regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "np.random.seed(0)\n",
    "x = 2*np.random.rand(100,1)\n",
    "y = 6 + 4*x + np.random.rand(100,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x25273dd75f8>"
      ]
     },
     "execution_count": 10,
     "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.scatter(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.]]\n",
      "[[0.]]\n"
     ]
    }
   ],
   "source": [
    "w1 = np.zeros((1,1))\n",
    "print(w1)\n",
    "print(np.zeros_like(w1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_weight_updates(w1, w0, x, y, learning_rate=0.01):\n",
    "    N = len(y)\n",
    "    w1_update = np.zeros_like(w1)\n",
    "    w0_update = np.zeros_like(w0)\n",
    "    y_pred = np.dot(x,w1.T) + w0\n",
    "    diff = y-y_pred\n",
    "\n",
    "    w0_factors = np.ones((N,1))\n",
    "\n",
    "    w1_update = -(2/N) * learning_rate*(np.dot(x.T, diff))\n",
    "    w0_update = -(2/N) * learning_rate*(np.dot(w0_factors.T, diff))\n",
    "    return w1_update, w0_update"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient_descent_steps(x,y, iters=10000):\n",
    "    w0 = np.zeros((1,1)) #[[0.]]\n",
    "    w1 = np.zeros((1,1)) #[[0.]]\n",
    "\n",
    "    for ind in range(iters):\n",
    "        w1_update, w0_update = get_weight_updates(w1,w0,x,y,learning_rate=0.01)\n",
    "        w1 = w1 - w1_update\n",
    "        w0 = w0 - w0_update\n",
    "        \n",
    "    return w1, w0\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_cost(y, y_pred):\n",
    "    N = len(y)\n",
    "    cost = np.sum(np.square(y-y_pred))/N\n",
    "    return cost\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w1:4.980, w0:5.256\n",
      "Gradient Descent Total Cost:0.5360\n",
      "w1:4.758, w0:5.665\n",
      "Gradient Descent Total Cost:0.3049\n",
      "w1:4.541, w0:5.912\n",
      "Gradient Descent Total Cost:0.1962\n",
      "w1:4.383, w0:6.090\n",
      "Gradient Descent Total Cost:0.1392\n",
      "w1:4.269, w0:6.219\n",
      "Gradient Descent Total Cost:0.1093\n",
      "w1:4.186, w0:6.313\n",
      "Gradient Descent Total Cost:0.0936\n",
      "w1:4.126, w0:6.380\n",
      "Gradient Descent Total Cost:0.0853\n",
      "w1:4.083, w0:6.429\n",
      "Gradient Descent Total Cost:0.0810\n",
      "w1:4.051, w0:6.465\n",
      "Gradient Descent Total Cost:0.0787\n",
      "w1:4.028, w0:6.490\n",
      "Gradient Descent Total Cost:0.0775\n"
     ]
    }
   ],
   "source": [
    "iters=[100,200,300,400,500,600,700,800,900,1000]\n",
    "for i in iters:\n",
    "    w1, w0 = gradient_descent_steps(x,y, iters=i)\n",
    "    print(f\"w1:{w1[0,0]:.3f}, w0:{w0[0,0]:.3f}\")\n",
    "    y_pred = w1[0,0]*x + w0\n",
    "    print(f\"Gradient Descent Total Cost:{get_cost(y,y_pred):.4f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w1:0.000, w0:0.000\n",
      "Gradient Descent Total Cost:111.6167\n",
      "w1:0.221, w0:0.206\n",
      "Gradient Descent Total Cost:102.6528\n",
      "w1:0.433, w0:0.404\n",
      "Gradient Descent Total Cost:94.4138\n",
      "w1:0.637, w0:0.594\n",
      "Gradient Descent Total Cost:86.8412\n",
      "w1:0.831, w0:0.776\n",
      "Gradient Descent Total Cost:79.8809\n",
      "w1:1.017, w0:0.951\n",
      "Gradient Descent Total Cost:73.4834\n",
      "w1:1.196, w0:1.119\n",
      "Gradient Descent Total Cost:67.6033\n",
      "w1:1.367, w0:1.280\n",
      "Gradient Descent Total Cost:62.1985\n",
      "w1:1.530, w0:1.435\n",
      "Gradient Descent Total Cost:57.2308\n",
      "w1:1.687, w0:1.584\n",
      "Gradient Descent Total Cost:52.6646\n",
      "w1:1.837, w0:1.726\n",
      "Gradient Descent Total Cost:48.4676\n",
      "w1:1.981, w0:1.863\n",
      "Gradient Descent Total Cost:44.6098\n",
      "w1:2.118, w0:1.995\n",
      "Gradient Descent Total Cost:41.0638\n",
      "w1:2.250, w0:2.121\n",
      "Gradient Descent Total Cost:37.8043\n",
      "w1:2.376, w0:2.242\n",
      "Gradient Descent Total Cost:34.8083\n",
      "w1:2.497, w0:2.359\n",
      "Gradient Descent Total Cost:32.0543\n",
      "w1:2.612, w0:2.471\n",
      "Gradient Descent Total Cost:29.5228\n",
      "w1:2.723, w0:2.578\n",
      "Gradient Descent Total Cost:27.1958\n",
      "w1:2.829, w0:2.681\n",
      "Gradient Descent Total Cost:25.0568\n",
      "w1:2.930, w0:2.780\n",
      "Gradient Descent Total Cost:23.0905\n",
      "w1:3.027, w0:2.875\n",
      "Gradient Descent Total Cost:21.2829\n",
      "w1:3.120, w0:2.967\n",
      "Gradient Descent Total Cost:19.6212\n",
      "w1:3.208, w0:3.055\n",
      "Gradient Descent Total Cost:18.0937\n",
      "w1:3.293, w0:3.139\n",
      "Gradient Descent Total Cost:16.6894\n",
      "w1:3.374, w0:3.220\n",
      "Gradient Descent Total Cost:15.3984\n",
      "w1:3.452, w0:3.298\n",
      "Gradient Descent Total Cost:14.2116\n",
      "w1:3.526, w0:3.373\n",
      "Gradient Descent Total Cost:13.1204\n",
      "w1:3.597, w0:3.445\n",
      "Gradient Descent Total Cost:12.1172\n",
      "w1:3.665, w0:3.515\n",
      "Gradient Descent Total Cost:11.1948\n",
      "w1:3.730, w0:3.581\n",
      "Gradient Descent Total Cost:10.3468\n",
      "w1:3.793, w0:3.645\n",
      "Gradient Descent Total Cost:9.5670\n",
      "w1:3.852, w0:3.707\n",
      "Gradient Descent Total Cost:8.8500\n",
      "w1:3.909, w0:3.766\n",
      "Gradient Descent Total Cost:8.1907\n",
      "w1:3.963, w0:3.823\n",
      "Gradient Descent Total Cost:7.5844\n",
      "w1:4.015, w0:3.878\n",
      "Gradient Descent Total Cost:7.0268\n",
      "w1:4.064, w0:3.931\n",
      "Gradient Descent Total Cost:6.5141\n",
      "w1:4.112, w0:3.981\n",
      "Gradient Descent Total Cost:6.0425\n",
      "w1:4.157, w0:4.030\n",
      "Gradient Descent Total Cost:5.6088\n",
      "w1:4.200, w0:4.077\n",
      "Gradient Descent Total Cost:5.2098\n",
      "w1:4.241, w0:4.122\n",
      "Gradient Descent Total Cost:4.8428\n",
      "w1:4.281, w0:4.166\n",
      "Gradient Descent Total Cost:4.5052\n",
      "w1:4.318, w0:4.208\n",
      "Gradient Descent Total Cost:4.1946\n",
      "w1:4.354, w0:4.248\n",
      "Gradient Descent Total Cost:3.9089\n",
      "w1:4.388, w0:4.287\n",
      "Gradient Descent Total Cost:3.6459\n",
      "w1:4.421, w0:4.325\n",
      "Gradient Descent Total Cost:3.4040\n",
      "w1:4.452, w0:4.361\n",
      "Gradient Descent Total Cost:3.1813\n",
      "w1:4.482, w0:4.395\n",
      "Gradient Descent Total Cost:2.9763\n",
      "w1:4.510, w0:4.429\n",
      "Gradient Descent Total Cost:2.7876\n",
      "w1:4.537, w0:4.461\n",
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      "w1:4.563, w0:4.493\n",
      "Gradient Descent Total Cost:2.4539\n",
      "w1:4.587, w0:4.523\n",
      "Gradient Descent Total Cost:2.3066\n",
      "w1:4.611, w0:4.552\n",
      "Gradient Descent Total Cost:2.1710\n",
      "w1:4.633, w0:4.580\n",
      "Gradient Descent Total Cost:2.0460\n",
      "w1:4.654, w0:4.607\n",
      "Gradient Descent Total Cost:1.9309\n",
      "w1:4.674, w0:4.633\n",
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      "w1:4.693, w0:4.658\n",
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      "w1:4.728, w0:4.706\n",
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      "Gradient Descent Total Cost:1.4061\n",
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      "Gradient Descent Total Cost:1.3408\n",
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      "w1:4.827, w0:4.849\n",
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      "w1:4.859, w0:4.901\n",
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      "w1:4.028, w0:6.490\n",
      "Gradient Descent Total Cost:0.0776\n"
     ]
    }
   ],
   "source": [
    "for i in range(1000):\n",
    "    w1, w0 = gradient_descent_steps(x,y, iters=i)\n",
    "    print(f\"w1:{w1[0,0]:.3f}, w0:{w0[0,0]:.3f}\")\n",
    "    y_pred = w1[0,0]*x + w0\n",
    "    print(f\"Gradient Descent Total Cost:{get_cost(y,y_pred):.4f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def stochastic_gradient_descent_steps(x,y, batch_size=10, iters=1000):\n",
    "    w0 = np.zeros((1,1)) #[[0.]]\n",
    "    w1 = np.zeros((1,1)) #[[0.]]\n",
    "\n",
    "    for ind in range(iters):\n",
    "        np.random.seed(ind)\n",
    "        stochastic_random_index = np.random.permutation(x.shape[0])\n",
    "        sample_x = x[stochastic_random_index[0:batch_size]]\n",
    "        sample_y = y[stochastic_random_index[0:batch_size]]\n",
    "        w1_update, w0_update = get_weight_updates(w1,w0,sample_x,sample_y,learning_rate=0.01)\n",
    "        w1 = w1 - w1_update\n",
    "        w0 = w0 - w0_update\n",
    "        \n",
    "    return w1, w0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w1:0.000, w0:0.000\n",
      "Gradient Descent Total Cost:111.6167\n",
      "w1:0.136, w0:0.181\n",
      "Gradient Descent Total Cost:104.9738\n",
      "w1:0.336, w0:0.379\n",
      "Gradient Descent Total Cost:96.8903\n",
      "w1:0.588, w0:0.584\n",
      "Gradient Descent Total Cost:87.9813\n",
      "w1:0.791, w0:0.770\n",
      "Gradient Descent Total Cost:80.7442\n",
      "w1:0.923, w0:0.928\n",
      "Gradient Descent Total Cost:75.5586\n",
      "w1:1.198, w0:1.122\n",
      "Gradient Descent Total Cost:67.5241\n",
      "w1:1.382, w0:1.289\n",
      "Gradient Descent Total Cost:61.8151\n",
      "w1:1.522, w0:1.440\n",
      "Gradient Descent Total Cost:57.2907\n",
      "w1:1.700, w0:1.594\n",
      "Gradient Descent Total Cost:52.3166\n",
      "w1:1.916, w0:1.751\n",
      "Gradient Descent Total Cost:47.0160\n",
      "w1:2.084, w0:1.892\n",
      "Gradient Descent Total Cost:42.8408\n",
      "w1:2.204, w0:2.019\n",
      "Gradient Descent Total Cost:39.6407\n",
      "w1:2.348, w0:2.145\n",
      "Gradient Descent Total Cost:36.2882\n",
      "w1:2.458, w0:2.263\n",
      "Gradient Descent Total Cost:33.5865\n",
      "w1:2.576, w0:2.379\n",
      "Gradient Descent Total Cost:30.9225\n",
      "w1:2.666, w0:2.487\n",
      "Gradient Descent Total Cost:28.7545\n",
      "w1:2.776, w0:2.594\n",
      "Gradient Descent Total Cost:26.4639\n",
      "w1:2.848, w0:2.690\n",
      "Gradient Descent Total Cost:24.7696\n",
      "w1:2.926, w0:2.786\n",
      "Gradient Descent Total Cost:23.0744\n",
      "w1:3.031, w0:2.883\n",
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      "Gradient Descent Total Cost:19.1714\n",
      "w1:3.250, w0:3.073\n",
      "Gradient Descent Total Cost:17.5940\n",
      "w1:3.322, w0:3.156\n",
      "Gradient Descent Total Cost:16.3281\n",
      "w1:3.404, w0:3.237\n",
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      "w1:3.695, w0:3.528\n",
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      "w1:3.763, w0:3.595\n",
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      "w1:3.852, w0:3.658\n",
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      "w1:3.936, w0:3.718\n",
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      "Gradient Descent Total Cost:7.6655\n",
      "w1:4.049, w0:3.829\n",
      "Gradient Descent Total Cost:7.1143\n",
      "w1:4.095, w0:3.883\n",
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      "Gradient Descent Total Cost:6.1862\n",
      "w1:4.192, w0:3.978\n",
      "Gradient Descent Total Cost:5.7005\n",
      "w1:4.246, w0:4.023\n",
      "Gradient Descent Total Cost:5.2646\n",
      "w1:4.289, w0:4.070\n",
      "Gradient Descent Total Cost:4.8856\n",
      "w1:4.327, w0:4.113\n",
      "Gradient Descent Total Cost:4.5502\n",
      "w1:4.358, w0:4.158\n",
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      "w1:4.393, w0:4.200\n",
      "Gradient Descent Total Cost:3.9654\n",
      "w1:4.428, w0:4.239\n",
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      "w1:4.469, w0:4.275\n",
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      "w1:4.497, w0:4.313\n",
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      "Gradient Descent Total Cost:0.0805\n",
      "w1:4.035, w0:6.444\n",
      "Gradient Descent Total Cost:0.0803\n",
      "w1:4.036, w0:6.446\n",
      "Gradient Descent Total Cost:0.0801\n",
      "w1:4.035, w0:6.446\n",
      "Gradient Descent Total Cost:0.0801\n",
      "w1:4.038, w0:6.448\n",
      "Gradient Descent Total Cost:0.0798\n",
      "w1:4.040, w0:6.449\n",
      "Gradient Descent Total Cost:0.0797\n",
      "w1:4.042, w0:6.451\n",
      "Gradient Descent Total Cost:0.0795\n",
      "w1:4.040, w0:6.449\n",
      "Gradient Descent Total Cost:0.0796\n",
      "w1:4.042, w0:6.451\n",
      "Gradient Descent Total Cost:0.0794\n",
      "w1:4.041, w0:6.450\n",
      "Gradient Descent Total Cost:0.0795\n",
      "w1:4.043, w0:6.453\n",
      "Gradient Descent Total Cost:0.0793\n",
      "w1:4.045, w0:6.456\n",
      "Gradient Descent Total Cost:0.0791\n",
      "w1:4.045, w0:6.457\n",
      "Gradient Descent Total Cost:0.0790\n",
      "w1:4.048, w0:6.459\n",
      "Gradient Descent Total Cost:0.0789\n",
      "w1:4.045, w0:6.458\n",
      "Gradient Descent Total Cost:0.0790\n",
      "w1:4.045, w0:6.459\n",
      "Gradient Descent Total Cost:0.0789\n",
      "w1:4.045, w0:6.460\n",
      "Gradient Descent Total Cost:0.0788\n",
      "w1:4.045, w0:6.460\n",
      "Gradient Descent Total Cost:0.0788\n",
      "w1:4.044, w0:6.459\n",
      "Gradient Descent Total Cost:0.0789\n",
      "w1:4.041, w0:6.459\n",
      "Gradient Descent Total Cost:0.0789\n",
      "w1:4.037, w0:6.457\n",
      "Gradient Descent Total Cost:0.0791\n",
      "w1:4.039, w0:6.460\n",
      "Gradient Descent Total Cost:0.0789\n",
      "w1:4.041, w0:6.462\n",
      "Gradient Descent Total Cost:0.0788\n",
      "w1:4.042, w0:6.463\n",
      "Gradient Descent Total Cost:0.0787\n",
      "w1:4.040, w0:6.463\n",
      "Gradient Descent Total Cost:0.0787\n",
      "w1:4.040, w0:6.464\n",
      "Gradient Descent Total Cost:0.0786\n",
      "w1:4.040, w0:6.465\n",
      "Gradient Descent Total Cost:0.0786\n",
      "w1:4.040, w0:6.465\n",
      "Gradient Descent Total Cost:0.0786\n",
      "w1:4.042, w0:6.467\n",
      "Gradient Descent Total Cost:0.0785\n",
      "w1:4.043, w0:6.468\n",
      "Gradient Descent Total Cost:0.0785\n",
      "w1:4.042, w0:6.467\n",
      "Gradient Descent Total Cost:0.0785\n",
      "w1:4.041, w0:6.467\n",
      "Gradient Descent Total Cost:0.0785\n",
      "w1:4.040, w0:6.466\n",
      "Gradient Descent Total Cost:0.0786\n",
      "w1:4.039, w0:6.466\n",
      "Gradient Descent Total Cost:0.0785\n",
      "w1:4.037, w0:6.464\n",
      "Gradient Descent Total Cost:0.0787\n",
      "w1:4.038, w0:6.467\n",
      "Gradient Descent Total Cost:0.0785\n",
      "w1:4.040, w0:6.469\n",
      "Gradient Descent Total Cost:0.0784\n",
      "w1:4.041, w0:6.472\n",
      "Gradient Descent Total Cost:0.0783\n",
      "w1:4.040, w0:6.472\n",
      "Gradient Descent Total Cost:0.0783\n",
      "w1:4.041, w0:6.475\n",
      "Gradient Descent Total Cost:0.0782\n",
      "w1:4.039, w0:6.472\n",
      "Gradient Descent Total Cost:0.0783\n",
      "w1:4.035, w0:6.471\n",
      "Gradient Descent Total Cost:0.0783\n",
      "w1:4.036, w0:6.470\n",
      "Gradient Descent Total Cost:0.0783\n",
      "w1:4.036, w0:6.471\n",
      "Gradient Descent Total Cost:0.0783\n",
      "w1:4.032, w0:6.468\n",
      "Gradient Descent Total Cost:0.0785\n",
      "w1:4.035, w0:6.472\n",
      "Gradient Descent Total Cost:0.0782\n",
      "w1:4.033, w0:6.472\n",
      "Gradient Descent Total Cost:0.0782\n",
      "w1:4.034, w0:6.473\n",
      "Gradient Descent Total Cost:0.0782\n",
      "w1:4.032, w0:6.471\n",
      "Gradient Descent Total Cost:0.0783\n",
      "w1:4.034, w0:6.473\n",
      "Gradient Descent Total Cost:0.0782\n",
      "w1:4.035, w0:6.476\n",
      "Gradient Descent Total Cost:0.0781\n",
      "w1:4.036, w0:6.477\n",
      "Gradient Descent Total Cost:0.0780\n",
      "w1:4.037, w0:6.478\n",
      "Gradient Descent Total Cost:0.0780\n",
      "w1:4.035, w0:6.478\n",
      "Gradient Descent Total Cost:0.0780\n",
      "w1:4.037, w0:6.481\n",
      "Gradient Descent Total Cost:0.0780\n",
      "w1:4.036, w0:6.481\n",
      "Gradient Descent Total Cost:0.0779\n",
      "w1:4.038, w0:6.483\n",
      "Gradient Descent Total Cost:0.0780\n",
      "w1:4.040, w0:6.485\n",
      "Gradient Descent Total Cost:0.0780\n",
      "w1:4.040, w0:6.486\n",
      "Gradient Descent Total Cost:0.0780\n",
      "w1:4.037, w0:6.484\n",
      "Gradient Descent Total Cost:0.0779\n",
      "w1:4.039, w0:6.486\n",
      "Gradient Descent Total Cost:0.0779\n",
      "w1:4.034, w0:6.483\n",
      "Gradient Descent Total Cost:0.0778\n",
      "w1:4.034, w0:6.482\n",
      "Gradient Descent Total Cost:0.0778\n",
      "w1:4.033, w0:6.482\n",
      "Gradient Descent Total Cost:0.0778\n",
      "w1:4.032, w0:6.484\n",
      "Gradient Descent Total Cost:0.0778\n",
      "w1:4.033, w0:6.485\n",
      "Gradient Descent Total Cost:0.0778\n",
      "w1:4.036, w0:6.488\n",
      "Gradient Descent Total Cost:0.0778\n",
      "w1:4.035, w0:6.486\n",
      "Gradient Descent Total Cost:0.0778\n",
      "w1:4.035, w0:6.488\n",
      "Gradient Descent Total Cost:0.0778\n",
      "w1:4.034, w0:6.487\n",
      "Gradient Descent Total Cost:0.0778\n",
      "w1:4.033, w0:6.486\n",
      "Gradient Descent Total Cost:0.0777\n",
      "w1:4.035, w0:6.488\n",
      "Gradient Descent Total Cost:0.0778\n",
      "w1:4.031, w0:6.486\n",
      "Gradient Descent Total Cost:0.0777\n",
      "w1:4.027, w0:6.483\n",
      "Gradient Descent Total Cost:0.0778\n",
      "w1:4.030, w0:6.486\n",
      "Gradient Descent Total Cost:0.0777\n",
      "w1:4.029, w0:6.485\n",
      "Gradient Descent Total Cost:0.0777\n"
     ]
    }
   ],
   "source": [
    "for i in range(1000):\n",
    "    w1, w0 = stochastic_gradient_descent_steps(x,y, iters=i)\n",
    "    print(f\"w1:{w1[0,0]:.3f}, w0:{w0[0,0]:.3f}\")\n",
    "    y_pred = w1[0,0]*x + w0\n",
    "    print(f\"Gradient Descent Total Cost:{get_cost(y,y_pred):.4f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## sklearn.linear_model.LinearRegression\n",
    "* class sklearn.linear_model.LinearRegression(*, fit_intercept=True, copy_X=True, n_jobs=None, positive=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## sklearn.linear_model.SGDRegressor\n",
    "* class sklearn.linear_model.SGDRegressor(loss='squared_error', *, penalty='l2', alpha=0.0001, l1_ratio=0.15, fit_intercept=True, max_iter=1000, tol=0.001, shuffle=True, verbose=0, epsilon=0.1, random_state=None, learning_rate='invscaling', eta0=0.01, power_t=0.25, early_stopping=False, validation_fraction=0.1, n_iter_no_change=5, warm_start=False, average=False) \n",
    "\n",
    "eta, power_t: learning rate\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[67.30998637]\n"
     ]
    }
   ],
   "source": [
    "reg = LinearRegression()\n",
    "X = [[174], [152], [138], [128], [186]]\n",
    "y = [71,55,46,38,88]\n",
    "reg.fit(X,y)\n",
    "\n",
    "print(reg.predict([[165]]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X,y,color='black')\n",
    "\n",
    "y_pred = reg.predict(X)\n",
    "plt.plot(X,y_pred,color='blue', linewidth=3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.82021132])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.7.1 64-bit",
   "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": "3.7.1"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "31f8360559af503f7d1219287c80e0cc362e8a430fe9b8335f384415946613ec"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}