` 오차 행렬 만들기"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[53892,   687],\n",
       "       [ 1891,  3530]], dtype=int64)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import confusion_matrix\n",
    "confusion_matrix(y_train_5, y_train_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "완벽한 분류기라면 diag matrix가 되어야 할 것!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[54579,     0],\n",
       "       [    0,  5421]], dtype=int64)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#완벽한 분류기\n",
    "y_train_perfect_predictions = y_train_5\n",
    "confusion_matrix(y_train_5, y_train_perfect_predictions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**`정밀도(precison)`**\n",
    "- TP/(TP+FP)\n",
    "- 양성 예측의 정확도\n",
    "- 모델이 True라고 분류한 것 중에서 실제 True인 것의 비율  \n",
    "*TP: 진짜 양성, FP: 거짓 양성*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**`재현율(recall)`**, 민감도, 진짜 양성 비율(TPR)\n",
    "- TP/(TP+FN)\n",
    "- 분류기가 정확하게 감지한 양성 샘플의 비율\n",
    "- 실제 True인 것 중에서 모델이 True라고 예측한 것의 비율"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.3.3 정밀도와 재현율"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8370879772350012"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import precision_score, recall_score\n",
    "precision_score(y_train_5, y_train_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6511713705958311"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "recall_score(y_train_5, y_train_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**F1점수**: 정밀도와 재현율의 조화 평균  \n",
    "`f1_score()` 호출로 사용"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7325171197343846"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import f1_score\n",
    "f1_score(y_train_5, y_train_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "상황에 따라 정밀도와 재현율을 추구하는 것이 달라진다.  \n",
    "아동을 위한 동영상 필터링의 경우 좋은 영상이 걸러지더라도 나쁜 영상이 나오지 않는 것이 중요하므로, <u>안정적인 높은 정밀도를 선호</u>할 것이다.  \n",
    "반면, 좀도둑을 잡는 분류기를 훈련시킨다면 좀도둑을 잡는 것이 중요하므로 <u>재현율을 선호</u>할 것이다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.3.4 정밀도/재현율 트레이드오프\n",
    "\n",
    "- 정밀도나 재현율은 한 쪽을 올리면 한 쪽이 낮아짐\n",
    "- 사이킷런에서는 임곗값을 직접 지정할 수는 없지만 예측에 사용된 점수를 확인할 수 있음\n",
    "- `decision_function()`으로 각 샘플의 점수를 확인하고, 원하는 임곗값을 정해 예측을 만들 수 있음  \n",
    "\n",
    "*cf. predict() 매서드도 decision_funtion()을 사용해 0보다 큰 경우를 양성으로 예측*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2164.22030239])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_scores = sgd_clf.decision_function([some_digit])\n",
    "y_scores"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "threshold = 0\n",
    "y_some_digit_pred = (y_scores > threshold)\n",
    "y_some_digit_pred"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "임곗값 높이기"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "threshold = 8000\n",
    "y_some_digit_pred = (y_scores > threshold)\n",
    "y_some_digit_pred"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "임곗값을 높이면 재현율이 줄어든다는 것을 확인"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "적절한 임곗값을 찾기 위해서는 cross_val_predict()를 사용하여 <u>예측 결과가 아니라 결정 점수를 반환</u>받도록 지정해야 함  \n",
    "`method='decision_function'`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_scores = cross_val_predict(sgd_clf, X_train, y_train_5, cv=3, method='decision_function')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`precision_recall_curve(분류기, 결정 점수)`로 가능한 모든 임곗값에 대해 정밀도와 재현율을 계산할 수 있음"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import precision_recall_curve\n",
    "\n",
    "precisions, recalls, thresholds = precision_recall_curve(y_train_5, y_scores)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "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": [
    "def plot_precision_recall_vs_threshold(precisions, recalls, thresholds):\n",
    "    plt.plot(thresholds, precisions[:-1], 'b--', label='정밀도')\n",
    "    plt.plot(thresholds, recalls[:-1], 'g-', label='재현율')\n",
    "\n",
    "plot_precision_recall_vs_threshold(precisions, recalls, thresholds)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_precision_recall_vs_threshold(precisions, recalls, thresholds):\n",
    "    plt.plot(thresholds, precisions[:-1], \"b--\", label=\"Precision\", linewidth=2)\n",
    "    plt.plot(thresholds, recalls[:-1], \"g-\", label=\"Recall\", linewidth=2)\n",
    "    plt.legend(loc=\"center right\", fontsize=16) # Not shown in the book\n",
    "    plt.xlabel(\"Threshold\", fontsize=16)        # Not shown\n",
    "    plt.grid(True)                              # Not shown\n",
    "    plt.axis([-50000, 50000, 0, 1])             # Not shown\n",
    "\n",
    "\n",
    "\n",
    "recall_90_precision = recalls[np.argmax(precisions >= 0.90)]\n",
    "threshold_90_precision = thresholds[np.argmax(precisions >= 0.90)]\n",
    "\n",
    "\n",
    "plt.figure(figsize=(8, 4))                                                                  # Not shown\n",
    "plot_precision_recall_vs_threshold(precisions, recalls, thresholds)\n",
    "plt.plot([threshold_90_precision, threshold_90_precision], [0., 0.9], \"r:\")                 # Not shown\n",
    "plt.plot([-50000, threshold_90_precision], [0.9, 0.9], \"r:\")                                # Not shown\n",
    "plt.plot([-50000, threshold_90_precision], [recall_90_precision, recall_90_precision], \"r:\")# Not shown\n",
    "plt.plot([threshold_90_precision], [0.9], \"ro\")                                             # Not shown\n",
    "plt.plot([threshold_90_precision], [recall_90_precision], \"ro\")                             # Not shown\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_precision_vs_recall(precisions, recalls):\n",
    "    plt.plot(recalls, precisions, \"b-\", linewidth=2)\n",
    "    plt.xlabel(\"Recall\", fontsize=16)\n",
    "    plt.ylabel(\"Precision\", fontsize=16)\n",
    "    plt.axis([0, 1, 0, 1])\n",
    "    plt.grid(True)\n",
    "\n",
    "plt.figure(figsize=(8, 6))\n",
    "plot_precision_vs_recall(precisions, recalls)\n",
    "plt.plot([recall_90_precision, recall_90_precision], [0., 0.9], \"r:\")\n",
    "plt.plot([0.0, recall_90_precision], [0.9, 0.9], \"r:\")\n",
    "plt.plot([recall_90_precision], [0.9], \"ro\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "좋은 젇밀도/재현율 트레이드오프를 선택하는 다른 방법은 재현율에 대한 정밀도 곡선을 그리는 것"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "최소한 90% 정밀도가 되는 가장 낮은 임곗값을 찾을 수 있음  \n",
    "`np.argmax()`는 최댓값의 첫 번째 인덱스를 반환"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "threshold_90_precision = thresholds[np.argmax(precisions >= 0.90)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "훈련 세트에 대한 예측을 만들기 위해서는 분류기의 predict() 대신 다음 코드를 실행"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_train_pred_90 = (y_scores > threshold_90_precision)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "precision_score(y_train_5, y_train_pred_90)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.47980077476480354"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "recall_score(y_train_5, y_train_pred_90)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.3.5 ROC 곡선\n",
    "\n",
    "- 거짓 양성 비율(FPR)에 대한 진짜 양성 비율(TPR) 곡선\n",
    "- 민감도(재현율)에 대한 1-특이도(TNR, 진짜 음성 비율) 그래프\n",
    "- `roc_curve()`를 사용해 여러 임곗값에서 TPR과 FPR을 계산해야 함"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import roc_curve\n",
    "\n",
    "fpr, tpr, thresholds = roc_curve(y_train_5, y_scores)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_roc_curve(fpr, tpr, label=None):\n",
    "    plt.plot(fpr, tpr, linewidth=2, label=label)\n",
    "    plt.plot([0, 1], [0, 1], 'k--') # 대각 점선\n",
    "    plt.axis([0, 1, 0, 1])                                    # Not shown in the book\n",
    "    plt.xlabel('False Positive Rate (Fall-Out)', fontsize=16) # Not shown\n",
    "    plt.ylabel('True Positive Rate (Recall)', fontsize=16)    # Not shown\n",
    "    plt.grid(True)                                            # Not shown\n",
    "\n",
    "plt.figure(figsize=(8, 6))                                    # Not shown\n",
    "plot_roc_curve(fpr, tpr)\n",
    "fpr_90 = fpr[np.argmax(tpr >= recall_90_precision)]           # Not shown\n",
    "plt.plot([fpr_90, fpr_90], [0., recall_90_precision], \"r:\")   # Not shown\n",
    "plt.plot([0.0, fpr_90], [recall_90_precision, recall_90_precision], \"r:\")  # Not shown\n",
    "plt.plot([fpr_90], [recall_90_precision], \"ro\")               # Not shown\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "재현율(TPR)이 높을수록 거짓 양성(FPR)이 높은 트레이드오프  \n",
    "점선은 완전 랜덤 분류기의 ROC 곡선을 뜻하며, 좋은 분류기는 점선에서 최대한 멀리 떨어져있어야 함"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**AUC**(곡선 아래의 면적)을 측정하여 분류기들을 비교할 수 있음  \n",
    "완벽한 분류기는 1, 완전 랜덤 분류기는 0.5  \n",
    "`roc_auc_score`로 auc를 계산"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9604938554008616"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import roc_auc_score\n",
    "roc_auc_score(y_train_5, y_scores)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**? ROC 곡선과 PR(정밀도/재현율) 곡선 중 뭘 사용해야 할까**  \n",
    "- 양성 class가 드물거나, 거짓 음성보다 거짓 양성이 더 중요할 땐 PR 곡선을 사용\n",
    "- 그렇지 않으면 ROC 곡선 사용\n",
    "- PR 곡선은 분류기의 성능 개선 여지가 얼마나 되는지 잘 보여줌"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "RandomForestClassifier를 사용한 예"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.ensemble import RandomForestClassifier\n",
    "\n",
    "forest_clf = RandomForestClassifier(random_state = 42)\n",
    "y_probas_forest = cross_val_predict(forest_clf, X_train, y_train_5, cv=3, method = 'predict_proba')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "roc_curve()는 레이블과 점수를 기대하지만, 점수 대신 클래스 확률을 전달할 수 있음  \n",
    "양성 클래스 확률을 점수로 사용"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_scores_forest = y_probas_forest[:, 1] #양성 클래스를 저수로 사용\n",
    "fpr_forest, tpr_forest, thresholds_forest = roc_curve(y_train_5, y_scores_forest)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "recall_for_forest = tpr_forest[np.argmax(fpr_forest >= fpr_90)]\n",
    "\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(fpr, tpr, \"b:\", linewidth=2, label=\"SGD\")\n",
    "plot_roc_curve(fpr_forest, tpr_forest, \"Random Forest\")\n",
    "plt.plot([fpr_90, fpr_90], [0., recall_90_precision], \"r:\")\n",
    "plt.plot([0.0, fpr_90], [recall_90_precision, recall_90_precision], \"r:\")\n",
    "plt.plot([fpr_90], [recall_90_precision], \"ro\")\n",
    "plt.plot([fpr_90, fpr_90], [0., recall_for_forest], \"r:\")\n",
    "plt.plot([fpr_90], [recall_for_forest], \"ro\")\n",
    "plt.grid(True)\n",
    "plt.legend(loc=\"lower right\", fontsize=16)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9983436731328145"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "roc_auc_score(y_train_5, y_scores_forest)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.4 다중 분류\n",
    "일부 알고리즘은 여러 클래스를 처리할 수 있지만 다른 알고리즘은 이진 처리만 가능  \n",
    "그러나 이진분류기를 여러 개 사용하여 다중 클래스를 분류하는 기법도 많음"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**OvR(One versus the rest)**  \n",
    "- N개의 클래스가 존재한다면, N개의 분류 함수가 필요\n",
    "- 이미지를 분류할 때 각 분류기의 결정 점수 중 가장 높은 것을 클래스로 선택\n",
    "- 대부분의 이진 분류 알고리즘은 OvR을 선호\n",
    "- 하나의 class와 그 외의 나머지 모든 class를 비교하는 classifier를 각각의 class마다 학습시키고, 생성된 모든 classifier 중 가장 큰 예측값을 가지는 class를 최종 예측값으로 선택"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**OvO(One versus one)**\n",
    "- N개의 클래스가 존재한다면 분류기는 N(N-1)/2개가 필요\n",
    "- 숫자의 조합마다 이진 분류기를 훈련\n",
    "- 가장 많이 양성으로 분류된 클래스를 선택\n",
    "- 장점으로는 두 클래스에 해당하는 샘플만 필요\n",
    "-  하나의 class와 또다른 하나의 class를 비교하는 classifier를 각각의 class마다 학습시키고, classifier들의 예측값들을 비교하여 가장 많이 예측된 class를 최종 예측값으로 선택하는 방법"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "사이킷런에서는 알고리즘에 따라 자동으로 OvR, OvO를 실행"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5], dtype=uint8)"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.svm import SVC\n",
    "\n",
    "svm_clf = SVC()\n",
    "svm_clf.fit(X_train, y_train)\n",
    "svm_clf.predict([some_digit])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`decision_function` 매서드를 호출하면 샘플당 10개의 점수를 반환하고, 점수는 클래스마다 하나씩임"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.72501977,  2.72809088,  7.2510018 ,  8.3076379 , -0.31087254,\n",
       "         9.3132482 ,  1.70975103,  2.76765202,  6.23049537,  4.84771048]])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "some_digit_scores = svm_clf.decision_function([some_digit])\n",
    "some_digit_scores"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.argmax(some_digit_scores)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "분류기가 훈련될 때 classes_ 속성에 타깃 클래스의 리스트를 값으로 정렬하여 지정"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=uint8)"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "svm_clf.classes_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "svm_clf.classes_[5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "사이킷런에서 OvO, OvR을 사용하도록 강제하려면 `OneVsOneClassifier`, `OneVsRestClassifier`를 사용"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5], dtype=uint8)"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.multiclass import OneVsRestClassifier\n",
    "\n",
    "ovr_clf = OneVsRestClassifier(SVC())\n",
    "ovr_clf.fit(X_train, y_train)\n",
    "ovr_clf.predict([some_digit])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(ovr_clf.estimators_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "SGDClassifier를 훈련시키기"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3], dtype=uint8)"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sgd_clf.fit(X_train, y_train)\n",
    "sgd_clf.predict([some_digit])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-31893.03095419, -34419.69069632,  -9530.63950739,\n",
       "          1823.73154031, -22320.14822878,  -1385.80478895,\n",
       "        -26188.91070951, -16147.51323997,  -4604.35491274,\n",
       "        -12050.767298  ]])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sgd_clf.decision_function([some_digit])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "분류기 평가하기"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.87365, 0.85835, 0.8689 ])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cross_val_score(sgd_clf, X_train, y_train, cv=3, scoring='accuracy')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.8983, 0.891 , 0.9018])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 입력 스케일을 조정하여 정확도 높이기\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "scaler = StandardScaler()\n",
    "X_train_scaled = scaler.fit_transform(X_train.astype(np.float64))\n",
    "cross_val_score(sgd_clf, X_train_scaled, y_train, cv=3, scoring='accuracy')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.5 에러 분석\n",
    "모델의 성능을 향상시킬 방법 중 하나는 만들어진 에러의 종류를 분석하는 것"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 오차 행렬"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[5577,    0,   22,    5,    8,   43,   36,    6,  225,    1],\n",
       "       [   0, 6400,   37,   24,    4,   44,    4,    7,  212,   10],\n",
       "       [  27,   27, 5220,   92,   73,   27,   67,   36,  378,   11],\n",
       "       [  22,   17,  117, 5227,    2,  203,   27,   40,  403,   73],\n",
       "       [  12,   14,   41,    9, 5182,   12,   34,   27,  347,  164],\n",
       "       [  27,   15,   30,  168,   53, 4444,   75,   14,  535,   60],\n",
       "       [  30,   15,   42,    3,   44,   97, 5552,    3,  131,    1],\n",
       "       [  21,   10,   51,   30,   49,   12,    3, 5684,  195,  210],\n",
       "       [  17,   63,   48,   86,    3,  126,   25,   10, 5429,   44],\n",
       "       [  25,   18,   30,   64,  118,   36,    1,  179,  371, 5107]],\n",
       "      dtype=int64)"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train_pred = cross_val_predict(sgd_clf, X_train_scaled, y_train, cv=3)\n",
    "conf_mx = confusion_matrix(y_train, y_train_pred)\n",
    "conf_mx"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "맷플롯립의 `matshow()`로 시각화하면 보기 편리함"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.matshow(conf_mx, cmap=plt.cm.gray)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "숫자 5가 다른 숫자보다 어두움 > 이미지가 적거나 분류기가 잘 분류하지 못한다는 뜻  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 에러에 초점을 맞추자  \n",
    "오차 행렬의 각 값을 대응되는 클래스의 이미지 개수로 나눠 에러 비율 비교"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "row_sums = conf_mx.sum(axis=1, keepdims=True)\n",
    "norm_conf_mx = conf_mx / row_sums"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#주대각선만 0으로 채우기\n",
    "np.fill_diagonal(norm_conf_mx, 0)\n",
    "plt.matshow(norm_conf_mx, cmap=plt.cm.gray)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 행: 실제 클래스\n",
    "- 열: 예측 클래스\n",
    "\n",
    "8행이 밝기 때문에 잘못 분류된 것 같지만 클래스 8의 행을 보면 적절히 분류되었음  \n",
    "**오차 행렬은 반드시 대칭인 것이 아님**. 오차 행렬을 분석하면 분류기의 성능 향상 방안의 통찰을 얻을 수 있음"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.6 다중 레이블 분류\n",
    "- 여러 개의 이진 꼬리표를 출력하는 분류 시스템\n",
    "- ex) 같은 사진에 여러 사람이 등장\n",
    "- 결정 트리, 랜덤 포레스트, OvR clf에서도 다중 레이블 분류를 지원"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "KNeighborsClassifier()"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "\n",
    "y_train_large = (y_train >= 7) \n",
    "y_train_odd = (y_train % 2 == 1)\n",
    "y_multilabel = np.c_[y_train_large, y_train_odd]\n",
    "\n",
    "knn_clf = KNeighborsClassifier() \n",
    "knn_clf.fit(X_train, y_multilabel) #다중 타깃 배열을 사용하여 훈련"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[False,  True]])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "knn_clf.predict([some_digit])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.976410265560605"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#모든 레이블에 대한 F1 점수의 평균 계산\n",
    "\n",
    "y_train_knn_pred = cross_val_predict(knn_clf, X_train, y_multilabel, cv=3)\n",
    "f1_score(y_multilabel, y_train_knn_pred, average='macro')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "해당 코드는 모든 레이블의 가중치가 같다고 가정  \n",
    "샘플들의 비중이 다르다면 레이블에 클래스의 `지지도(타깃 레이블에 속한 샘플 수)`를 가중치로 줄 수 있음! `average='weighted'`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.7 다중 출력 분류\n",
    "- 다중 레이블 분류에서 한 레이블이 다중 클래스가 될 수 있도록 일반화(값을 두 개 이상 가질 수 있음)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "MNIST 이미지에서 추출한 train/test set에 `randint()`로 픽셀 강도에 잡음을 추가"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "noise = np.random.randint(0, 100, (len(X_train), 784))\n",
    "X_train_mod = X_train + noise\n",
    "\n",
    "noise = np.random.randint(0, 100, (len(X_test), 784))\n",
    "X_test_mod = X_test + noise\n",
    "\n",
    "y_train_mod = X_train\n",
    "y_test_mod = X_test"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "깨끗한 이미지로 만들기"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'numpy.ndarray' object has no attribute 'mod'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-66-3502bb54375f>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[0msome_index\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      2\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 3\u001b[1;33m \u001b[0mknn_clf\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfit\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mX_train\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmod\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my_train_mod\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      4\u001b[0m \u001b[0mclean_digit\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mknn_clf\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpredict\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mX_test_mod\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0msome_index\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[0mplot_digit\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mclean_digit\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mAttributeError\u001b[0m: 'numpy.ndarray' object has no attribute 'mod'"
     ]
    }
   ],
   "source": [
    "some_index = 0\n",
    "\n",
    "knn_clf.fit(X_train.mod, y_train_mod)\n",
    "clean_digit = knn_clf.predict([X_test_mod[some_index]])\n",
    "plot_digit(clean_digit)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
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   "nbconvert_exporter": "python",
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