{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Regularized Linear Regression and Bias vs Variance\n", "\n", "In the first half of the example, we will implement regularized linear regression to predict the amount of water flowing out of a dam using the change of water level in a reservoir. In the next half, you will go through some diagnostics of debugging learning algorithms and examine the effects of bias v.s. variance.\n", "\n", "NOTE: The example and sample data is being taken from the \"Machine Learning course by Andrew Ng\" in Coursera." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# initial imports\n", "import numpy as np\n", "from matplotlib import pyplot as plt\n", "%matplotlib notebook\n", "import seaborn as sns" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# imports from my models designed for these examples\n", "from models.linear_regression import compute_cost, gradient_descent, compute_gradient, train_linear_reg, validation_curve\n", "from models.data_preprocessing import add_bias_unit, map_feature, feature_normalize" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Loading and Visualizing Data\n", "\n", "We start the exercise by first loading and visualizing the dataset. \n", "The following code will load the dataset into your environment and plot the data.\n", "\n", "We will begin by visualizing the dataset containing historical records on the\n", "change in the water level, x, and the amount of water flowing out of the dam,\n", "y.\n", "\n", "This dataset is divided into three parts: \n", "<li>A training set that your model will learn on: X, y\n", "<li>A cross validation set for determining the regularization parameter: Xval, yval\n", "<li>A test set for evaluating performance. These are “unseen” examples which your model did not see during training: Xtest, ytest.\n", "\n", "\n", "In the following parts, we will implement linear regression and use that to fit a straight line to the data and plot learning curves. Following that, we will implement polynomial regression to find a better fit to the data." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Loading & Visualizing Data\n", "(21, 1)\n" ] } ], "source": [ "# loading dataset\n", "print(\"Loading & Visualizing Data\")\n", "import scipy.io as sio # sio for loading matlab file .mat\n", "data = sio.loadmat('data/ex5data1.mat') # it geneates a dictionary of arrays found in the mat file\n", "X = data['X'] # (12, 1)\n", "y = data['y'][:, 0] # (12,)\n", "X_val = data['Xval'] # (21, 1)\n", "y_val = data['yval'][:, 0] # (21,)\n", "X_test = data['Xtest'] # (21, 1)\n", "y_test = data['ytest'][:, 0] # (21,)\n", "print(X_test.shape)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Plotting training data\n" ] }, { "data": { "image/png": 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tTXa7XeHh4RowYIAeeOABde3a1R1fCgAAAAAANxVLH1fxBU899ZS++uorl11v5cqVmj17ttOcI8ePH9fx48e1cuVKPf7445o8ebLL7gkAAAAAwM2IkKMUm81W4nVYWJjCwsJ0/Pjxal9r7dq1mjlzpiQpICBAw4cPV//+/VWrVi0lJiZqzZo1ys/P19tvv63g4GBNnDjRFV8CAAAAAAA3Ja8IOex2u65cuSKbzaYmTZp4tJbY2FhFRkYqJiZGMTExatOmjT799FM9//zz1bpOenq6Zs2aJel6wLFgwQINHjzYPH7PPfdoxIgReuSRR5Sbm6u33npLQ4YM8ZnHegAAAAAA8DYeCzk2btyodevWaefOnbpw4YKk68vK7t+/v0S7jIwMbdiwQZLUtm1bxcfHu7WuSZMmueQ6f/3rX5WVlSVJGjNmTImAo0iPHj305JNPas6cOSosLNTChQs1f/58l9wfAAAAAICbjeUhx8mTJ/X0009r37595r6Klo8NDQ3Ve++9p9OnTys8PFybNm2SYRhWlFojX375pbn98MMPl9tu5MiR+vOf/6ycnBxt3LhR165dU506dawoEQAAAAAAvxJg5c2OHz+ukSNHat++fXI4HHI4HAoMDFTt2rXLPScgIEAPPfSQHA6Hzp8/rx07dlhY8Y05cuSITp8+LUmKjIxUmzZtym3boEED9e7dW5KUk5Oj7du3W1IjAAAAAAD+xrKQw263a8qUKbp8+bIcDod69eqlZcuWac+ePbr//vsrPHfYsGHm9tatW91dao0dOnTI3O7evXul7Yu3KX4uAAAAAACoOsseV1m/fr0OHz4swzB0xx13aMGCBQoMDKzSua1atVKrVq2Ulpam5ORkN1dac0ePHjW3IyIiKm1fvM2xY8fcUhMAAAAAAP7OspDjq6++kiQFBwdr1qxZVQ44inTq1Elnzpy5oaVcrXb16lVzu1GjRpW2DwsLK/Ncqx05ckQBAZY+wQSLFBQUmP9NSkrycDWAd6BfAM7oF0BJ9AnAWU37hd1ud3VJJVgWcuzdu1eGYah3795q1qxZtc8vCgsyMjJcXZrL5eTkmNsVzTdSpPhEo9nZ2W6pqSpsNptsNpvH7g9rFH1TAvAf9AvAGf0CKIk+ATjzxn5hWciRnp4uqWqPb5QlKChIklRYWOiymlBSYGAgIzn8VPFvPkV9CbjZ0S8AZ/QLoCT6BOCspv3Cbre79cN1y0KOoKAg5efn33DSc/nyZUnXl5T1dvXq1TO38/LyKm1/7do1c7t+/fpuqakqoqKi1KBBA4/dH+6TlJSkgoICBQUFKTY21tPlAF6BfgE4o18AJdEnAGc17RdZWVlKSUlxQ2XXWfaxfZMmTSRJJ0+evKHzk5OTZRiGmjdv7sqy3KJhw4bmdlUerykKcEqfCwAAAAAAqs6ykOPWW2+Vw+FQUlKS+ehKVf3www9KS0uTJMXFxbmjPJfq2LGjuX3q1KlK2xdv06FDB7fUBAAAAACAv7Ms5Bg8eLCk68/vvPnmm1U+Lzc3V6+88or5+mc/+5nLa3O1Tp06mdtVWfK2eJvo6Gi31AQAAAAAgL+zLOT46U9/qujoaDkcDq1evVqvv/56pZONHDt2TGPHjtWRI0dkGIb69OmjXr16WVTxjYuKilKrVq0kSampqRWO5sjOztbOnTslSXXr1lV8fLwlNQIAAAAA4G8sCzkMw9CcOXNUt25dSdLixYs1dOhQvfrqqzp06JDZbsWKFVqwYIHGjx+vu+++W/v27ZMkhYSE6I9//KNV5dbYsGHDzO2//e1v5bZbtWqVueTsXXfdZf79AAAAAACA6rF0vdCYmBi98847Cg0NlcPhUFpamv72t78pISFBhmFIkn7/+99r4cKF+v7772Wz2eRwONS4cWO9++67atOmjZXl1siECRPMlVI+/PBDbdiwwanNnj179NZbb0mSatWqpd/+9reW1ggAAAAAgD+xbAnZIv3799fatWs1d+5c/etf/1JhYWG5bQMCAjRs2DBNmzZNLVu2tKS+kydP6uOPPy6xr/jyNvv379cbb7xR4ni/fv3Uv3//EvuaNGmiGTNmaPr06bLb7Zo8ebKGDx+u2267TQEBAUpMTNRnn31mLjE7ZcoURUZGuumrAgAAAADA/1keckhS8+bNNX/+fP3ud7/T1q1btXv3bp0/f15Xr15V3bp11bRpU8XGxmrgwIGKiIiwtLYzZ87ovffeK/d4SkqK05q+tWrVcgo5JOnee+9Vbm6u5syZo7y8PH3++ef6/PPPS7QJDAzUpEmTNGnSJNd8AQAAAAAA3KQ8EnIUad68uUaMGKERI0Z4sgy3Gj16tAYMGKAVK1Zoy5YtSktLk8PhUHh4uPr166cHH3xQ3bp183SZAAAAAAD4PI+GHN6ob9++TiM1aqp9+/aaPn26pk+f7tLrAgAAAACA/7As5Hj55ZclXQ8Riq88UlVfffWV/u///k+GYeill15ycXUAAAAAAMDXWRZyrFixQoZhqFatWjcUcuzatcu8BiEHAAAAAAAozdIlZAEAAAAAANzF50IOwzA8XQIAAAAAAPBCPhNyXL58WZJUr149D1cCAAAAAAC8kU+EHDk5Oeakoy1btvR0OQAAAAAAwAu5ZeLRxYsXl3ts3759FR4vrrCwUOfOndPmzZt17tw5GYahnj17uqpMAAAAAADgR9wScsyfP7/MuTMcDod2796t3bt339B1AwMDNXr06JqWBwAAAAAA/JDblpB1OBzV2l+Zpk2baubMmerSpUtNygIAAAAAAH7KLSHHo48+6rRv8eLFMgxD3bp104ABAyq9hmEYCg4OVqNGjRQdHa3evXsrMDDQHeUCAAAAAAA/4JaQY+rUqU77iubh6NmzZ5nHAQAAAAAAasJtj6uUFhsbK8MwFBERYdUtAQAAAADATcSykGPVqlVW3QoAAAAAANyEAjxdAAAAAAAAgCtYNpIDAAAA8BUFmZnaPm58iX3xy5YoKDTUQxUBAKrCoyFHfn6+Dh06pIyMDGVnZ8tut1fpvOHDh7u5MgAAAAAA4Gs8EnJ89dVX+uCDD7Rr1y7ZbLZqnWsYBiEHAAAAAABwYmnIkZ+fr2nTpunf//63JMnhcJTb1jCMCo8DAAAAAAAUZ2nIMXPmTH311VfXb1yrlnr37q2zZ8/qxIkTMgxDw4YNU3Z2ts6cOaPU1FQ5HA4ZhqG6detq0KBBMgzDynIBAAAAAIAPsSzkSE5O1meffSbDMNS6dWstWbJEbdu21R/+8AedOHFCkvT666+b7TMyMrRixQotWrRIubm5ys/P12uvvaZ69epZVTIAAAAAAPAhli0hu2bNGnN79uzZatu2bYXtGzVqpMcee0yrV69WkyZNtHHjRv2///f/3F0mAAAAAADwUZaFHDt37pQkRUREKD4+vsrnRUVFafbs2XI4HPryyy+1ZcsWd5UIAACAm0hBZmYFf66U0f5KhecAADzPssdVzp49K8MwFBMTU2J/8Xk28vPzFRwc7HTuwIED1bFjRx07dkyfffaZbr/9drfXCwAAAP+2fdz4arXfNeWpCo/ftvaTmpQDAHABy0ZyZGdnS5LCwsJK7K9du7ZTm7Lccsstcjgc2rt3r3sKBAAAAAAAPs2ykKNOnTqSpMLCwhL7GzZsaG6fOXOm3POLRnycP3/eDdUBAAAAAABfZ1nI0aJFC0lSZqnnFdu3b29u7969u9zzU1NT3VIXAAAAAADwD5bNyREdHa0jR47o2LFjJfbHxsaa26tXr9ZDDz2kgICS2cv333+vvXv3yjAMRUREWFIvAAAA/Fv8siXlHivIvOI0B0fPt99UUGiIu8sCANSAZSM54uLiJEnHjh0rMZqjVatW6tmzpxwOh1JSUvTEE0/oyJEjkqS8vDx9+eWXmjZtmtn+jjvusKpkAAAA+LGg0NAK/jiHGUGhIRWeAwDwPMtCjkGDBkmS7Ha7vv322xLHpk6das65sWHDBv3yl79UTEyMevTooWeeeUbp6emSpJCQED388MNWlQwAAAAAAHyIZSFHRESExowZo7vuuktnz54tcSwuLk4zZsyQYRhyOBxyOByy2WzmtsPhUGhoqBYuXKimTZtaVTIAAAAAAPAhls3JIUkzZswo99jo0aPVq1cvLVmyRD/88IMuXryogIAAtW7dWnfeead+/etfq3nz5hZWCwAAAAAAfImlIUdlunTporlz50qSHA6H+QgLAAAAAABAZSx7XKW6CDgAAAAAAEB1eG3IAQAAAAAAUB0uf1xl1KhR6tOnj+Li4tS7d281aNDA1bcAAAAA3CooNFS3rf3E02UAAKrJ5SHH7t27tWfPHv3lL39RQECAOnfurPj4eMXFxalPnz4KZQ1xAAAAAADgBm6beLRoGdgDBw7owIEDWrp0qQzDUFRUlPr06WP+adKkibtKAAAAAAAANxGXhxzjxo1TQkKCUlJSZLPZ5HA4zGMOh0OHDx/W4cOH9dFHH0mS2rdvXyL0aNGihatLAgAAAAAANwGXhxwvvPCCJCkrK0u7du1SQkKCduzYoeTkZBUUFJQIPSTp+PHjOn78uFavXi1Jat26dYnQo02bNq4uEQAAAAAA+CG3Pa7SoEED3X777br99tslSfn5+dqzZ4927NihhIQE7dq1S7m5uU6hx+nTp3X69Gl99tlnkqTmzZub83n06dNHHTt2dFfJAAAAAADAh7kt5CgtODjYDCokyWazad++feZIj8TERGVmZjqFHmfPntX69eu1fv16SVKTJk303XffWVU2AAAAAADwEZaFHKUFBgYqNjZWsbGxGj9+vCTp0KFD5kiPhIQEXbhwQZJKBB+XLl3ySL0AAAAAAMC7eSzkKEunTp3UqVMnjRkzRpK0Z88evfvuu9q0aZMMw3Aa5QEAAAAAAFDEq0KOCxcumCM5duzYodTUVDkcDhmG4enSAAAAAACAl/NoyHHq1Ckz0EhISNCPP/5oHis9aiM0NFQ9e/ZUXFyc1WUCAAAAAAAfYGnIcfTo0RKhxtmzZ81jpUONVq1aqVevXoqLi1Pv3r0VHR1tZakAAAAAAMDHuDXkOHjwoHbs2KEdO3Zo586dSk9PN48VDzUMw1B0dLR69+5thhotW7Z0Z2kAAAAAAMDPuDzk+Mtf/qKEhAQlJibq6tWr5v7ioUZQUJBuueUWM9Do1auXQkJCXF0KAAAAAAC4ibg85Jg3b57TSigNGzZUjx49zFAjNjZWwcHBrr41AAAAAAC4ibntcRXDMNSyZUtNmDBB999/v2rXru2uWwEAAAAAALh3To60tDS98sormjt3rrp3727OudGrVy/Vr1/fnbcGAAAAAAA3GZeHHM8884x27txZYk6OvLw87dy5Uzt37tSiRYsUEBCgzp07Ky4uzvzTuHFjV5cCAAAAAABuIi4POSZOnCjp+kSjRaurJCQkKCEhwVxdxWaz6cCBAzpw4IA++OADSVK7du3Up08fc7RHRESEq0sDAAAAAAB+zK1zcnTt2lVdu3bVuHHjJEmpqalKSEgwl5RNS0sz2x8/flwnTpzQxx9/LEkKDw8vMdIjOjraXaUCAAAAAAA/4NY5OUqLjIxUZGSkHnzwQUnSqVOnzFEeO3bs0IkTJ8y2586d0xdffKEvvvhCkhQSEqJevXqpT58+Gj9+vJVl37CxY8dq+/btVW6/YcMGRrAAAAAAAHCDLA05SouIiFBERITuueceSdLFixfNx1t27Nihw4cPm0vRZmZm6ptvvtGmTZt8JuQAAAAAAADW8WjIUVrTpk01bNgwDRs2TJK0Z88evfvuu9q0aZMMwzADD1+0cOHCSts0adLEgkoAAAAAAPBPXhVypKSkmKM4EhISdOnSJUnX5/fwdUOGDPF0CQAAAAAA+DWPhRw2m0379u0zQ43ExERduXLFPF7eqA2WmgUAAAAAAGWxLOTIz8/Xnj17zFEau3fvVm5urnm8vFCjefPmiouLU58+fdSnTx9FRkZaVTIAAAAAAPAhbgs5cnJylJiYaIYaycnJKigoMI+XF2q0bt1a8fHxiouLU3x8vNq0aeOuEgEAAAAAgB9xecjx6quvaseOHTp48KBsNpu5v7xQo0OHDuYojT59+qhFixauLskr/OY3v9H+/fuVkZGhunXrKjw8XD179tTdd9+tfv36ebo8AAAAAAB8nstDjvfff7/clVAMw1B0dLQ5UqNPnz43zYoimzZtMrcLCgp05coVHTlyRKtXr1a/fv302muvKTw83HMFAgAAAADg4wyHi9dl7dKli7kdGBiorl27qk+fPoqLi1NcXJxCQ0NdeTuvNnbsWKWkpGjAgAG65ZZb1Lx5cwUGBurcuXP6/vvvtXnzZjMMat26tVauXKlmzZpZVl9WVpZSUlLM14GBgQoICLDs/rBO8UfFgoKCPFgJ4D3oF4Az+gVQEn0CcFbTfmG320s89dG5c2c1aNDAJbVJbgg5HnroIfPRk169eql+/fquvLxP2bVrl2JiYhQcHFzm8eTkZD3xxBM6c+aMJGngwIFavHixZfWVDjkAAAAAALCS14ccqJ7U1FTdc889ys/PlyStXr1asbGxltybkRw3Dz6FAJzRLwBn9AugJPoE4MzbR3JYtoQsyhYZGan/+q//0urVqyVdn7vDqpCjtKioKJe+ueA9kpKSVFBQoKCgII+9vwBvQ78AnNEvgJLoE4CzmvYLdz9RwMf2XqBv377mdmpqqgcrAQAAAADAdxFyeIHGjRub21evXvVgJQAAAAAA+C5CDi+QkZFhbjds2NCDlQAAAAAA4LsIObzAtm3bzO0OHTp4sBIAAAAAAHwXIYeHHTt2TGvXrjVf33nnnR6sBgAAAAAA30XI4SbLli1TYmJihW3279+vCRMmKC8vT5L0k5/8RLfeeqsV5QEAAAAA4HdYQtZNfvjhB/3xj39U27Zt1b9/f3Xq1ElhYWEKCAjQ+fPn9cMPP+jbb7+V3W6XJLVu3VqzZ8/2cNUAAABVU5CZqe3jxpfYF79siYJCQz1UEQAAhBxu9+OPP+rHH3+ssM1PfvITzZ49W82bN7eoKtQEP9QBAAAAgHci5HCT6dOn684771RSUpIOHjyoS5cuKSMjQwUFBWrQoIFat26tnj176pe//CWPqAAAAAAA4AKEHG7Stm1btW3bViNHjvR0KQAAAAAA3BSYeBQAAAAAAPgFQg4AAAAAAOAXCDkAAAAAAIBfYE4OAAAAlKkgM7OCY1eqtK84ViIDALgbIQdQBn6oAwBATkumV2bXlKcqPH7b2k9qUg4AAJUi5ADKwA91AAAAAOB7mJMDAAAAAAD4BUIOAAAAAADgF3hcBQAAAGWKX7ak3GMFmVecHtfs+fabCgoNcXdZAACUi5ADKAM/1AEAUP2Js4NCQ5hsGwDgUYQcQBn4oQ4AAAAAfA8hB7xeQWam02on8cuWECoAAAAAAEpg4lEAAAAAAOAXCDkAAAAAAIBf4HEVAD6Fx5cAAAAAlIeRHAAAAAAAwC8wkgMAAADVFhQaqtvWfuLpMgAAKIGQA6gmfqgDAAAAAO9EyAGvUJCZWcGxK1XaVxzzMwAAAADAzYeQA16h9ESSldk15akKjzPSAgAAAABuPkw8CgAAAAAA/AIjOQB4HR5fws2MZZKd8XcCAACqipADgNfh8SUAAAAAN4KQA14hftmSco8VZF5x+iW259tvKig0xN1lAQAAAAB8CCEHvEJ1hxwHhYYwTBkAAAAAUAITjwIAAAAAAL/ASA4AXofHlwAAAADcCEIOAF6Hx5cAAAAA3AhCDgAALMYyyc74OwEAAK5AyAEAgMVYJtkZfycAAMAVmHgUAAAAAAD4BUZywOsFhYbyiRwAAAAAoFKM5AAAAAAAAH6BkRwAAFiMZZKd8XcCAABcgZADgE/h8SX4A5ZJdsbfCQAAcAUeVwEAAAAAAH6BkRwA4CUKMjOdltGMX7aET6sBAACAKmIkBwAAAAAA8AuEHAAAAAAAwC8QcgAAAAAAAL9AyAEAAAAAAPwCE49heYqiAAAgAElEQVQCAOBFWCbZGX8nAACgqhjJAQAAAAAA/AIjOQDAQgWZmRUcu1KlfcWxvCwAAADwH4QcAGCh7ePGV6v9rilPVXicIfwAAADAf/C4CgAAAAAA8AuEHAAAAAAAwC8QcgAAAAAAAL/AnBwAYKH4ZUvKPVaQecVpDo6eb7+poNAQd5cFAAAA+AVCDgCwUHVXQwkKDWEFFQAAAKCKeFwFAAAAAAD4BUIOAAAAAADgFwg5AAAAAACAXyDkAAAAAAAAfoGJRy2yYcMGrV27Vnv37tWFCxfUoEEDtWvXTkOGDNGoUaPUoEEDT5cIAAAAAIBPI+Rws+zsbE2bNk0bN24ssT89PV3p6enatWuX/v73v+vNN99Ujx49PFQlAAAAAAC+j5DDjWw2m5588klt2bJFktS0aVONHDlSUVFRyszM1Oeff67ExESlpaVp4sSJWr58uSIjIz1cNQBPCQoN1W1rP/F0GQAAAIDPIuRwo9WrV5sBR1RUlJYuXaqmTZuax8eMGaNXX31VS5YsUWZmpmbOnKkPP/zQU+UCAAAAAODTmHjUTWw2mxYsWGC+njt3bomAo8i0adPUtWtXSVJCQoK+++47y2oEAAAAAMCfEHK4yY4dO3ThwgVJUnx8vGJiYspsFxgYqLFjx5qv169fb0l9AAAAAAD4G0ION9m8ebO5PXDgwArbFj9e/DwAAAAAAFB1hBxucujQIXO7e/fuFbZt1qyZWrZsKUm6ePGi0tPT3VobAAAAAAD+iJDDTY4dO2ZuR0REVNq+eJujR4+6pSYAAAAAAPwZq6u4ydWrV83tRo0aVdo+LCyszHOtdOTIEQUEkHv5o4KCAvO/SUlJHq4G8A70C8AZ/QIoiT4BOKtpv7Db7a4uqQRCDjfJyckxt2vXrl1p++JtsrOz3VJTZWw2m2w2m0fuDesUfVMC8B/0C8AZ/QIoiT4BOPPGfkHIAVNgYCAjOfxU8W8+QUFBHqwE8B70C8AZ/QIoiT4BOKtpv7Db7W79cJ2Qw03q1aunzMxMSVJeXp5q1ar4rzovL8/crl+/vltrK09UVJQaNGjgkXvDvZKSklRQUKCgoCDFxsZ6uhzAK9AvAGf0C6Ak+gTgrKb9IisrSykpKW6o7Do+tneThg0bmtsZGRmVtr98+XKZ5wIAAAAAgKoh5HCTDh06mNunTp2qtH3xNh07dnRLTQAAAAAA+DNCDjfp1KmTuZ2cnFxh24sXLyotLU2S1KRJEzVu3NittQEAAAAA4I8IOdzk9ttvN7c3b95cYdtvv/3W3B40aJDbagIAAAAAwJ8RcrhJfHy8mjVrJknavn279u3bV2Y7m82mDz74wHw9fPhwS+oDAAAAAMDfsLqKmwQGBurxxx/X73//e0nSc889p6VLl6pJkyYl2s2bN08HDhyQJPXq1avECBB3K71sT05OjmX3hrXsdrv536ysLA9XA3gH+gXgjH4BlESfAJzVtF+U/r3T1cvJGg6Hw+HSK8JUWFioiRMnauvWrZKkZs2aaeTIkYqKitLly5e1fv167dy5U5IUEhKijz76SNHR0ZbVd/78eZ08edKy+wEAAAAAUFybNm0UHh7ususRcrhZVlaWpk2bpm+++abcNi1atNAbb7yhXr16WVgZIQcAAAAAwLMIOXzU119/rbVr1yo5OVmXLl1S/fr11bZtWw0dOlSjRo1Sw4YNLa+JkAMAAAAA4EmEHHCZ/Px8Xb582Xxdu3ZtBQYGerAiAAAAAIA/s9lsysvLM1+HhYUpODjYZdcn5AAAAAAAAH6BJWQBAAAAAIBfIOQAAAAAAAB+gZADAAAAAAD4BUIOAAAAAADgFwg5AAAAAACAXyDkAAAAAAAAfoGQAwAAAAAA+AVCDgAAAAAA4BcIOQAAAAAAgF8g5AAAAAAAAH6BkAMAAAAAAPgFQg4AAAAAAOAXCDkAAAAAAIBfIOQAAAAAAAB+gZADAAAAAAD4BUIOAAAAAADgFwg5AAAAAACAXyDkAAAAAAAAfoGQAwAAAAAA+AVCDgAAAAAA4BcIOQAAAAAAgF8g5AAAAAAAAH6BkAMAAAAAAPiFWp4uAIC1UlNTde+99yovL8/cl5KSUqVz7Xa71q1bp/Xr1+vgwYNKT09XWFiYOnbsqJ///Oe6//77FRwc7K7SgRo7ePCgtm7dqsTERB0+fFjnz59XYWGhQkJCFBkZqQEDBui+++5TeHh4la9Jv4Cv27Bhg9auXau9e/fqwoULatCggdq1a6chQ4Zo1KhRatCggadLBGokKytLW7du1bZt27R//34dP35cV69eVe3atRUeHq7Y2Fjdfffduv3222UYRpWueeLECa1YsUJbtmxRWlqa7Ha7wsPDNWDAAD3wwAPq2rWrm78qwH2mT5+uNWvWmK8nT56sKVOmVHqet/QLw+FwOCy5EwCPs9vtGj16tHbt2lVif1VCjgsXLuiJJ55QYmJiuW2io6P19ttvq0OHDjWuFXClK1euaOTIkTp+/HilbevWratnn31WY8aMqbQt/QK+LDs7W9OmTdPGjRvLbdOyZUu9+eab6tGjh4WVAa7z/vvv64033ijx4U554uLi9Nprr6lVq1YVtlu5cqVmz56ta9eulXk8MDBQjz/+uCZPnnxDNQOe9O2332rixIkl9lUl5PCmfsFIDuAmsmzZMu3atUv16tVTTk5Olc/Lzs7Wo48+qgMHDkiS2rRpo/vvv19t2rTR+fPntWbNGqWkpOjw4cOaMGGCVq1apaZNm7rrywCqLS8vzww4AgMD1bt3b8XFxalNmzaqW7euzpw5o3/+859KSkpSbm6uZs2apWvXrmnChAnlXpN+AV9ms9n05JNPasuWLZKkpk2bauTIkYqKilJmZqY+//xzJSYmKi0tTRMnTtTy5csVGRnp4aqB6jt27JgZcDRv3lwDBgxQTEyMmjRpory8PO3evVv/+Mc/lJOTo4SEBI0dO1arVq1SkyZNyrze2rVrNXPmTElSQECAhg8frv79+6tWrVpKTEzUmjVrlJ+fr7ffflvBwcFOvywC3iwrK0svvfSSJFXr9wVv6xeM5ABuEj/++KN+9atfKTc3V88//7z+9Kc/mccqG8kxf/58LVq0SJIUHx+v9957T/Xr1zePFxQU6He/+52++OILSdKvfvUrvfbaa274KoAbc+HCBd1999165JFHKnwcZdGiRZo/f74kKSgoSOvXr1e7du3KbEu/gC9bsWKF+YNsVFSUli5d6hTCvfrqq1qyZImk659wf/jhh5bXCdTUSy+9pFOnTmn8+PHq37+/AgKcpyQ8ffq0JkyYoGPHjkmSRowYUeLnpCLp6ekaOnSosrKyFBAQoAULFmjw4MEl2uzevVuPPPKIcnNzVatWLa1bt04dO3Z0zxcHuNjMmTO1cuVKtWzZUj//+c/1/vvvS6p4JIc39gsmHgVuAg6HQy+++KJyc3MVGxurcePGVfncy5cva+nSpZKk2rVra968eSV+kZOu/zL4yiuvqFmzZpKkdevWKTU11XVfAFBDYWFh2rhxox577LEK59uYOHGihgwZIul6SPGPf/yjzHb0C/gym82mBQsWmK/nzp1b5iijadOmmc9PJyQk6LvvvrOsRsBVnn76af31r3/VbbfdVmbAIUmtW7fWm2++ab7+8ssvlZub69Tur3/9q7KysiRJY8aMcfpFTpJ69OihJ598UpJUWFiohQsXuuLLANzu+++/16pVqyRdDwdL/1xTHm/sF4QcwE1g+fLl2r59u/lLV3n/yJdlw4YN5jDP4cOHq3nz5mW2q1+/vh544AFJ10OVL7/8suaFAy4SFBRU5X+shw8fbm6XN8qJfgFftmPHDl24cEHS9VFIMTExZbYLDAzU2LFjzdfr16+3pD7AlcLCwqrUrkuXLubcSbm5uTpx4oRTm+Lfwx9++OFyrzVy5EjVq1dPkrRx48Zy5ygAvEVubq5mzJghh8Oh4cOH684776zyud7YLwg5AD935swZzZs3T5I0YcIEde7cuVrnb9682dweOHBghW0HDRpU5nmALym+kkR5/wDTL+DLqvP+LX6c9y/8XfHv/6UnKj1y5IhOnz4tSYqMjFSbNm0qvE7v3r0lSTk5Odq+fbsbqgVcZ/78+Tp58qTCwsL04osvVvk8b+0XhByAn5sxY4ays7PVvn17/fa3v632+YcOHTK3u3fvXmHbbt26KTAwUJJ0+PBhMeUPfFHx0RvlzbBPv4Avq877t1mzZmrZsqUk6eLFi0pPT3drbYCn5Ofnl1iBq/T3/+r0m9Jtip8LeJvExERzzqXf/e531Zok3Vv7BSEH4Mc++eQTfffddzIMQ6+88oqCg4Ordb7dbtePP/4o6fqw5aIfdMsTFBRkDtvPycnRuXPnbqxwwEMKCgr0ySefmK/vuOMOpzb0C/i6oskVJSkiIqLS9sXbHD161C01AZ72+eef6+rVq5KkmJgYcz6lIsXf+9XtN8X7HOBN8vLy9MILL8hut6t///667777qnW+t/YLQg7AT507d05z5syRJD3wwAPq06dPta+Rk5OjwsJCSVLDhg1Vq1blq04Xf/b1ypUr1b4n4En/+7//a36S17Vr1zJDDvoFfF3RL3KS1KhRo0rbF3//Fj8X8Bfp6enmo72S9Nhjjzm1od/AH7311ls6duyY6tSpo1mzZlX7fG/tF4QcgJ96+eWXdeXKFYWHh+vZZ5+9oWtkZ2eb27Vr167SOcXbFT8f8HabNm0yZ/sOCgrSrFmzypykl34BX5eTk2NuV+U9zPsX/iw/P19TpkzRpUuXJElDhgzR0KFDndpVt9/UqVPH3KbfwBslJSXpb3/7myRpypQpatu2bbWv4a39ovKPnwC43NixY1022c7rr7+uX/ziFyX2rVu3Ths3bpR0fb3rhg0buuRegDu5u19UJDk5Wc8884zsdrsk6bnnnlNsbKxLagEAeCe73a4XXnhBCQkJkqS2bdtq9uzZHq4KcL/8/Hy9+OKLstlsiomJ0a9//WtPl+RSjOQA/MylS5f0xz/+UZI0dOjQMj+NqKriS26WnmW8PMXbVXXJTsCTDh48qP/5n/8xP1F4/PHHSyybWRr9Ar6uaAk/qWrvYd6/8EcOh0MvvfSS1q1bJ+n6RKPvv/++QkNDy2xf3X5TfHUu+g28zbvvvqtDhw4pMDBQf/jDH8wJ0qvLW/sFIzkAD/jZz36mLl26uORaRWu6F5k1a5YyMjLUsGFDzZw5s0bXrlevnmrVqqXCwkJdvXpVhYWFlc4/cPnyZXM7JCSkRvfHzcWd/aI8KSkpeuSRR8z37W9+8xs9+eSTFZ5Dv4Cva9iwoTIzMyVJGRkZlf6gWfz9y8hA+AOHw6GXX35Zq1atkiS1aNFCS5curXDixOLv/YyMjErvQb+Btzp48KAWL14sSXrkkUcUExNzw9fy1n5ByAF4wH//93+75bpXr17VP//5T0lSVFSUPv744yqd984775jbDzzwgLl0VEBAgNq2baujR4/KZrMpLS2twvWvCwoKzJUj6tWrZ64oAVSFu/pFeYoCjqJ/lB999FE988wzlZ5Hv4Cv69Chg06dOiVJOnXqVKUz4he1laSOHTu6tTbA3RwOh37/+99rxYoVkqTmzZtr2bJllc5HUPy9X7xPlKd4m6oG74AVPv30UxUUFCggIEBBQUElfg8obseOHSW2i9p16NBBw4YNk+S9/YKQA/AjDofD3N61a5d27dpVpfPeeustc/vOO+8ssT52p06dzOWhkpOTK/xlbv/+/bLZbJKuhyyGYVSrfsAqRQFHenq6JGn8+PGaNm1alc+nX8CXderUSVu2bJF0/f3br1+/cttevHhRaWlpkqQmTZqocePGltQIuENRwLF8+XJJUnh4uJYtW6Z27dpVem6nTp3M7eTk5ErbF28THR19A9UC7lH0+4Ldbtd7771XpXO2bdumbdu2SZIGDx5shhze2i+YkwNAhW6//XZzu+iH4vJ8++235vagQYPcVhNQE6UDjl//+td67rnnqnUN+gV8WfH37+bNmytsy/sX/qJ0wNGsWTMtW7ZM7du3r9L5UVFRatWqlSQpNTW1wk+ts7OztXPnTklS3bp1FR8fX7PiAS/lrf2CkAPwIyEhIUpJSanSn+KK7+/atWuJY4MHDzaXhFq/fr057L607Oxs89lWwzDMhBfwJocPHy4RcDzyyCOaPn16ta9Dv4Avi4+PV7NmzSRJ27dv1759+8psZ7PZ9MEHH5ivhw8fbkl9gDvMmjXLKeCo7nD54t/Di5beLMuqVavMpTXvuusu1a1bt/oFA27y4osvVul3hcmTJ5vnTJ482dxf+vEWb+wXhBwAKtSoUSNzpYm8vDxNmzbNaV3rwsJCzZgxQxcuXJAk3X333YqMjLS8VqAiR44c0cMPP1wi4Hj++edv6Fr0C/iywMBAPf744+br5557TpcuXXJqN2/ePB04cECS1KtXrxIjQABf8oc//EEfffSRpP8EHDcyv8yECRPMiXo//PBDbdiwwanNnj17zMeAa9Wqpd/+9rc1qBzwft7YLwxH8Yf4Adw0OnfubG6XHtlRWlZWlkaPHm22a9OmjR544AFFRETo/Pnz+vTTT81jrVq10sqVKxUeHu6+4oFqOnv2rO677z5dvHhRktStW7cq/QNbp04d/eQnPynzGP0CvqywsFATJ07U1q1bJV3/xW/kyJGKiorS5cuXtX79enNYcUhIiD766CPmFYBPeuONN8x5BwzD0DPPPFOlgKNbt27mMPzi1qxZY44ADAgI0PDhw3XbbbcpICBAiYmJ+uyzz8ylNJ9++mlNmjTJhV8NYJ23335bCxYskHR9JMeUKVPKbett/YKQA7hJVSfkkKRz587piSee0O7du8ttExUVpT//+c98Wg2vs23bNo0bN67a57Vu3VobN24s9zj9Ar4sKytL06ZN0zfffFNumxYtWuiNN95Qr169LKwMcJ2xY8dq+/bt1T7vT3/6k0aMGFHmsY8++khz5swxf2krLTAwUJMmTdITTzxR7fsC3qI6IYfkXf2C1VUAVEnz5s21fPly/eMf/9Dnn3+ulJQUZWRkKDQ0VB07dtTPf/5zjRw5UsHBwZ4uFbAM/QK+rEGDBnrvvff09ddfa+3atUpOTtalS5dUv359tW3bVkOHDtWoUaPUsGFDT5cKeJXRo0drwIABWrFihbZs2aK0tDQ5HA6Fh4erX79+evDBB9WtWzdPlwlYypv6BSM5AAAAAACAX2DiUQAAAAAA4BcIOQAAAAAAgF8g5AAAAAAAAH6BkAMAAAAAAPgFQg4AAAAAAOAXCDkAAAAAAIBfIOQAAAAAAAB+gZADAAAAAAD4BUIOAAAAAADgFwg5AAAAAACAXyDkAAAAAAAAfoGQAwAAAAAA+AVCDgAAAAAA4BcIOQAAAAAAgF8g5AAAAAAAAH6BkAMAAAAAAPgFQg4AAAAAAOAXCDkAAH5l7Nix6ty5szp37qxt27Z5uhzUwPTp083/l59++qmny4GPOnXqlPk+uuuuuzxdjtfg7wWAv6rl6QIAAJCkrKwsbd68WVu3btXevXuVnp6ujIwMBQUFKTQ0VO3bt1f37t111113qWfPnp4uFwAAAF6IkAMA4FG5ublaunSplixZoszMTKfjBQUFysnJUVpamr7//nstWrRI7du315QpU/SLX/xChmF4oGrAP3Tu3NncTklJ8WAlAAC4BiEHAMBjzpw5o0mTJjn9ctWqVSt17txZjRo1kt1u18WLF3Xw4EFdvHhRknT8+HFNnTpVaWlpevTRRz1ROgAAALwQIQcAwCNOnTqlUaNG6cKFC5IkwzD0i1/8QpMmTVJ0dLRTe4fDoeTkZP3973/XunXrZLfbde3aNavLhoXmzJmjOXPmeLoMAADgQ5h4FABgufz8fD355JNmwFG7dm0tWLBA8+fPLzPgkK6HILGxsZo7d67Wrl2rTp06WVkyAAAAfAAjOQAAlvvLX/6ivXv3mq/nzJmjIUOGVPn8Tp06aeXKlTpw4IA7ygMAAICPIuQAAFjq2rVr/7+9O49q6kz/AP4FZEcWKeJeEEUQBRRFsY6ixRUHRY/SU8XtdDxadTqOo2DHhTMdF7rY06rVTq2izlRkFLAuqEWrgLKJAhbZ6ggKVVzYJIAhkN8fnNzfDWRTESt+P3/dJG/ufZPcKPfJ8z4PDh06JNyeOHEipk6d+sz7MTMzg5eXl05jKysrERUVhbNnz6KkpAR1dXWws7PDiBEjsHDhQp2yQurr65GUlISUlBTk5OSguLgY1dXVMDQ0hI2NDVxdXeHr64vp06fDyMhI475SU1Mxf/58AIC3t7fwfiQnJyMqKgrZ2dl48OABzMzM0K9fP0yZMgVBQUEwNDTU6fXW19cjMjISZ86cwe3bt1FXV4euXbvC3d0ds2fPho+PDwBg/PjxKC0tBQCcP38evXr10rjf2tpaxMbGIiEhAfn5+SgvL4e+vj7s7Ozg5eWFgIAAYd9tITQ0FDExMQCArVu3YubMma3G7NixAzt37gQArFixAitXroRMJsPJkycRGxuLW7duoaKiAtbW1sLrHzdu3AvPLTMzE0FBQQAADw8PREVFqRz39OlTDBs2DFKpFADg5uamth2uVCrF8OHDUV9fD0NDQ1y9ehUmJiZKYxoaGpCSkoLk5GTcuHEDt2/fRlVVFfT09GBtbQ1nZ2eMHj0as2fPhrm5ucrjiM8/MXERUjFN58a9e/cQHR2Ny5cv486dO6isrISZmRl69OgBHx8fzJkzB46Ojiqfq6Dqc66urkZMTAzOnTuHO3fu4PHjx2hsbER6ejosLS017q8tVFRUICYmBomJifjf//6H8vJyGBsbo2vXrhgxYgRmzpyJwYMHq3zuuXPnsHLlSgCAg4MDzp49q9Mx79+/j3HjxqGpqQkGBga4dOkS7OzsVI5taGjAqVOn8PPPPwvdqORyObp06QJPT09MmTIFfn5+LMxMRG8kBjmIiKhdnTlzBuXl5cLthQsXvtTjZWRkYNWqVSgrK1O6v6SkBCUlJYiNjUVYWBjmzJmjdh9ZWVlYuHAhamtrWz2m6P5SWlqK+Ph47N69Gzt37sTAgQN1nqNUKsUnn3zS6kJZKpXi6tWruHr1KqKjo7F371506dJF477y8/OxYsUK3LlzR+n+u3fv4u7duzh16hSCgoKwYcMGnecHAHFxcdi8ebOwxEisuLgYxcXFiI6Oxrhx4/DZZ5+hc+fOz7T/tlJWVoaPPvoI169fV7r/4cOHOH/+PM6fP4+ZM2di8+bN0Nd//lW7gwYNgpmZGWpra5GTkwOJRKIyqHD9+nUhwAEAeXl5ePLkicr3Jzs7W6gz4+7u3irAce/ePcyYMQOVlZUq51RWVoaysjIkJiZi9+7d2L59O955553nfo2aNDU1YceOHfj+++/x9OlTpceqqqpQVVWF3NxcHDx4EB988AH+8pe/6HzBnZGRIRQWfhX+85//4Msvv8STJ0+U7pdKpXjy5Alu3bqFw4cPY+bMmQgLC2sV1PT19YWlpSWqq6tRVFSE7OxsuLu7az2uotYQAPj4+KgNcKSmpmL9+vWtvuMAUFpaitLSUpw6dQqenp74+uuvYW9vr+tLJyLqEBjkICKidpWamips9+jRQ+dsjOdRWFiIL774ArW1tbC1tcWwYcNgbW2NsrIypKSkoL6+Ho2Njdi0aROcnZ3h6empcj9VVVVCgMPW1hb9+vVDt27dYGpqivr6ehQXF+PGjRuQyWQoLS3FvHnzEBMTg7fffluneW7cuBExMTHQ19eHh4cHHB0dIZfLkZmZidu3bwMAcnJyEBISgu+++07tfoqLi7Fw4UKlIJKzszNcXV2hr6+P3Nxc5OXl4ciRI2p/5VclIiIC27Ztg1wuBwBYWFjA09MT3bp1Q1NTEwoLC/HLL79ALpfj559/RnBwMA4fPgxTU1Odj9EWamtr8cEHH6CgoACmpqbw8vJC9+7dIZFIkJqaisePHwMAoqOj4ejoiCVLljz3sTp16oShQ4ciKSkJMpkMV69exdixY1uNS0tLU7qtyEYYP358q7Hi74a3t7fK16cIcFhZWaFfv37o0aMHzMzM0NDQgJKSEmRlZeHp06eorKzEkiVLcOjQIQwdOlRpP/b29pg7dy6A5gt6BcV9LVlYWLR6DatWrVLKULC3t4e7uzu6dOkCiUSC7Oxs3LlzBzKZDHv27EF5eTk++eQTlfsXKy4uxpYtW/DkyROYm5tj+PDh6Nq1K6qqqnD16lWtz39RmzdvxsGDB4XbNjY28PT0hJ2dHZ4+fYrc3FwUFBRALpfj2LFjePDgAf71r38pBcyMjIwwefJkIWh54sQJnYMcCgEBASrHxMXFYc2aNWhoaAAAmJiYwMPDAz179oS+vj6KioqQmZkJmUwmZBsdPXoUb7311nO9H0REryMGOYiIqF2JL1R0+cP/RYSHh6OxsRGhoaEIDg5Gp07//9/evXv3sGTJEhQUFKCpqQnbt29XurgRs7KywtKlS+Hv7692acvjx48RHh6O48ePQyKRYNOmTYiIiNA6x8zMTKSlpWHw4MEIDw+Hk5OT8JhcLsfBgwexZcsWAEBCQgLS09MxfPjwVvuRy+X4+9//LgQ4rK2t8fnnn+MPf/iD0rjk5GSsXr0a+/fvV3o/1ElOTkZ4eDjkcjkMDQ3x5z//GcHBwa0CGLm5ufjb3/6GX3/9Fbm5uQgPD0dYWJjW/belf//735BKpQgMDERoaCisra2Fx+rq6rB+/XqcPHkSALB7927MmzcPZmZmz328ESNGICkpCUBzgEJTkMPGxgaVlZWQy+VITU1VGeQQB0RGjBjR6nETExMEBwcjICAAgwYNUpmJUlNTg127dmHfvn2QyWRYt24d4uLilMY6ODhg48aNAJSDHIr7tNm5c6cQ4LCzs8PGjRsxYcKEVpkacXFx2LBhA548eYKoqCj4+PuRN2QAABNKSURBVPhoXZq2d+9eyGQyzJ07F6tXr1YKxjU0NMDAwECnOT6Po0ePCv8GWFhYIDQ0FDNmzGi1TCwlJQVr164Vsma+//77Vq2sAwIChCDH6dOnERoaqnHuBQUFQittMzMzTJgwodWYwsJChIaGoqGhAXp6eli0aBGWLVvWavnO3bt3ERISgoyMDNy7dw/r1q3TGBwlIupo2F2FiIja1W+//SZsq+uk0lakUik2bdqERYsWtbqg7969O7744gvhwiwtLQ0PHjxQuR8PDw+sWrVKY+0OW1tbfPrppxgzZgyA5uDArVu3dJqjg4MDDhw4oBTgAJo7yixYsACTJk0S7lNcpLeUmJiI9PR0AIC+vj6++eabVgEOoDkN/ttvv4W+vr7wa7A6TU1NCAsLE1Lov/zySyxZskRlhoarqysiIiKEX4yPHj2K+/fva9x/W5NKpZg2bRq2bdumFOAAAFNTU2zZsgXdu3cH0JwVcfHixRc6njgQ0TJjA2iux5GVlQUAGDt2rHC+qxorlUqRmZkJADA0NMSQIUNajenZsyfWr18Pd3d3tUttLCwsEBISgvfeew8AUFRUhMTExGd8ZeqVlJTg22+/BdAcSPvhhx8wceJElUtRpkyZItRLAZqDI4psIHVkMhlmz56NjRs3tso2MjQ0fKElRprU1NQgPDxcOM6+ffswe/ZslXVwRo4cif3798PY2BhAc2Cmrq5OacywYcPQs2dPAMCjR49w5coVjcf/8ccfhW0/Pz+Vwbd//vOfwnKm0NBQhISEqKxP0rt3b+zduxf9+vUD0BwcVZyHRERvAgY5iIio3dTU1EAmkwm3X3bdBmdnZ6E4pLrHFcUD5XK5UseX5xUYGChsa7uwUWj5i3VLs2bNErZv3LihcszRo0eF7alTp2pcBjR48GBMnz5d67wuXLiAoqIiAM0XXqp+XRazs7PDggULADT/6h4XF6f1GG3J0NAQoaGhah83NjaGv7+/cDs7O/uFjufm5iZ8bjdv3kRNTY3S49euXRPqcXh7ewtBkby8PFRVVSmNzcrKEi5gPTw8WtXjeFbicyY5OfmF9iV28OBBNDY2AgA+/PBD9OnTR+P4kSNHYvTo0QCAW7du4ebNmxrHGxsbY82aNW0z2Wdw7NgxVFdXAwDef/99eHh4aBzv5OSEGTNmAGgubNwykKSnp4c//vGPwm1xEKMluVyuFLxUtVQlLy8PKSkpAICBAwcK3zN1zMzM8OGHHwq3xUthiIg6Oi5XISKidiORSJRuv8hSAV1MnjxZ6xhXV1fhYlfRaUSTuro6ZGZmoqCgAOXl5ZBIJEKmAwClAqe6tLg1NjbW2u1DXMRU3RwVWRyA+vX8YgEBAWq7fCgkJCQI29OmTdO6T6D5olYhIyMDixYt0ul5bcHLy0ttsUYFXd5LXSnqciQmJgq1NsSfZcvlJ507d8ahQ4fQ1NSE9PR0pbbJ2upxtNTQ0ICsrCzk5+fj4cOHkEgkQvABUP6utWWr5UuXLgnb4ot4TUaOHCks68nIyICbm5vase+88w6srKxebJLP4XnP9SNHjgBofl0TJ05UejwgIAB79uwBAMTHx6Ourk5lFlR6erpQZNXOzg6jRo1qNUb8vvv7++tUxLXld5GI6E3BIAcREbWbltkKqrqVtCV1LTHFbGxshO2Wv8SLVVZW4uuvv0ZsbGyrYI06FRUVWsc4OjpqbQ0rXnqhao5lZWVKxUa1/QoNNGdz6OnpaVw+IO5Qcu7cOaVAijrijhTt3R1Dl1bA2t7LZ+Xt7S38ip+amqoyyNGzZ0/06tUL5ubmwnuekpKiFOQQB0Q0BTnq6+uxZ88eREZG6nR+Abqdh7ruR5HZY2hoqLQURZNff/1V2NZ2TmgKgLxM4nM9KioKsbGxWp8jXo6l6nU5OTnBzc0NOTk5qK2tRXx8vMrAkDjLw9/fX2XtDvH8UlNTlZb9qSP+br+qTjVERK8CgxxERNRuLCws0KlTJ2HJSssWjS/jeNqIa3WIl9KIKTqm6HJhIaZLMESXJTviIIiqOYoDHKampq3qUahiYWGBzp07Cyn6qohrlJw+fVrrPlvStO+XQZf3UpfP+1moq8tRX18vZAgpxtjY2MDZ2Rn5+flKY6VSqVAzwcjISGU9DqC5y8+CBQueOTND16CcNuL2wQ0NDUpFS3Wl7ZzQ1iL5ZZBIJErv0X//+99n3oe61xUQEICcnBwAzUtGWgY5pFKpUpcadVlY4u+iOOvkRedHRNQRMchBRETtqkePHrhz5w4A5V94XwZdUrp1sXr1aiHAYW5ujtmzZ2P06NFwcHCAra0tTExMhIKIqampmD9/PgBoLbLYVnMUX6A9Sy0HMzMzjRc/L5rpIF4+0R7a6vN+Foq6HBKJBLm5uaiuroalpSWuX78u1OMQB0K8vb2Rn5+PgoICVFRUwMbGRud6HP/4xz+EAIehoSFmzJiBcePGwcnJCXZ2djAxMRGyAEpKSvDuu+8C0O081EVbBCW1nRMvWovkebRFRo+61+Xv749PP/0UjY2NuHz5MsrLy5UCORcvXhS+g/369VObyfK6fReJiF4lBjmIiKhdeXl5CUGOFy382B6uXbsmpIqbmZkhKipK6FqgSlv9av4sxMuAFBfLumjZEaIlU1NT4cI2JiZGqZ4FNevUqRO8vLyQkJCApqYmpKWlwc/PT6nGhjjIMXLkSBw6dAhyuRxpaWmYNGmSTvU4ysrKcOrUKQDN3XP27t2rVHOhpZdxHopr6FhYWHSYOg8t62SkpaW1WV0QOzs7+Pj4ICkpCTKZDKdPn8a8efOEx8UFQTXV0hHPcefOnVqLABMRvcnYXYWIiNqV+MKstLQU165de4Wz0U7cmSIwMFBjgAPAMy9paQviuiJ1dXWtOneoIpFItKaw29raCtvipQqkTByYUAQsFMtR+vTpI7StBZpbiyoyThRjdQlyJCcnCxkZY8aM0RjgAF7OeSg+H2pqarQGyV4XlpaWMDIyEm4/evSoTfcvDl6I629UV1cLbYxbdmNpSdGaGeB3kYhIGwY5iIioXU2ePFnpojwiIuLVTUYH4rXwuhS21KU4Z1vr1q2b0nuqqO+gyS+//KJ1GYO4gOnvPRj1KrWsyyGux9EyaGFtbQ0XFxdhrK71OH4P52HXrl2VAjbiYpivO3d3d2G7rc/1CRMmCFkwWVlZQibb2bNnhSVNw4cPR48ePV7J/IiIOhoGOYiIqF2ZmJggODhYuH327Fmlwnu6qq2tbZc/9hW1NgDtS0HKyspw/vz5lz0llcQX0+IUeHXEvyir4+vrK2wfO3YMT58+fa65dXSKuhwAkJ+fjwsXLqChoQGAcgBEQfFZFRYW4vz588L76uHhAWNjY5XHEJ+H2jIo6urqcPz4cZ3mLj6eYs6aiM+JH374QadjvA7Er+vw4cNtVscEaF7mo6iPAvz/d0/8HdTW9lncteenn35q82wTIqKOhEEOIiJqd3/605+UCuytXbsWFy5c0Pn5BQUFCAoKwuXLl1/G9JT07t1b2NYUwGhsbMTGjRt1ulB8GWbNmiVsnzx5EpmZmWrH5uTk6NQic9KkSXj77bcBNKfIh4WF6XzxJ5FIXnqL4N8LAwMDDBs2DEBzkc/du3cLj6kKcojv++abbzSOVRCfhwkJCRoLSW7btk3ni2BxJ56ysjKt4xcvXiwUN/3pp58QHR2t03GA3/cyi/feew+WlpYAmr8furbHBZq7G2kr7Dl9+nRh+8SJE7h3756QbWNsbIzJkydrfL67u7sQHKuvr8fatWuFLBBtpFKpTkvYiIg6CgY5iIio3RkZGeGrr74S1vjX19dj+fLlWLt2LW7duqXyOXK5HNnZ2QgJCcH06dNRUFDQLnMdO3asUEMhLS0N4eHhrTI6Hj58iJUrV+LixYtKxRnb05gxY+Dl5QUAaGpqwtKlS3HlypVW41JTU7FkyRI0NjYqtaZVxcDAAGFhYcJFbXR0NJYsWaL2MwKA3NxcfPbZZ/D19UVJSckLvKLXiziTRnFuOjg4wN7evtXY4cOHC5kZ4vNYXT0OoLmWjaL4ZHFxMUJCQlrVVKmpqcGGDRsQGRmp83nYv39/YfvMmTNax/fp0wfLli0Tbn/88ccIDw9XamMsJpPJkJSUhDVr1iAwMFCnOb0KnTt3xrp164TbO3fuREhIiNraJnK5HBkZGQgLC8O4ceO0ZnmNGjUKdnZ2AICioiJs3bpVCBj6+vrq1P54w4YNwud6+fJlzJs3T+PStNu3b2PXrl0YP348l7gQ0RuF3VWIiOiV6N27N6KiorBs2TIUFBSgqakJx48fx/Hjx9GzZ08MGDAANjY2aGpqwsOHD5GXl9fq12lxV5GXxcnJCdOnTxcyH/bt24cTJ05g8ODBsLW1RWlpKdLT09HQ0ABzc3OsXbsWmzZteunzaklPTw9btmxBUFAQKisrUVFRgUWLFsHFxQWurq4AgLy8PKEF6eLFi3H27FmUlpYCUF4OITZq1CiEhYUhLCwMjY2NSEhIQGJiIvr164cBAwbA3Nwc9fX1wmek7mK3o1MVoFCXmWFpaQlXV1fk5OQI9xkZGcHT01Pt/q2srLB48WLs2rULQHM2QGJiItzd3WFvb4+HDx8iLS0NtbW16NSpEzZt2oSQkBCt8540aRKSkpIAAJ9//jkSEhLQv39/pUKcS5cuVeo2smLFCpSWliImJgZyuRz79u3DoUOHMGjQIPTp0wcmJiaQSCQoLS1Ffn6+kNEjzhr5PZo5cybu3r0rZNfExsbixIkTcHFxQd++fWFmZoba2lqUlZUhNzf3mVrqGhgYYOrUqThw4AAAKC3RE2d5aOLs7Izt27dj1apVqKurQ1ZWFubMmYM+ffpg4MCBsLKyglQqxePHj5Gfn69TZg4RUUfEIAcREb0yvXr1QmRkJCIiIhARESH8Ml1aWipcfKvi4uKClStXws/Pr13mGRYWhkePHgkXgw8fPmy1vKZbt27Yvn07ZDJZu8xJFQcHBxw4cADLly8Xsijy8vKQl5enNC4oKAh//etfcfLkSeE+CwsLtftVXEht2rQJRUVFkMvlKCwsRGFhodrn9O/fv83acL4O3NzcYGFhgZqaGuE+TctPvL29lYIcnp6eautxKCxfvhylpaVCwK2yshIJCQlKYywtLbF161ahuKk2gYGB+PHHH5Geng65XI7U1FSlbi8AMHfuXKXPUk9PD9u2bYObmxt27NiBqqoqNDQ04Pr162qLkerp6WHo0KE6zelV+uijj9C/f39s3boVDx48QGNjI3JycpQ+q5bc3d21ZkUBzXU3FEEOBWtra4wZM0bn+Y0bNw6RkZH4+OOPhTnduXNHKGaqSs+ePdGtWzedj0FE9LpjkIOIiF4pc3NzLF++HPPnz8elS5dw+fJl5OTkoLy8HJWVlTA0NIS1tTX69u0Ld3d3+Pn5KdXzaA+mpqb47rvvcOLECcTGxuLmzZuQSCSwtrZG7969MWnSJAQGBsLKyqrVBWJ7c3FxwcmTJxEZGYkzZ86gqKgIdXV1sLOzg7u7O+bMmQMfHx8AEIJK+vr6GoMcQPNyidOnTyM+Ph4XL15EVlYWHj16hJqaGpiYmOCtt95C3759MWTIEIwZM0bIHnlTKOpyKFqCApqXn4wYMQL79+/Xaaz4GOHh4Zg8eTKOHDmC7OxsVFdXw9LSEt27d8e7776LWbNmwd7eXuelQoaGhti/fz+OHj2Kc+fOobCwEJWVlTrVlgkODkZgYCCOHz+OK1euCJk8UqkU5ubmsLe3R//+/eHt7Y2xY8cqdWb5PZs6dSr8/Pxw6tQpJCUl4caNGygvL0dtbS1MTU1hb28PJycneHl5YezYsXB0dNRpv4MGDYKTk5PScq8pU6boFCARc3FxQXR0NJKSkhAfH49r167hwYMHePLkCYyMjGBjYwNHR0d4eHhg9OjRGDJkiLDkjojoTaAnb8vy0URERPRaKCoqwqRJkwAAffv2RVxc3CueEREREdGLY+FRIiKiN9Dp06eF7cGDB7/CmRARERG1HQY5iIiI3jB3797Fvn37hNvTpk17hbMhIiIiajsMchAREXUgixcvRkJCgtoCqBcvXsT7778vdIZwdXXF6NGj23OKRERERC8Na3IQERF1IAMGDADQ3HJ04MCB6N69OwwNDVFRUYHs7Gzcv39fGGtubo7Dhw8LzyEiIiJ63THIQURE1IHoGrBwcHDAV199pXOrUSIiIqLXAYMcREREHUhhYSHi4+Nx/fp1/Pbbb6ioqEBVVRWMjIzQpUsXuLu7w9fXF/7+/jAwMHjV0yUiIiJqUwxyEBEREREREVGHwMKjRERERERERNQhMMhBRERERERERB0CgxxERERERERE1CEwyEFEREREREREHQKDHERERERERETUITDIQUREREREREQdAoMcRERERERERNQhMMhBRERERERERB0CgxxERERERERE1CEwyEFEREREREREHQKDHERERERERETUITDIQUREREREREQdAoMcRERERERERNQhMMhBRERERERERB0CgxxERERERERE1CEwyEFEREREREREHQKDHERERERERETUITDIQUREREREREQdwv8BX7YmC7/0lnoAAAAASUVORK5CYII=\n", "text/plain": [ "<Figure size 1200x800 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "m = X.shape[0] # number of examples = 12\n", "print(\"Plotting training data\")\n", "plt.rcParams['figure.dpi'] = 200 # setting figure dpi for better quality graphs\n", "sns.set(context=\"notebook\", style=\"whitegrid\") # graph styling using seaborn\n", "\n", "# the following lines generate a figure with 1 subplot\n", "fig, ax = plt.subplots()\n", "ax.scatter(X, y, marker='+', color='r', s=50);\n", "ax.set_xlabel(\"Change in water level\");\n", "ax.set_ylabel('Water Flowing out of dam');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Regualrized linear regression cost and gradient testing\n", "\n", "The regularized linear regression has the following cost function:\n", "\n", "\\begin{equation}J(\\theta)=\\frac{1}{2 m}\\left(\\sum_{i=1}^{m}\\left(h_{\\theta}\\left(x^{(i)}\\right)-y^{(i)}\\right)^{2}\\right) + \\frac{\\lambda}{2 m}\\left(\\sum_{j=1}^{n} \\theta_{j}^{2}\\right)\\end{equation}\n", "\n", "where λ is a regularization parameter which controls the degree of regularization (thus, help preventing overfitting). The regularization term puts a\n", "penalty on the overal cost J. As the magnitudes of the model parameters $\\theta_{j}$\n", "increase, the penalty increases as well. Note that you should not regularize\n", "the $\\theta_{0}$ term.\n", "\n", "Correspondingly, the partial derivative of regularized linear regression’s cost\n", "for $\\theta_{j}$ is defined as:\n", "\n", "\\begin{align*}\n", "& \\frac{\\delta J(\\theta)}{\\delta\\theta_{0}} = \\frac{1}{m}\\sum_{i=1}^{m}\\left(h_{\\theta}\\left(x^{(i)}\\right)-y^{(i)}\\right)x^{(i)}_{j} & \\text{for j}&=0 \\\\\n", "& \\frac{\\delta J(\\theta)}{\\delta\\theta_{j}} = \\left(\\frac{1}{m}\\sum_{i=1}^{m}\\left(h_{\\theta}\\left(x^{(i)}\\right)-y^{(i)}\\right)x^{(i)}_{j}\\right) + \\frac{\\lambda}{m}\\theta_{j} & \\text{for j}&>=1\n", "\\end{align*}\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we are testing the cost and gradient function in the models.linear_regression file" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Cost at theta [1,1] is [303.99319222]\n", "(this value should be 303.993192)\n", "Gradient at theta [1,1] is [-15.30301567 598.25074417]\n", "(this value should be [-15.303016, 598.250744])\n" ] } ], "source": [ "# initializing testing parameters\n", "theta_test = np.array([1,1])\n", "J = compute_cost(add_bias_unit(X), y, theta_test, lamda=1)\n", "grad = compute_gradient(add_bias_unit(X), y, theta_test, lamda=1)\n", "print(\"Cost at theta [1,1] is {}\\n(this value should be 303.993192)\".format(J))\n", "print(\"Gradient at theta [1,1] is {}\\n(this value should be [-15.303016, 598.250744])\".format(grad.flatten()))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Training Linear Regression\n", "\n", "For training the linear regression model we are going to define a function which is going to use scipy.optimize.minimize function to find the optimum theta or weights according to the given data.\n", "\n", "In this part, we set regularization parameter λ to zero. Because our current implementation of linear regression is trying to fit a 2-dimensional θ, regularization will not be incredibly helpful for a θ of such low dimension. In the later parts of the example, we will be using polynomial regression with regularization." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# adding bias unit to X\n", "bias_added_X = add_bias_unit(X)\n", "\n", "# res will point to the result object generated by scipy minimize function.\n", "# cst is the list of thetas after each iteration\n", "res, cst = train_linear_reg(bias_added_X, y, 0)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 1200x800 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#plotting the data and curve trained by model\n", "fig1, ax1 = plt.subplots()\n", "ax1.scatter(X, y, marker='+', color='r', s=50);\n", "ax1.set_xlabel(\"Change in water level\")\n", "ax1.set_ylabel('Water Flowing out of dam')\n", "ax1.plot(X, bias_added_X@res.x); # plotting best fit line" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The best fit line tells us that the model is not a good fit to the data because the data has a non-linear pattern. While visualizing the best fit as shown is one possible way to debug your learning algorithm, it is not always easy to visualize the data and model. In the next section, you will implement a function to generate learning curves that can help you debug your learning algorithm even if it is not easy to visualize the data.\n", "\n", "## Bias-variance\n", "\n", " An important concept in machine learning is the bias-variance tradeoff. Models with high bias are not complex enough for the data and tend to underfit, while models with high variance overfit to the training data.\n", "\n", "### Learning Curves\n", "\n", "We will now implement code to generate the learning curves that will be useful in debugging learning algorithms. **A learning curve plots training and cross validation error as a function of training set size.** \n", "\n", "To plot the learning curve, we need a training and cross validation set error for different training set sizes. To obtain different training set sizes, we will use different subsets of the original training set X. Specifically, for a training set size of i, we will use the first i examples (i.e., X(1:i,:) and y(1:i)). \n", "You can use the train_linear_reg function to find the θ parameters. \n", "\n", "After learning the θ parameters, we will compute the error on the training and cross validation sets. Recall that the training error for a dataset is defined as\n", "\n", "\\begin{equation}\n", "J_{train}(\\theta) = \\frac{1}{2m}\\left[\\sum_{i=1}^{m}\\left( h_{\\theta}\\left( x^{(i)} \\right) - y^{(i)} \\right)^{2} \\right]\n", "\\end{equation}\n", "\n", "In particular, note that the training error does not include the regularization term. One way to compute the training error is to use your existing cost function and set λ to 0 only when using it to compute the training error and cross validation error. When you are computing the training set error, make sure you compute it on the training subset (i.e., X(1:n,:) and y(1:n)) (instead of the entire training set). However, for the cross validation error, you should compute it over the entire cross validation set. You should store the computed errors in the vectors error train and error val." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Plotting Learning Curves\n", "\n", "processing dataset from 0 to 1\n", "temp_theta is [ 0.00837049 -0.13339852]\n", "processing complete!!\n", "\n", "processing dataset from 0 to 2\n", "temp_theta is [3.29303644 0.07271423]\n", "processing complete!!\n", "\n", "processing dataset from 0 to 3\n", "temp_theta is [14.15499007 0.53912266]\n", "processing complete!!\n", "\n", "processing dataset from 0 to 4\n", "temp_theta is [14.62429855 0.55985727]\n", "processing complete!!\n", "\n", "processing dataset from 0 to 5\n", "temp_theta is [17.21375974 0.44974975]\n", "processing complete!!\n", "\n", "processing dataset from 0 to 6\n", "temp_theta is [15.40485112 0.45741711]\n", "processing complete!!\n", "\n", "processing dataset from 0 to 7\n", "temp_theta is [14.26678005 0.4368173 ]\n", "processing complete!!\n", "\n", "processing dataset from 0 to 8\n", "temp_theta is [14.62343987 0.42312838]\n", "processing complete!!\n", "\n", "processing dataset from 0 to 9\n", "temp_theta is [13.29660996 0.41299409]\n", "processing complete!!\n", "\n", "processing dataset from 0 to 10\n", "temp_theta is [13.85366299 0.37780979]\n", "processing complete!!\n", "\n", "processing dataset from 0 to 11\n", "temp_theta is [12.93724155 0.36342988]\n", "processing complete!!\n", "\n", "processing dataset from 0 to 12\n", "temp_theta is [13.08790351 0.36777923]\n", "processing complete!!\n" ] } ], "source": [ "print(\"Plotting Learning Curves\")\n", "\n", "lamda = 0\n", "error_train = []\n", "error_val = []\n", "bias_added_X_val = add_bias_unit(X_val)\n", "\n", "# computing training and cross validation error using training examples \n", "for i in range(1,m+1):\n", " print()\n", " print(\"processing dataset from 0 to {}\".format(i))\n", " \n", " # training the model\n", " temp_result, _ = train_linear_reg(bias_added_X[0:i, :], y[0:i], lamda)\n", " temp_theta = temp_result.x\n", " \n", " print(\"temp_theta is {}\".format(temp_theta))\n", " \n", " # storing errors in list\n", " error_train.append(compute_cost(bias_added_X[0:i, :], y[0:i], temp_theta, lamda))\n", " error_val.append(compute_cost(bias_added_X_val, y_val, temp_theta, lamda))\n", " \n", " print(\"processing complete!!\")\n" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Generating Learning curve\n" ] }, { "data": { "text/plain": [ "<matplotlib.legend.Legend at 0x7ff943dd1fd0>" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 1200x800 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "print(\"Generating Learning curve\")\n", "plt.plot(np.arange(m), error_train, label=\"Training Curve\")\n", "plt.plot(np.arange(m), error_val, label=\"Cross Validation Curve\")\n", "plt.xlabel(\"Number of training examples\")\n", "plt.ylabel('Error')\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In above Figure, you can observe that both the train error and cross validation\n", "error are high when the number of training examples is increased. This reflects a high bias problem in the model – the linear regression model is too simple and is unable to fit our dataset well. In the next section, we will implement polynomial regression to fit a better model for this dataset.\n", "## Polynomial Regression\n", "The problem with our linear model was that it was too simple for the data\n", "and resulted in underfitting (high bias). In this part of the exercise, you will\n", "address this problem by adding more features.\n", " For use polynomial regression, our hypothesis has the form:\n", " \n", "\\begin{align*} h_{\\theta}(x) & = \\theta_{0} + \\theta_{1} * (waterLevel) + \\theta_{2} *(waterLevel)^{2} + ... + \\theta_{p} * (waterLevel)^{p} \\\\\n", "& = \\theta_{0} + \\theta_{1}x_{2} + \\dots + \\theta_{p}x_{p}\n", "\\end{align*}\n", "\n", "Notice that by defining $x_{1} = (waterLevel), x_{2} = (waterLevel)^{2}, \\dots , x_{p} = (waterLevel)^{p}$, we obtain a linear regression model where the features are the\n", "various powers of the original value $(\\text{waterLevel})$. \n", "Now, you will add more features using the higher powers of the existing feature x in the dataset. NOw we are going to define a map_feature function, so that the function maps the original training set X of size $m × 1$ into its higher powers. Specifically, when a training set X of size $m × 1$ is passed into the function, the function should return a $m×p$ matrix $X poly$,where column 1 holds the original values of $X$, column 2 holds the values of $X^{2}$, column 3 holds the values of $X^{3}$, and so on. Note that you don’t have to account for the zero-eth power in this function." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "First 5 Normalized training examples: \n", "[[ 1. -0.3782437 -0.78866232 0.19032872 -0.7375913 0.32025197 -0.6171516 0.35983501 -0.53109126]\n", " [ 1. -0.8389201 0.0013142 -0.25896174 -0.34156482 0.09754927 -0.45519664 0.26677343 -0.46887381]\n", " [ 1. 1.43871736 0.61083158 1.30534069 0.25622 1.02186338 -0.01269621 0.79021001 -0.17792698]\n", " [ 1. 1.4841233 0.73806846 1.4203124 0.41312183 1.1553483 0.13122371 0.91070022 -0.06228954]\n", " [ 1. -1.49791929 1.93643966 -2.12774745 2.43510061 -2.51876748 2.71792174 -2.7633169 2.88908182]]\n" ] } ], "source": [ "max_degree = 8 # maximum degree upto which the polynomial terms are to be formed\n", "# mapping X to polynomial features with degree upto 8\n", "X_poly = map_feature(X, degree=max_degree, bias_unit=False)\n", "\n", "# since the values of X_poly vary too much we are normalizing them\n", "# mu is the mean values of individual features\n", "# sigma is the standard daviation of individual features\n", "X_poly, mu, sigma = feature_normalize(X_poly)\n", "\n", "# adding bias unit to the polymerised data\n", "X_poly = add_bias_unit(X_poly)\n", "\n", "# mapping and normalizing the test dataset with the mu and sigma\n", "X_poly_test = map_feature(X_test, degree=max_degree, bias_unit=False)\n", "X_poly_test, _, __ = feature_normalize(X_poly_test, mean=mu, sigma=sigma)\n", "X_poly_test = add_bias_unit(X_poly_test)\n", "\n", "# mapping and normalizing the cross validation dataset with the mu and sigma\n", "X_poly_val = map_feature(X_val, degree=max_degree, bias_unit=False)\n", "X_poly_val, _, __ = feature_normalize(X_poly_val, mean=mu, sigma=sigma)\n", "X_poly_val = add_bias_unit(X_poly_val)\n", "\n", "\n", "print(\"First 5 Normalized training examples: \")\n", "with np.printoptions(precision=8, suppress=True, linewidth=150):\n", " print(X_poly[:5, :])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Training using Polynomial Regression\n", "\n", "In this section we are going to train the model using the new features(i.e. X_poly) generated by map_features function. \n", "\n", "Keep in mind that even though we have polynomial terms in our feature vector, we are still solving a linear regression optimization problem. The polynomial terms have simply turned into features that we can use for linear regression. We are using the same cost function and gradient that we used for the earlier part of this exercise. \n", "\n", "For this part of the exercise, we will be using a polynomial of degree 8. It turns out that if we run the training directly on the projected data, will not work well as the features would be badly scaled (e.g., an example with x = 40 will now have a feature x8 = 408 = 6.5 × 1012). Therefore, we used feature normalization in above section. \n" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Training of polynomial regressor completed\n", "Training Cost: [0.03193852]\n" ] } ], "source": [ "lamda = 0\n", "\n", "result_poly, cost_lst_poly = train_linear_reg(X_poly, y, lamda)\n", "print(\"Training of polynomial regressor completed\")\n", "print(\"Training Cost: {}\".format(result_poly.fun))" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'Polynomial Fit, λ = 0')" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 1200x800 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.scatter(X, y)\n", "\n", "# generating an array containing X_intercepts\n", "X_intercepts = np.arange(X.min()-15, X.max()+15, 0.05).reshape([-1,1])\n", "\n", "# mapping the X-intercepts to max 8 degree\n", "X_intercepts_poly = map_feature(X_intercepts, 8, bias_unit=False)\n", "X_intercepts_poly, _, __ = feature_normalize(X_intercepts_poly, mean=mu, sigma=sigma)\n", "X_intercepts_poly = add_bias_unit(X_intercepts_poly)\n", "\n", "# plotting the curve using the thetas found by polynomial data\n", "plt.plot(X_intercepts, X_intercepts_poly@result_poly.x)\n", "plt.ylabel(\"Water flowing out of Dam\")\n", "plt.xlabel(\"Change in Water level\")\n", "plt.title(\"Polynomial Fit, λ = 0\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "After learning the parameters $\\theta_{polynomial}$, from above Figure, you could see that the polynomial fit is able to follow the datapoints very well - thus, obtaining a low training error. However, the polynomial fit is very complex and even drops off at the extremes. This is\n", "an indicator that the polynomial regression model is overfitting the training\n", "data and will not generalize well." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Learning Curve for Polynomial Regression\n", " To better understand the problems with the unregularized (λ = 0) model, we are going to plot learning curve for the new model." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Computing Training and Cross Validation Error\n", "\n", "Training Data size\tTrain cost\tCross Validation Cost\n", "\t1\t\t0.000000\t161.442168\n", "\t2\t\t0.000000\t160.792292\n", "\t3\t\t0.000000\t68.190945\n", "\t4\t\t0.000000\t84.863965\n", "\t5\t\t0.000000\t6.486683\n", "\t6\t\t0.000000\t10.782185\n", "\t7\t\t0.000000\t27.972688\n", "\t8\t\t0.000004\t20.371517\n", "\t9\t\t0.009334\t29.825986\n", "\t10\t\t0.039082\t20.788307\n", "\t11\t\t0.041092\t16.836138\n", "\t12\t\t0.031939\t45.501432\n", "processing complete!!\n" ] } ], "source": [ "print(\"Computing Training and Cross Validation Error\\n\")\n", "lamda = 0\n", "error_train_poly = []\n", "error_val_poly = []\n", "\n", "print(\"Training Data size\\tTrain cost\\tCross Validation Cost\")\n", "# computing training and cross validation error using training examples \n", "for i in range(1,m+1): \n", " # training the model\n", " temp_result_poly, _ = train_linear_reg(X_poly[0:i, :], y[0:i], lamda)\n", " temp_theta_poly = temp_result_poly.x\n", " \n", " # storing errors in list\n", " error_train_poly.append(compute_cost(X_poly[0:i, :], y[0:i], temp_theta_poly, lamda))\n", " error_val_poly.append(compute_cost(X_poly_val, y_val, temp_theta_poly, lamda))\n", " \n", " print(\"\\t{}\\t\\t{:0.6f}\\t{:0.6f}\".format(i, error_train_poly[-1][0], error_val_poly[-1][0]))\n", " \n", "print(\"processing complete!!\")" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Plotting Learning curve with above generated data\n" ] }, { "data": { "text/plain": [ "[<matplotlib.lines.Line2D at 0x7ff943cf1a90>]" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "<Figure size 1200x800 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "print(\"Plotting Learning curve with above generated data\")\n", "\n", "plt.plot(np.arange(1,m+1), error_train_poly)\n", "plt.plot(np.arange(1,m+1), error_val_poly)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " You can see that the learning curve (Figure 5) shows the same effect where the low training error is low, but the cross validation error is high. There is a gap between the training and cross validation errors, indicating a high variance problem." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Adjusting the regularization parameter\n", "\n", "In this section, we will observe how the regularization parameter affects the bias-variance of regularized polynomial regression. \n", "\n", "We are now going to modify the lambda paramter(λ) and try λ = 1, 100. For\n", "each of these values, the script should generate a polynomial fit to the data\n", "and also a learning curve. \n", "\n", "For λ = 1, you should see a polynomial fit that follows the data trend\n", "well and a learning curve showing that both the cross\n", "validation and training error converge to a relatively low value. This shows\n", "the λ = 1 regularized polynomial regression model does not have the highbias or high-variance problems. In effect, it achieves a good trade-off between\n", "bias and variance. \n", "For λ = 100, you should see a polynomial fit that does not\n", "follow the data well. In this case, there is too much regularization and the model is unable to fit the training data." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Lambda λ = 1" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Training of polynomial regressor completed (λ = 1)\n", "Training Cost: [6.83046332]\n" ] } ], "source": [ "lamda = 1\n", "\n", "result_poly_1, cost_lst_poly_1 = train_linear_reg(X_poly, y, lamda)\n", "print(\"Training of polynomial regressor completed (λ = 1)\")\n", "print(\"Training Cost: {}\".format(result_poly_1.fun))" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'Polynomial Fit, λ = 1')" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 1200x800 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.scatter(X, y)\n", "\n", "# generating an array containing X_intercepts\n", "X_intercepts = np.arange(X.min()-15, X.max()+15, 0.05).reshape([-1,1])\n", "\n", "# mapping the X-intercepts to max 8 degree\n", "X_intercepts_poly = map_feature(X_intercepts, 8, bias_unit=False)\n", "X_intercepts_poly, _, __ = feature_normalize(X_intercepts_poly, mean=mu, sigma=sigma)\n", "X_intercepts_poly = add_bias_unit(X_intercepts_poly)\n", "\n", "# plotting the curve using the thetas found by polynomial data\n", "plt.plot(X_intercepts, X_intercepts_poly@result_poly_1.x)\n", "plt.ylabel(\"Water flowing out of Dam\")\n", "plt.xlabel(\"Change in Water level\")\n", "plt.title(\"Polynomial Fit, λ = 1\")" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Computing Training and Cross Validation Error (λ = 1)\n", "\n", "Training Data size\tTrain cost\tCross Validation Cost\n", "\t1\t\t0.000000\t138.846776\n", "\t2\t\t0.070327\t143.505063\n", "\t3\t\t17.182727\t7.845035\n", "\t4\t\t13.476899\t9.212261\n", "\t5\t\t10.781524\t9.222846\n", "\t6\t\t9.347014\t11.024707\n", "\t7\t\t8.754387\t8.290400\n", "\t8\t\t7.682189\t8.001082\n", "\t9\t\t7.277291\t8.793858\n", "\t10\t\t6.592031\t8.528102\n", "\t11\t\t5.994056\t8.585953\n", "\t12\t\t6.830463\t7.047218\n", "processing complete!!\n" ] } ], "source": [ "print(\"Computing Training and Cross Validation Error (λ = 1)\\n\")\n", "lamda = 1\n", "error_train_poly = []\n", "error_val_poly = []\n", "\n", "print(\"Training Data size\\tTrain cost\\tCross Validation Cost\")\n", "# computing training and cross validation error using training examples \n", "for i in range(1,m+1): \n", " # training the model\n", " temp_result_poly, _ = train_linear_reg(X_poly[0:i, :], y[0:i], lamda)\n", " temp_theta_poly = temp_result_poly.x\n", " \n", " # storing errors in list\n", " error_train_poly.append(compute_cost(X_poly[0:i, :], y[0:i], temp_theta_poly, lamda))\n", " error_val_poly.append(compute_cost(X_poly_val, y_val, temp_theta_poly, lamda))\n", " \n", " print(\"\\t{}\\t\\t{:0.6f}\\t{:0.6f}\".format(i, error_train_poly[-1][0], error_val_poly[-1][0]))\n", " \n", "print(\"processing complete!!\")" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Plotting Learning curve with above generated data\n" ] }, { "data": { "text/plain": [ "Text(0.5, 1.0, 'Learning Curve (λ = 1)')" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "<Figure size 1200x800 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "print(\"Plotting Learning curve with above generated data\")\n", "\n", "plt.plot(np.arange(1,m+1), error_train_poly)\n", "plt.plot(np.arange(1,m+1), error_val_poly)\n", "plt.title(\"Learning Curve (λ = 1)\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Lambda λ = 100" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Training of polynomial regressor completed (λ = 100)\n", "Training Cost: [65.95095506]\n" ] } ], "source": [ "lamda = 100\n", "\n", "result_poly_100, cost_lst_poly_100 = train_linear_reg(X_poly, y, lamda)\n", "print(\"Training of polynomial regressor completed (λ = 100)\")\n", "print(\"Training Cost: {}\".format(result_poly_100.fun))" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'Polynomial Fit, λ = 100')" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 1200x800 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.scatter(X, y)\n", "\n", "# generating an array containing X_intercepts\n", "X_intercepts = np.arange(X.min()-15, X.max()+15, 0.05).reshape([-1,1])\n", "\n", "# mapping the X-intercepts to max 8 degree\n", "X_intercepts_poly = map_feature(X_intercepts, 8, bias_unit=False)\n", "X_intercepts_poly, _, __ = feature_normalize(X_intercepts_poly, mean=mu, sigma=sigma)\n", "X_intercepts_poly = add_bias_unit(X_intercepts_poly)\n", "\n", "# plotting the curve using the thetas found by polynomial data\n", "plt.plot(X_intercepts, X_intercepts_poly@result_poly_100.x)\n", "plt.ylabel(\"Water flowing out of Dam\")\n", "plt.xlabel(\"Change in Water level\")\n", "plt.title(\"Polynomial Fit, λ = 100\")" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Computing Training and Cross Validation Error (λ = 1)\n", "\n", "Training Data size\tTrain cost\tCross Validation Cost\n", "\t1\t\t0.000000\t138.846777\n", "\t2\t\t0.114717\t144.124099\n", "\t3\t\t112.255156\t70.935873\n", "\t4\t\t131.638608\t79.137897\n", "\t5\t\t116.062526\t66.126942\n", "\t6\t\t108.778507\t61.957759\n", "\t7\t\t93.297101\t62.018723\n", "\t8\t\t86.349367\t61.581277\n", "\t9\t\t80.206754\t62.481408\n", "\t10\t\t73.060272\t62.979548\n", "\t11\t\t66.883255\t63.626911\n", "\t12\t\t65.950955\t61.559272\n", "processing complete!!\n" ] } ], "source": [ "print(\"Computing Training and Cross Validation Error (λ = 1)\\n\")\n", "lamda = 100\n", "error_train_poly = []\n", "error_val_poly = []\n", "\n", "print(\"Training Data size\\tTrain cost\\tCross Validation Cost\")\n", "# computing training and cross validation error using training examples \n", "for i in range(1,m+1): \n", " # training the model\n", " temp_result_poly, _ = train_linear_reg(X_poly[0:i, :], y[0:i], lamda)\n", " temp_theta_poly = temp_result_poly.x\n", " \n", " # storing errors in list\n", " error_train_poly.append(compute_cost(X_poly[0:i, :], y[0:i], temp_theta_poly, lamda))\n", " error_val_poly.append(compute_cost(X_poly_val, y_val, temp_theta_poly, lamda))\n", " \n", " print(\"\\t{}\\t\\t{:0.6f}\\t{:0.6f}\".format(i, error_train_poly[-1][0], error_val_poly[-1][0]))\n", " \n", "print(\"processing complete!!\")" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Plotting Learning curve with above generated data\n" ] }, { "data": { "text/plain": [ "[<matplotlib.lines.Line2D at 0x7ff943b3bf60>]" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "<Figure size 1200x800 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "print(\"Plotting Learning curve with above generated data\")\n", "\n", "plt.plot(np.arange(1,m+1), error_train_poly)\n", "plt.plot(np.arange(1,m+1), error_val_poly)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Selecting λ using cross validation curve\n", "From the previous parts of the exercise, we observed that the value of λ can significantly affect the results of regularized polynomial regression on the training and cross validation set. \n", "\n", "In particular, a model without regularization (λ = 0) fits the training set well, but does not generalize. Conversely,a model with too much regularization (λ = 100) does not fit the training set and testing set well. A good choice of λ (e.g., λ = 1) can provide a good fit to the data. \n", "\n", "\n", "In this section, we will implement training with different lambda values to select the λ parameter. Concretely, we will use a cross validation set to evaluate how good each λ value is. After selecting the best λ value using the cross validation set, we can then evaluate the model on the test set to estimate\n", "how well the model will perform on actual unseen data. \n", "\n", "\n", "Specifically, we will use the train_linear_reg function to train the model using different values of λ and compute the training error and cross validation error.\n", "\n", "**You should try λ in the following range: {0, 0.001, 0.003, 0.01, 0.03, 0.1, 0.3, 1, 3, 10}**" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "<matplotlib.legend.Legend at 0x7ff93b1a8668>" ] }, "execution_count": 56, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "<Figure size 1200x800 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "lambda_list = [0, 0.001, 0.003, 0.01, 0.03, 0.1, 0.3, 1, 3, 10]\n", "\n", "_, train_cost_lst, cv_cost_lst = validation_curve(X_poly, y, X_poly_val, y_val, lambda_list)\n", "\n", "# train_cost_lst - training cost corresponding to lamda values\n", "# cv_cost_lst - cross validation cost corresponding to lamda values\n", "\n", "# plotting training cost and cross validation cost\n", "plt.plot(np.array(lambda_list), train_cost_lst, label=\"Train\")\n", "plt.plot(np.array(lambda_list), cv_cost_lst, label=\"Cross Validation\")\n", "plt.xlabel(\"Lambda\")\n", "plt.ylabel(\"Error\")\n", "plt.legend()\n", "#plt.xticks(np.arange(len(lambda_list)),lambda_list)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this\n", "figure, we can see that the best value of λ is around 3. Due to randomness\n", "in the training and validation splits of the dataset, the cross validation error\n", "can sometimes be lower than the training error." ] } ], "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": "3.6.8" } }, "nbformat": 4, "nbformat_minor": 4 }