07_autodiff_and_linear_regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "c4113faf",
   "metadata": {},
   "source": [
    "## Autodiff with a Linear Regression example\n",
    "\n",
    "So far, we've seen all the fine  Jax transformations. Now let's see how we can apply them. In this example, I'm going to use a very simple linear regression model and estimate the parameters using gradient descent (which in turn requires finding gradients).\n",
    "\n",
    "But first, let's complete the ritual of creating keys for the PRNG. (Seems kinda annoying that you've to do this every time but that's how Jax is, sadly.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c52f3329",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-02-12T22:45:57.859139Z",
     "start_time": "2023-02-12T22:45:57.086833Z"
    }
   },
   "outputs": [],
   "source": [
    "import jax\n",
    "import jax.numpy as jnp\n",
    "\n",
    "masterkey = jax.random.key(0)\n",
    "masterkey, *subkeys = jax.random.split(masterkey, 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e4daa74a",
   "metadata": {},
   "source": [
    "## Function to generate data\n",
    "\n",
    "The function basically is:\n",
    "\n",
    "$$\n",
    "f(x) = 4x + 3\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "9e2e9aba",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-02-12T22:45:57.865224Z",
     "start_time": "2023-02-12T22:45:57.860200Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f = lambda x: 4 * x + 3\n",
    "f(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1cd9767d",
   "metadata": {},
   "source": [
    "The function is defined, now to get some inputs for the function to generate the outputs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "18fab3ce",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-02-12T22:45:58.035339Z",
     "start_time": "2023-02-12T22:45:57.866003Z"
    }
   },
   "outputs": [],
   "source": [
    "xs = jax.random.normal(subkeys[0], shape=(1000, ))\n",
    "ys = f(xs)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dd6508c0",
   "metadata": {},
   "source": [
    "If you've your doubts over f being linear, well, there's always matplotlib!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "228dbd7c",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-02-12T22:45:58.553576Z",
     "start_time": "2023-02-12T22:45:58.036403Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f9058724820>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.plot(xs, ys)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "617fb3d9",
   "metadata": {},
   "source": [
    "So, as of this notebook cell, we've data for regression and we've the PRNG keys for Jax. What's next then? THE MODEL!\n",
    "\n",
    "## Model\n",
    "### Model definition\n",
    "\n",
    "The python function should be pretty self explanatory. We pass in the parameters and the input array and the function will predict some output based on the given parameters. On academic terms, this function serves as the \"forward\" pass."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "586344e4",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-02-12T22:45:58.556494Z",
     "start_time": "2023-02-12T22:45:58.554534Z"
    }
   },
   "outputs": [],
   "source": [
    "@jax.jit\n",
    "def lin_reg_model(params, x):\n",
    "    w, b = params\n",
    "    \n",
    "    y_pred = w * x + b\n",
    "    return y_pred"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec87a3bf",
   "metadata": {},
   "source": [
    "### Initial parameters\n",
    "\n",
    "Okay, so the model has been defined, it takes in parameters, churns out some output, all good. But where are the params going to come from? We already have x. \n",
    "\n",
    "(Paramters initialisation, anybody? To keep things simple, I'm just initialising them from a normal distribution. Sure there are well established ways of initialising paramters but we're not writing this model to win any Kaggle competitions.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "52359e5a",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-02-12T22:45:58.653635Z",
     "start_time": "2023-02-12T22:45:58.557296Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DeviceArray([ 0.97020763, -0.12123348], dtype=float32)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def init_params():\n",
    "    return jax.random.normal(subkeys[1], shape=(2, ))\n",
    "\n",
    "params = init_params()\n",
    "params"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ece77a2c",
   "metadata": {},
   "source": [
    "### Error / Objective / Loss\n",
    "\n",
    "To be honest, academicians need to sit together and fix a single name for the same thing so people get less confused. Just get your thing together people! Anyways, so a error / loss / ........... just say loss function, we have to find one and define it. \n",
    "\n",
    "[Mean Squared Error](https://en.wikipedia.org/wiki/Mean_squared_error) is a pretty simple \n",
    "loss function for discrete estimation tasks such as linear regression. You can read more [here](https://en.wikipedia.org/wiki/Ordinary_least_squares)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "d09295a6",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-02-12T22:45:58.710608Z",
     "start_time": "2023-02-12T22:45:58.655199Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DeviceArray(20.059916, dtype=float32)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# jit, because speed\n",
    "@jax.jit\n",
    "def compute_loss(params, x, y):\n",
    "    y_pred = lin_reg_model(params, x)\n",
    "    \n",
    "    # mse error\n",
    "    error = jnp.mean((y - y_pred) ** 2)\n",
    "    \n",
    "    return error\n",
    "\n",
    "# test\n",
    "compute_loss(params, xs, ys)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e73748d",
   "metadata": {},
   "source": [
    "## Gradient Descent\n",
    "\n",
    "If you're already lost in the middle of all the text in the notebook, we have to update the parameters iteratively. \n",
    "\n",
    "So to update using gradient descent, we need the gradients. `jax.grad` will give us the gradients, but I also want to keep track of the loss values for each iteration. Does jax have anything for this? Yes. `jax.value_and_grad`. \n",
    "\n",
    "So just to recall, a gradient descent update roughly looks like this in terms of pseudocode:\n",
    "```python\n",
    "params = params - learning_rate * gradients\n",
    "```\n",
    "\n",
    "This can be done in two ways in jax. Either via using `tree_map` or just simply like the pseudocode above. I've initialised the parameters as an array. What if you've a dictionary for params? In that case, jax forbids using the regular pythonic way to update dict values recommends using `tree_map`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "558add86",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-02-12T22:45:58.713676Z",
     "start_time": "2023-02-12T22:45:58.711533Z"
    }
   },
   "outputs": [],
   "source": [
    "# keeping the learning rate as 0.01 here. feel free to experiment with other values\n",
    "\n",
    "@jax.jit\n",
    "def update(params, x, y, lr=0.01): \n",
    "    # get loss value and also gradients\n",
    "    values, grads = jax.value_and_grad(compute_loss)(params, x, y)\n",
    "    \n",
    "    updated_params = params - lr * grads\n",
    "    # alternative\n",
    "    # updated_params = jax.tree_map(lambda p, g: p - lr * g, params, grads)\n",
    "\n",
    "    return values, updated_params"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8197b6a9",
   "metadata": {},
   "source": [
    "## Train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ba2459dd",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-02-12T22:45:58.801595Z",
     "start_time": "2023-02-12T22:45:58.714632Z"
    }
   },
   "outputs": [],
   "source": [
    "epochs = 100\n",
    "\n",
    "losses = list() # keep a list to plot later\n",
    "\n",
    "\n",
    "for e in range(epochs):\n",
    "    values, params = update(params, xs, ys)\n",
    "    \n",
    "    # append the loss\n",
    "    losses.append(values)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c29c3787",
   "metadata": {},
   "source": [
    "Let's check on the updated params. They should be as close as possible to 4 and 3 (compare with the data generation function)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "deff959f",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-02-12T22:45:58.805123Z",
     "start_time": "2023-02-12T22:45:58.802591Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DeviceArray([3.679284 , 2.5969446], dtype=float32)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "params"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f6cbb354",
   "metadata": {},
   "source": [
    "Looks quite close. How about the loss values though? Did the overall loss decrease well over the iterations (epochs)?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "af960baa",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-02-12T22:45:59.080829Z",
     "start_time": "2023-02-12T22:45:58.805997Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f9058725bd0>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(jnp.arange(epochs), losses, c=\"r\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10d65608",
   "metadata": {},
   "source": [
    "## Comparing the actual and predicted function\n",
    "\n",
    "We have the estimated parameters and now can use these to generate outputs using our linear regression model. (Estimating parameters is basically estimating a function). However one question lingers, how much of a deviation does our predicted function/model/parameters show?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "eff57421",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-02-12T22:45:59.204191Z",
     "start_time": "2023-02-12T22:45:59.081727Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f90585379d0>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(xs, ys, c=\"r\", label=\"actual\")\n",
    "plt.plot(xs, lin_reg_model(params, xs), c=\"g\", label=\"predicted\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "410db8cd",
   "metadata": {},
   "source": [
    "You're pretty good - [Revolver Ocelote](https://youtu.be/8xVfjkb-xVs)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.8"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
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