{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simple Linear Regression with Tensorflow\n",
    "> In this post, it will cover Simple linear regression with tensorflow 2.x. Hypothesis and cost fuction will be also mentioned.\n",
    "\n",
    "- toc: true \n",
    "- badges: true\n",
    "- comments: true\n",
    "- author: Chanseok Kang\n",
    "- categories: [Python, Tensorflow]\n",
    "- image: images/linear_regression_epoch.png"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "import tensorflow as tf\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hypothesis and cost function\n",
    "**Hypothesis** is a sort of function that expect to represent the pattern of given data. It is usually expressed with some linear equation, but in this post, it will cover the simple linear regression, so the hypothesis may be simple linear equation like this,\n",
    "\n",
    "$$ H(x) = W x + b $$\n",
    "\n",
    "Here, $x$ is the given data, and $W$ is weight vector, and $b$ is bias. So the output $H(x)$ is the form of product weight vector and given data, adding bias. The purpose of hypothesis is to clearly represent the actual output($y$) with this formula. To do this, hypothesis should be same as actual output.\n",
    "\n",
    " Maybe the simple hypothesis can be drawn as line on 2D-space. But as you know that, it is hard to clearly represent all the data with given hypothesis. There're must be the error between the output of hypothesis and actual output. Through this process, we should find the way to minimize the error between them.\n",
    " \n",
    " **Cost** is the error I mentioned. Usually, lots of data is given, so the cost can be expressed with the average of error. And as you notice that, hypothesis is related on weight vector($W$) and bias($b$), so the cost can be described as a function:\n",
    " \n",
    " $$ \\text{cost}(W, b) = {1 \\over m} \\sum_{i=1}^m (H(x_i) - y_i)^2 $$\n",
    " \n",
    " And there are lots of cost function in the world. The expression above is the **mean squared error**(MSE for short), cause we measure the error with **euclidean distance** ($(x-y)^2$). Maybe we can use the cost function with **mean absolute error**(MAE for short). Anyway, we'll use cost function with MSE.\n",
    " \n",
    "So, we need to find the best $W$ and $b$ for minimizing the cost function. The process we try to find this is called **learning** or **training**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Build Hypothesis and cost"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's consider the simple case. Suppose we have the dataset like this,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_data = [*range(0, 6)]\n",
    "y_data = [*range(0, 6)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see without arithmatic, we know that the hypothesis maybe $y=x$, that is $W = 1$ and $b = 0$. If we initialize the weight and bias with different value, can we find the right answer through learning? In tensorflow, we can define the parameter and hypothesis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Tensor: shape=(6,), dtype=float32, numpy=array([ 0.1,  4.1,  8.1, 12.1, 16.1, 20.1], dtype=float32)>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "W = tf.Variable(4.0)\n",
    "b = tf.Variable(0.1)\n",
    "\n",
    "h = W * x_data + b\n",
    "h"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is definitely incorrect hypothesis. Our purpose is to find best paramter with cost function. So we need to define cost function. Tensorflow offers some APIs to calculate the arithmatic operation. Note that `reduce` in `reduce_mean` means that it can calculating the mean while the rank of given data is decreasing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "cost = tf.reduce_mean(tf.square(h - y_data))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gradient descent\n",
    "Mentioned earlier, we need to find the $W$ and $b$ to minimize the cost function. Widely used algorithm to do this is **Gradient Descent**. This algorithm tends to find the global minimum (sometimes it finds local minimum) using the difference of gradient. If the gradient is 0, it assumes that the point may be the minimum. In tensorflow 2.x, Gradient Tape is used to calculate the gradient. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tf.Tensor(55.500004, shape=(), dtype=float32)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<tf.Variable 'UnreadVariable' shape=() dtype=float32, numpy=-0.05200001>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Learning rate initialize\n",
    "learning_rate = 0.01\n",
    "\n",
    "# Store the history of gradient in tape\n",
    "with tf.GradientTape() as tape:\n",
    "    h = W * x_data + b\n",
    "    cost = tf.reduce_mean(tf.square(h - y_data))\n",
    "    \n",
    "# Calculate the gradient with tape\n",
    "W_grad, b_grad = tape.gradient(cost, [W, b])\n",
    "print(W_grad)\n",
    "\n",
    "# Update W and b\n",
    "W.assign_sub(learning_rate * W_grad)\n",
    "b.assign_sub(learning_rate * b_grad)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Learning rate is the ratio of applying gradient difference. Ususally, it is initialized with small value(0.01). In the code, when the gradient is calculated, the original parameter is changed with gradient applying learning rate.\n",
    "\n",
    "This is example of learning in one step(also known as **epoch**). If we want to find more accurate $W$ and $b$, more learning step must be processed."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Parameter update"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    0 |      3.455 |     -0.248 |  81.010002\n",
      "  100 |      1.136 |    -0.4814 |   0.074779\n",
      "  200 |      1.075 |    -0.2661 |   0.022854\n",
      "  300 |      1.041 |    -0.1471 |   0.006985\n",
      "  400 |      1.023 |   -0.08133 |   0.002135\n",
      "  500 |      1.013 |   -0.04496 |   0.000652\n",
      "  600 |      1.007 |   -0.02486 |   0.000199\n",
      "  700 |      1.004 |   -0.01374 |   0.000061\n",
      "  800 |      1.002 |  -0.007597 |   0.000019\n",
      "  900 |      1.001 |    -0.0042 |   0.000006\n"
     ]
    }
   ],
   "source": [
    "# Initialize paramter \n",
    "W = tf.Variable(4.0)\n",
    "b = tf.Variable(-0.1)\n",
    "\n",
    "# Learning rate initialize\n",
    "learning_rate = 0.01\n",
    "\n",
    "for i in range(1000):\n",
    "    # Gradient descent\n",
    "    with tf.GradientTape() as tape:\n",
    "        h = W * x_data + b\n",
    "        cost = tf.reduce_mean(tf.square(h - y_data))\n",
    "    W_grad, b_grad = tape.gradient(cost, [W, b])\n",
    "    \n",
    "    W.assign_sub(learning_rate * W_grad)\n",
    "    b.assign_sub(learning_rate * b_grad)\n",
    "    \n",
    "    if i % 100 ==0:\n",
    "        print(\"{:5} | {:10.4} | {:10.4} | {:10.6f}\".format(i, W.numpy(), b.numpy(), cost))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After 1000 epochs, $W$ gets 1.001, and $b$ gets -0.004. Let's visualize it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "h_x = 4.0 * np.array(x_data) - 0.1\n",
    "h_xp = 1.001 * np.array(x_data) - 0.004\n",
    "plt.figure(figsize=(16, 8))\n",
    "plt.plot(h_x, c='red', label='epoch=1');\n",
    "plt.plot(h_xp, c='red', linestyle='--', label='epoch=900');\n",
    "plt.scatter(x_data, y_data);\n",
    "plt.title('i=0 (Epoch=1)');\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary\n",
    "In this post, it is explained what the hypothesis and cost function are. And using Gradient Descent with several epochs, we can get optimal weight vector and bias for representing given data. "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}