{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-07-03T12:02:43.936941Z",
     "start_time": "2018-07-03T12:02:43.930614Z"
    }
   },
   "source": [
    "*For full screen view & to download, visit *\n",
    "- `HTML` : <a href=\"https://prasanth-ntu.github.io/html/ML-Course/Intro-to-ML-with-Python/2b-Supervised-Learning-Linear-Regression.html\" target=\"_blank\">Click here</a>\n",
    "- `GITHUB` : <a href=\"https://prasanth-ntu.github.io/html/ML-Course/Intro-to-ML-with-Python/2b-Supervised-Learning-Linear-Regression.ipynb\" target=\"_blank\">Click here</a>\n",
    "\n",
    "*To get back to ML website*, <a href=\"https://prasanth-ntu.github.io/html/ML-Course-13.html\" target=\"_blank\">Click here</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "toc": "true"
   },
   "source": [
    "<h1>Table of Contents<span class=\"tocSkip\"></span></h1>\n",
    "<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#Linear-Models-for-regression\" data-toc-modified-id=\"Linear-Models-for-regression-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>Linear Models for regression</a></span><ul class=\"toc-item\"><li><span><a href=\"#Linear-Regression--Theory\" data-toc-modified-id=\"Linear-Regression--Theory-1.1\"><span class=\"toc-item-num\">1.1&nbsp;&nbsp;</span>Linear Regression- Theory</a></span><ul class=\"toc-item\"><li><span><a href=\"#Linear-regression-with-one-variable\" data-toc-modified-id=\"Linear-regression-with-one-variable-1.1.1\"><span class=\"toc-item-num\">1.1.1&nbsp;&nbsp;</span>Linear regression with one variable</a></span><ul class=\"toc-item\"><li><span><a href=\"#Model-Representation\" data-toc-modified-id=\"Model-Representation-1.1.1.1\"><span class=\"toc-item-num\">1.1.1.1&nbsp;&nbsp;</span>Model Representation</a></span></li><li><span><a href=\"#Cost-function\" data-toc-modified-id=\"Cost-function-1.1.1.2\"><span class=\"toc-item-num\">1.1.1.2&nbsp;&nbsp;</span>Cost function</a></span></li><li><span><a href=\"#Gradient-Descent\" data-toc-modified-id=\"Gradient-Descent-1.1.1.3\"><span class=\"toc-item-num\">1.1.1.3&nbsp;&nbsp;</span>Gradient Descent</a></span></li><li><span><a href=\"#Gradient-Descent-for-linear-regression\" data-toc-modified-id=\"Gradient-Descent-for-linear-regression-1.1.1.4\"><span class=\"toc-item-num\">1.1.1.4&nbsp;&nbsp;</span>Gradient Descent for linear regression</a></span></li></ul></li></ul></li></ul></li><li><span><a href=\"#Linear-Models-for-regression\" data-toc-modified-id=\"Linear-Models-for-regression-2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span>Linear Models for regression</a></span><ul class=\"toc-item\"><li><span><a href=\"#Linear-Regression\" data-toc-modified-id=\"Linear-Regression-2.1\"><span class=\"toc-item-num\">2.1&nbsp;&nbsp;</span>Linear Regression</a></span><ul class=\"toc-item\"><li><span><a href=\"#makewave:-1-D-dataset\" data-toc-modified-id=\"makewave:-1-D-dataset-2.1.1\"><span class=\"toc-item-num\">2.1.1&nbsp;&nbsp;</span>makewave: <em>1</em>-D dataset</a></span></li><li><span><a href=\"#boston-housing:-n-D-dataset\" data-toc-modified-id=\"boston-housing:-n-D-dataset-2.1.2\"><span class=\"toc-item-num\">2.1.2&nbsp;&nbsp;</span>boston housing: <em>n</em>-D dataset</a></span></li></ul></li><li><span><a href=\"#Ridge-Regression\" data-toc-modified-id=\"Ridge-Regression-2.2\"><span class=\"toc-item-num\">2.2&nbsp;&nbsp;</span>Ridge Regression</a></span><ul class=\"toc-item\"><li><span><a href=\"#boston-housing:-n-D-dataset\" data-toc-modified-id=\"boston-housing:-n-D-dataset-2.2.1\"><span class=\"toc-item-num\">2.2.1&nbsp;&nbsp;</span>boston housing: <em>n</em>-D dataset</a></span></li><li><span><a href=\"#alpha\" data-toc-modified-id=\"alpha-2.2.2\"><span class=\"toc-item-num\">2.2.2&nbsp;&nbsp;</span><code>alpha</code></a></span></li><li><span><a href=\"#alpha---Qualitative-insight\" data-toc-modified-id=\"alpha---Qualitative-insight-2.2.3\"><span class=\"toc-item-num\">2.2.3&nbsp;&nbsp;</span>alpha - Qualitative insight</a></span></li><li><span><a href=\"#Training-size---insight\" data-toc-modified-id=\"Training-size---insight-2.2.4\"><span class=\"toc-item-num\">2.2.4&nbsp;&nbsp;</span>Training size - insight</a></span></li></ul></li><li><span><a href=\"#Lasso\" data-toc-modified-id=\"Lasso-2.3\"><span class=\"toc-item-num\">2.3&nbsp;&nbsp;</span>Lasso</a></span><ul class=\"toc-item\"><li><span><a href=\"#boston-housing:-n-D-dataset\" data-toc-modified-id=\"boston-housing:-n-D-dataset-2.3.1\"><span class=\"toc-item-num\">2.3.1&nbsp;&nbsp;</span>boston housing: <em>n</em>-D dataset</a></span></li><li><span><a href=\"#alpha\" data-toc-modified-id=\"alpha-2.3.2\"><span class=\"toc-item-num\">2.3.2&nbsp;&nbsp;</span><code>alpha</code></a></span></li><li><span><a href=\"#alpha---Qualitative-insight\" data-toc-modified-id=\"alpha---Qualitative-insight-2.3.3\"><span class=\"toc-item-num\">2.3.3&nbsp;&nbsp;</span>alpha - Qualitative insight</a></span></li></ul></li></ul></li><li><span><a href=\"#Miscallaneous\" data-toc-modified-id=\"Miscallaneous-3\"><span class=\"toc-item-num\">3&nbsp;&nbsp;</span>Miscallaneous</a></span><ul class=\"toc-item\"><li><span><a href=\"#Additional-Datasets\" data-toc-modified-id=\"Additional-Datasets-3.1\"><span class=\"toc-item-num\">3.1&nbsp;&nbsp;</span>Additional Datasets</a></span><ul class=\"toc-item\"><li><span><a href=\"#Dataset-1:-1-D\" data-toc-modified-id=\"Dataset-1:-1-D-3.1.1\"><span class=\"toc-item-num\">3.1.1&nbsp;&nbsp;</span>Dataset 1: 1-D</a></span></li><li><span><a href=\"#Dataset-2:-2-D\" data-toc-modified-id=\"Dataset-2:-2-D-3.1.2\"><span class=\"toc-item-num\">3.1.2&nbsp;&nbsp;</span>Dataset 2: 2-D</a></span></li><li><span><a href=\"#Dataset-3:-n-D\" data-toc-modified-id=\"Dataset-3:-n-D-3.1.3\"><span class=\"toc-item-num\">3.1.3&nbsp;&nbsp;</span>Dataset 3: <em>n</em>-D</a></span></li></ul></li><li><span><a href=\"#ElasticNet\" data-toc-modified-id=\"ElasticNet-3.2\"><span class=\"toc-item-num\">3.2&nbsp;&nbsp;</span>ElasticNet</a></span></li></ul></li><li><span><a href=\"#Summary\" data-toc-modified-id=\"Summary-4\"><span class=\"toc-item-num\">4&nbsp;&nbsp;</span>Summary</a></span></li></ul></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Models for regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-08T14:58:57.398114Z",
     "start_time": "2018-09-08T14:58:57.392122Z"
    }
   },
   "source": [
    "## Linear Regression- Theory"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Refer \"`Coursera > Introduction to Machine Learning > Week 1 & 2`\" for in-depth theory behind Linear Regression with one variable and multi variable"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-08T14:59:18.297117Z",
     "start_time": "2018-09-08T14:59:18.290141Z"
    }
   },
   "source": [
    "### Linear regression with one variable "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-08T15:09:14.905786Z",
     "start_time": "2018-09-08T15:09:14.900789Z"
    }
   },
   "source": [
    "#### Model Representation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-08T15:12:46.144727Z",
     "start_time": "2018-09-08T15:12:46.135731Z"
    }
   },
   "source": [
    "<p><img src=\"https://prasanth-ntu.github.io/html/ML-Course/Intro-to-ML-with-Python/images/linear_regression_model_representation_1.png\" alt=\"linear_regression_model_representation_1\" title=\"linear_regression_model_representation_1-wikipedia\" style=\"max-width:400px;\"></p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Cost function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-08T15:17:00.530928Z",
     "start_time": "2018-09-08T15:17:00.525930Z"
    }
   },
   "source": [
    "#### Gradient Descent"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-08T15:17:32.968583Z",
     "start_time": "2018-09-08T15:17:32.960587Z"
    }
   },
   "source": [
    "#### Gradient Descent for linear regression "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Models for regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-09T02:45:36.362215Z",
     "start_time": "2018-09-09T02:45:36.100519Z"
    }
   },
   "source": [
    "For regression, the prediction formula for **a linear model with one input feature (variable)** is\n",
    "\n",
    "- `ŷ = w[0]*x[0] + b = w*x + b`\n",
    "\n",
    "<p style=\"color:green; font-size:110%;  border-left: 5px solid blue; padding-left: 10px;\"><b>This is nothing but equation for a line.</b></p>\n",
    "\n",
    "Here, \n",
    "- `x` denotes the input features (`x[0]` is input feature of a single data point) and, \n",
    "- `ŷ` denotes the prediction made by the model.\n",
    "- `w` is the slope (*weights or coefficients*) along each feature axis (`w[0]` is slope along axis `x[0]`)\n",
    "- `b` is the intercept (offset) along `y-axis`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Trying to learn the parameters, `w` and `[b]` is the task of the linear models. \n",
    "\n",
    "For models with `n` input features, the prediction formula will become as\n",
    "\n",
    "- `ŷ = w[0]*x[0] + w[1]*x[1] + ... + w[n-1]*x[n-1] + b = w*x + b`\n",
    "\n",
    "Let's look at an one-dimensional (one input variable) `wave` dataset which will have a following linear line that best approximates the input features with output values.\n",
    "\n",
    "From the output below, we see that the slope `w[0]` of the linear line is around 0.4. The intercept `b` is close to 0.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-09T03:12:31.652230Z",
     "start_time": "2018-09-09T03:12:31.151966Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w[0]: 0.393906  b: -0.031804\n"
     ]
    },
    {
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T1gtPzx2NOWMHeqSWjRGmV3YUi6cRwfGeqFFp9ePc3mjDidN1+PhIPS7/21ak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\nJyIyCQY+EZFJ/H+gDGFjX+b0vAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c12369fa58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import mglearn\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib\n",
    "\n",
    "mglearn.plots.plot_linear_regression_wave(); plt.title('Linear Regression on One-dimensional wave dataset')\n",
    "fig = matplotlib.pyplot.gcf(); fig.set_size_inches(8, 6); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p><b>Linear models for regression can be characterized as regression models for which the prediction is </b>\n",
    "<ul style=\"color:purple; font-size:110%;  border-left: 5px solid blue; padding-left: 20px; list-style: none; line-height: 190%;\">\n",
    "<li>a line for a single input feature (1D),</li>\n",
    "<li>a plane when using two features (2D), or</li>\n",
    "<li>a hyper‐plane in higher dimensions (that is, when using more features).</li></ul></p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are many different linear models for regression. The difference lies in how the model parameters `w` and `b` are learned from the training data, and how model complexity can be controlled. In this post, we will look at the most popular linear models for regression, namely\n",
    "- <p><code style=\"font-size:120%;color:green\">Linear Regression</code></p>\n",
    "<p><img src=\"https://prasanth-ntu.github.io/html/ML-Course/Intro-to-ML-with-Python/images/Cost_function_3_LR.png\" alt=\"Cost function - Linear Regression\" title=\"Cost function - Ridge Regression\" style=\"max-width:250px;\"></p>\n",
    "- <p><code style=\"font-size:120%;color:green\">Ridge Regression</code></p>\n",
    "<p><img src=\"https://prasanth-ntu.github.io/html/ML-Course/Intro-to-ML-with-Python/images/Cost_function_3_RR.png\" alt=\"Cost function - Ridge Regression\" title=\"Cost function - Ridge Regression\" style=\"max-width:280px;\"></p>\n",
    "- <p><code style=\"font-size:120%;color:green\">Lasso</code></p>\n",
    "<p><img src=\"https://prasanth-ntu.github.io/html/ML-Course/Intro-to-ML-with-Python/images/Cost_function_3_Lasso.png\" alt=\"Cost function - Lasso\" title=\"Cost function - Lasso\" style=\"max-width:320px;\"></p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear Regression "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Aka ordinary least squares (OLS), is the simplest and most classic linear method. \n",
    "- Linear Regression finds the best parameters `w` and `b` that minimises the mean squared error between true output, y and predicted output, h(x) or  on the training set.\n",
    "- `mean squared error (MSE)`= sum of squared differences between between the true and prediction values \n",
    "<p><img src=\"https://prasanth-ntu.github.io/html/ML-Course/Intro-to-ML-with-Python/images/MSE_1.png\" alt=\"MSE\" title=\"MSE\" style=\"max-width:250px;\"></p>\n",
    "\n",
    "\n",
    "<p style=\"color:red; font-size:110%;  border-left: 5px solid blue; padding-left: 10px;\"><b>Linear regression has no parameters to control/tune which makes it easy to use, but it also has no way to control model complexity. </b></p>\n",
    "\n",
    "For more details, refer http://scikit-learn.org/stable/modules/linear_model.html#ordinary-least-squares"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### makewave: *1*-D dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at an one-dimensional (one input variable) `wave` dataset for which we will find a linear line that best approximates the input features with output values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-14T03:21:16.320509Z",
     "start_time": "2018-09-14T03:21:09.336340Z"
    }
   },
   "outputs": [],
   "source": [
    "import mglearn\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.model_selection import train_test_split\n",
    "import numpy as np\n",
    "\n",
    "X,y = mglearn.datasets.make_wave(n_samples=60)\n",
    "X_train, X_test, y_train, y_test = train_test_split(X,y, random_state=42)\n",
    "\n",
    "lr = LinearRegression().fit(X_train, y_train)        # Fit the linear regression model on the training data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- The `intercept_` attribute learned by the `LinearRegression().fit(X_train, y_train)` method will always be a single float number.\n",
    "- The `coef_` learned is a `numpy` array with one entry per input feature. \n",
    "    - As the `wave` dataset code has only one input feature, `coef_` only has a single entry."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-09T04:15:01.729514Z",
     "start_time": "2018-09-09T04:15:01.720520Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--- Slope and intercept learned from the wave training data by Linear Regressor ---\n",
      "lr.coef_: [ 0.39390555]\n",
      "lr.intercept_: -0.031804343026759746\n"
     ]
    }
   ],
   "source": [
    "print ('--- Slope and intercept learned from the wave training data by Linear Regressor ---')\n",
    "print (\"lr.coef_: {}\".format(lr.coef_))              # slope or weight parameter learned from the training data\n",
    "print (\"lr.intercept_: {}\".format(lr.intercept_))    # intercept along y-axis learned from the training data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-09T04:15:31.572468Z",
     "start_time": "2018-09-09T04:15:31.562815Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--- Compute the linear line learned to include in the plot ---\n"
     ]
    }
   ],
   "source": [
    "print ('--- Compute the linear line learned to include in the plot ---')\n",
    "linear_x = np.array([min(X), max(X)])\n",
    "predicted_y = lr.coef_ * linear_x + lr.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-09T04:09:23.915959Z",
     "start_time": "2018-09-09T04:09:23.623307Z"
    }
   },
   "outputs": [
    {
     "data": {
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9e/a86HPffvstU6dOpU+fPgAsWLDAERBzc3NZsGABJ0+epLq62mW3ZneXaw8p4QghAkJe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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c12333a080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(7,5))\n",
    "\n",
    "plt.plot(X_train,y_train, 'o')                        # plot the training data\n",
    "plt.plot(X_test,y_test, 'x')                          # plot the test data\n",
    "\n",
    "plt.plot(linear_x, predicted_y)                       # plot the predicted linear line learned by the LR model\n",
    "\n",
    "# --- Center the axis tick marks --- #\n",
    "ax = plt.gca(); plt.ylim([-3,3])\n",
    "ax.spines['right'].set_color('none'); ax.spines['top'].set_color('none')\n",
    "ax.xaxis.set_ticks_position('bottom'); ax.spines['bottom'].set_position(('data',0))\n",
    "ax.yaxis.set_ticks_position('left'); ax.spines['left'].set_position(('data',0))\n",
    "\n",
    "plt.legend(['training data', 'test data', 'model'])\n",
    "plt.title('Input data and corresponding linear model')\n",
    "plt.grid(); plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-09T05:48:50.207539Z",
     "start_time": "2018-09-09T05:48:50.196548Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training set score: 0.67\n",
      "Test set score: 0.66\n"
     ]
    }
   ],
   "source": [
    "print(\"Training set score: {:.2f}\".format(lr.score(X_train, y_train)))\n",
    "print(\"Test set score: {:.2f}\".format(lr.score(X_test, y_test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- <p>An <code>R<sup>2</sup></code> test score of 0.66 is not very good. </p>\n",
    "    - *We achieved a training score of 0.819 & Test score of 0.834 using KNN with `n=3` in previous post for the same dataset.*\n",
    "- However, *scores on training and test sets are very close when using Linear Regression*.\n",
    "    - This implies **we are likely undefitting**.\n",
    "    - For 1D dataset, the model is usually very simple and restricted and there's little danger of overfitting.\n",
    "    \n",
    " \n",
    "- However, for higher dimensional datasets (i.e. dataseets with more number of features), linear models become more powerful, and there's more chance of overfitting. \n",
    "- If we compare the predictions made by straight line with those made by the `KNN` in previous post, using a straight line to make predictions seems very restrictive. \n",
    "    - It's somewhat unrealistic to assume that our target y is a linear combination of features.\n",
    "    - This gives a skewed perspective when we look at 1D data\n",
    "- For multi dimensional dataset, linear models can be very powerful. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### boston housing: *n*-D dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Let’s take a look at how `LinearRegression` performs on a more complex dataset, like the `Boston Housing dataset`.\n",
    "- This dataset has *506 input samples* and *105 derived features (or) variables*.\n",
    "- First, we load the dataset and split it into a training and a test set. Then we build the linear regression model as before:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-14T03:21:31.080398Z",
     "start_time": "2018-09-14T03:21:30.916138Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of training set: (379, 104)\n",
      "Shape of test set    : (127, 104)\n",
      "\n",
      "First 5 lr coefficients: [-402.75223586  -50.07100112 -133.31690803  -12.00210232  -12.71068728] ...\n",
      "lr intercept: 31.64517410082808\n",
      "No of lr coefficients learned: 104\n",
      "\n",
      "Training set score: 0.95\n",
      "Test set score    : 0.61\n"
     ]
    }
   ],
   "source": [
    "import mglearn\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.model_selection import train_test_split\n",
    "import numpy as np\n",
    "\n",
    "X,y = mglearn.datasets.load_extended_boston()\n",
    "X_train, X_test, y_train, y_test = train_test_split(X,y, random_state=0)\n",
    "print (\"Shape of training set: {}\".format(X_train.shape))\n",
    "print (\"Shape of test set    : {}\".format(X_test.shape))\n",
    "\n",
    "lr = LinearRegression().fit(X_train, y_train)       # Fit the linear regression model on the training data\n",
    "\n",
    "print (\"\\nFirst 5 lr coefficients: {}\".format(lr.coef_[:5]), \"...\")\n",
    "print (\"lr intercept: {}\".format(lr.intercept_))\n",
    "print (\"No of lr coefficients learned: {}\".format(len(lr.coef_))) # Same as number of input features\n",
    "\n",
    "print(\"\\nTraining set score: {:.2f}\".format(lr.score(X_train, y_train)))\n",
    "print(\"Test set score    : {:.2f}\".format(lr.score(X_test, y_test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- <p>From the training and test scores, we find that <i>the prediction is good on training set, but <code>R<sup>2</sup></code> score is worse on the test set</i>.</p>\n",
    "- This discrepancy is **a clear sign of overfitting**\n",
    "    - So, we should find a model that allow us to control complexity\n",
    "    - `Ridge regression` - Most commonly used alternative to standard linear regression, which we will look into next."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-08T15:49:22.293503Z",
     "start_time": "2018-09-08T15:49:22.289484Z"
    }
   },
   "source": [
    "## Ridge Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Rigde regression addresses some of the problems of standard Linear Regression (Ordinary Least Squares) by *imposing a penalty on the size of the coefficients*. \n",
    "- *We want the magnitude of coefficients (weights or slope) to be as small as possible;  in other words, all values of `w` should be close to zero*.  \n",
    "    - Intuitively, this means each feature should have as little effect on the outcome (=> having a small slope) while still predicting well.\n",
    "    - This constraint is called as `Regularization`\n",
    "    \n",
    "<p style=\"color:green; font-size:110%;  border-left: 5px solid blue; padding-left: 10px;\"><b>Regularization</b> means explicitly restricting a model to avoid overfitting.</p>\n",
    "\n",
    "- The ridge regression used here is also known as `L2 regularization`, which penalizes the Euclidean length of w\n",
    "\n",
    "The ridge coefficients minimize the penalized residual sum of squares. \n",
    "<p><img src=\"https://prasanth-ntu.github.io/html/ML-Course/Intro-to-ML-with-Python/images/Cost_function_2.PNG\" alt=\"Cost function\" title=\"Cost function\" style=\"max-width:250px;\"></p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### boston housing: *n*-D dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's ses how well `ridge regression` performs on the `boston house dataset`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-14T03:26:28.139772Z",
     "start_time": "2018-09-14T03:26:26.542060Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of training set: (379, 104)\n",
      "Shape of test set    : (127, 104)\n",
      "Training set score: 0.89\n",
      "Test set score: 0.75\n"
     ]
    }
   ],
   "source": [
    "import mglearn\n",
    "from sklearn.linear_model import Ridge\n",
    "from sklearn.model_selection import train_test_split\n",
    "import numpy as np\n",
    "\n",
    "X,y = mglearn.datasets.load_extended_boston()\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X,y, random_state=0)\n",
    "print (\"Shape of training set: {}\".format(X_train.shape))\n",
    "print (\"Shape of test set    : {}\".format(X_test.shape))\n",
    "\n",
    "ridge = Ridge().fit(X_train, y_train)\n",
    "\n",
    "print(\"Training set score: {:.2f}\".format(ridge.score(X_train, y_train)))\n",
    "print(\"Test set score: {:.2f}\".format(ridge.score(X_test, y_test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-08T15:51:11.109572Z",
     "start_time": "2018-09-08T15:51:11.059582Z"
    }
   },
   "source": [
    "- When trained using `linear regression`, the training score was `0.95` whereas test score was `0.61`.\n",
    "- When trained using  `ridge regression`, the training score was `0.89` (*lower* than `LR`) but test score was `0.75` (*higher* than `LR`).\n",
    "\n",
    "**The results are consitent with our expectation. **\n",
    "- With `linear regression`, we were overfitting our training data.\n",
    "- `Ridge` is a more restricted model, and we are less likely to overfit\n",
    "    - A less complex model => worse performance on train set, but better generalization on unknown test set."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `alpha`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p style=\"color:green; font-size:110%;  border-left: 5px solid blue; padding-left: 10px;\">The Ridge model makes a trade-off between the model simplicity (near-zero `w` coefficients) and its performance on training set.</p>\n",
    "\n",
    "- The tradeoff can be specified by the us, using the `alpha` parameter (called as `Regularization strength`)\n",
    "- When `alpha` parameter is not specified as in previous case, it uses default value of `alpha=1.0`, which have to be optimized for each dataset.\n",
    "\n",
    "<p style=\"color:orangered; font-size:110%;  border-left: 5px solid blue; padding-left: 10px;\"> Larger values specify stronger regularization (by forcing the coefficients <code>w</code> to move toward zero), which decreases the training set performance but might help generalization </p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-14T03:26:35.003014Z",
     "start_time": "2018-09-14T03:26:34.939071Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "alpha:   0.0010 | Training score: 0.95 | Test score: 0.63\n",
      "alpha:   0.0030 | Training score: 0.95 | Test score: 0.65\n",
      "alpha:   0.0100 | Training score: 0.94 | Test score: 0.70\n",
      "alpha:   0.0300 | Training score: 0.94 | Test score: 0.75\n",
      "alpha:   0.1000 | Training score: 0.93 | Test score: 0.77\n",
      "alpha:   0.3000 | Training score: 0.91 | Test score: 0.77\n",
      "alpha:   1.0000 | Training score: 0.89 | Test score: 0.75\n",
      "alpha:   3.0000 | Training score: 0.85 | Test score: 0.71\n",
      "alpha:  10.0000 | Training score: 0.79 | Test score: 0.64\n",
      "alpha:  30.0000 | Training score: 0.72 | Test score: 0.55\n",
      "alpha: 100.0000 | Training score: 0.60 | Test score: 0.42\n"
     ]
    }
   ],
   "source": [
    "training_score = []\n",
    "test_score = []\n",
    "alpha_settings = [0.001, 0.003, 0.01, 0.03, 0.1, 0.3, 1.0, 3, 10, 30, 100]\n",
    "for alpha in alpha_settings:\n",
    "    ridge = Ridge(alpha=alpha).fit(X_train, y_train)\n",
    "    training_score.append(ridge.score(X_train, y_train))\n",
    "    test_score.append(ridge.score(X_test, y_test))\n",
    "    print(\"alpha: {:8.4f} | Training score: {:.2f} | Test score: {:.2f}\".format(\n",
    "           alpha, ridge.score(X_train, y_train), ridge.score(X_test, y_test)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-14T03:28:33.882071Z",
     "start_time": "2018-09-14T03:28:33.118299Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--- Based on test set/ generalization ---\n",
      "\n",
      "Best alpha  = 0.3 | Training score = 0.914 | Test score = 0.773\n",
      "Worst alpha = 100 | Training score = 0.596 | Test score = 0.415\n"
     ]
    },
    {
     "data": {
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pp4k71i5PdFgQKWmGlLR0UtLSSU1zpuN8xGt+Ow+dYO/Rk5nd783bzOqdR3KNsUmVMvxw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\nD5Mn4ZQ6kfXaAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x19e93556940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import matplotlib\n",
    "\n",
    "plt.figure(figsize=(6,4))\n",
    "\n",
    "plt.semilogx(alpha_settings, training_score, '-.', label=\"training R^2 score\")\n",
    "plt.plot(alpha_settings, test_score, '-.', label=\"test R^2 accuracy\")\n",
    "plt.ylabel(\"R^2 score\")\n",
    "plt.xlabel(\"alpha (in log scale)\")\n",
    "plt.title(\"Comparison of training and test R^2 score as a function of alpha\\n\")\n",
    "plt.legend(); plt.grid()\n",
    "\n",
    "print ('--- Based on test set/ generalization ---\\n')\n",
    "\n",
    "index = test_score.index(max(test_score))\n",
    "print ('Best alpha  = {} | Training score = {:0.3f} | Test score = {:0.3f}'.\n",
    "       format(alpha_settings[index], training_score[index], test_score[index]))\n",
    "\n",
    "plt.plot(alpha_settings[index], training_score[index], 'x')\n",
    "plt.plot(alpha_settings[index], test_score[index], 'x')\n",
    "\n",
    "index = test_score.index(min(test_score))\n",
    "print ('Worst alpha = {} | Training score = {:0.3f} | Test score = {:0.3f}'.\n",
    "       format(alpha_settings[index], training_score[index], test_score[index]))\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the above plot, we see how the `alpha` corresponds to the model complexity.\n",
    "- It's evident that decreasing `alpha` from 100 to 0.1 allows the coefficients to be less restricted (we fix *underfitting* issue).\n",
    "- However if the `alpha` value is set too low (below 0.1), coefficients are barely restricted (we start facing *overfitting* issue) as the penalty for cost function is very low.\n",
    "    - Think, what happens when α is set to a very small value (close to 0). \n",
    "<p><img src=\"https://prasanth-ntu.github.io/html/ML-Course/Intro-to-ML-with-Python/images/Cost_function_2b.png\" alt=\"Cost function - Ridge > Linear regression\" title=\"Cost function - Ridge > Linear regression\" style=\"max-width:350px;\"></p>    \n",
    "    - We end up with a ridge model that is similar to `Linear Regression`.\n",
    "\n",
    "`alpha = 0.1 or 0.3` seems to work well.  We will discuss more about parameter optimization in later topics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-14T03:29:12.076069Z",
     "start_time": "2018-09-14T03:29:11.017493Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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NdnY2K1eupE+fPnTr1o3HH3+chx9+GIDbbruNkSNHVtpQLiwsjPvuu49nn322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\nAM8DB+eyhwFPF7adRbpbeWOrriuK7w3Sb6mtNnh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      "text/plain": [
       "<matplotlib.figure.Figure at 0x19e93606f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--- Based on test set/ generalization ---\n",
      "\n",
      "Best n_neighour  = 1 | Training score = 1.000 | Test score = 0.652\n",
      "Worst n_neighour = 20 | Training score = 0.675 | Test score = 0.479\n"
     ]
    }
   ],
   "source": [
    "# compare the different models (KNN with linear and ridge regression) on the multi dimensional `boston` dataset\n",
    "from sklearn.neighbors import KNeighborsRegressor\n",
    "\n",
    "training_score = []\n",
    "test_score = []\n",
    "# try n_neighbors from 1 to 20\n",
    "neighbors_settings = range(1, 21)\n",
    "\n",
    "for n_neighbors in neighbors_settings:\n",
    "    # intialize the knn model parameters\n",
    "    knn = KNeighborsRegressor(n_neighbors=n_neighbors)\n",
    "    # build/ train the model\n",
    "    knn.fit(X_train, y_train)\n",
    "    # save training set accuracy\n",
    "    training_score.append(knn.score(X_train, y_train))\n",
    "    # save test set (generalization) accuracy\n",
    "    test_score.append(knn.score(X_test, y_test))\n",
    "\n",
    "plt.figure(figsize=(6,4))\n",
    "plt.plot(neighbors_settings, training_score, label=\"training R^2 score\")\n",
    "plt.plot(neighbors_settings, test_score, '--', label=\"test R^2 accuracy\")\n",
    "plt.ylabel(\"Accuracy\")\n",
    "plt.xlabel(\"n_neighbors\")\n",
    "plt.title(\"Comparison of training and test R^2 score as a function of n_neighbors [in KNN]\\n\")\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "print ('--- Based on test set/ generalization ---\\n')\n",
    "\n",
    "index = test_score.index(max(test_score))\n",
    "print ('Best n_neighour  = {} | Training score = {:0.3f} | Test score = {:0.3f}'.\n",
    "       format(neighbors_settings[index], training_score[index], test_score[index]))\n",
    "\n",
    "index = test_score.index(min(test_score))\n",
    "print ('Worst n_neighour = {} | Training score = {:0.3f} | Test score = {:0.3f}'.\n",
    "       format(neighbors_settings[index], training_score[index], test_score[index]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-09T09:40:45.501147Z",
     "start_time": "2018-09-09T09:40:45.493152Z"
    }
   },
   "source": [
    "- Best test score using `Linear Regression   = 0.610`\n",
    "- Best test score using `Ridge Regression    = 0.773` \n",
    "- Best test score using `K-NearestNeighbours = 0.652` "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### alpha - Qualitative insight "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also get a more qualitative insight into how `alpha` parameter changes the model by inspecting the `coef_` (slope or weight) attribute of models.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 222,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-09T09:56:35.902317Z",
     "start_time": "2018-09-09T09:56:35.102218Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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cUUQAgKGKY7L7qpk1SFLwtz3ieJAwLTNaVGX9N/0qq1JLY0tEEQEA4qK7ra2o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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c1259c5940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "No of features = No of coefficients = 104\n"
     ]
    }
   ],
   "source": [
    "ridge = Ridge(alpha=1).fit(X_train, y_train)\n",
    "ridge10 = Ridge(alpha=10).fit(X_train, y_train)\n",
    "ridge01 = Ridge(alpha=0.1).fit(X_train, y_train)\n",
    "lr = LinearRegression().fit(X_train, y_train)\n",
    "\n",
    "plt.figure(figsize=(16,6))\n",
    "plt.title('Comparing coefcient magnitudes for ridge regression with different values of alpha and for linear regression')\n",
    "plt.plot(ridge.coef_, 's', label=\"Ridge alpha=1\")\n",
    "plt.plot(ridge10.coef_, '^', label=\"Ridge alpha=10\")\n",
    "plt.plot(ridge01.coef_, 'v', label=\"Ridge alpha=0.1\")\n",
    "plt.plot(lr.coef_, 'o', label=\"LinearRegression\")\n",
    "plt.xlabel(\"Coefficient index\")\n",
    "plt.ylabel(\"Coefficient magnitude\")\n",
    "plt.hlines(0, 0, len(lr.coef_))\n",
    "plt.xlim(0,50)\n",
    "plt.ylim(-25,25)\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "print (\"No of features = No of coefficients = {}\".format(len(lr.coef_)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p style=\"color:green; font-size:110%;  border-left: 5px solid blue; padding-left: 10px;\"> A higher <code>alpha</code> means a more restricted model (more penalty), so we execpt the <code>coef_</code> (weights) to have smaller magnitude for a higher value of <code>alpha</code>.</p>\n",
    "\n",
    "This is confirmed by the above plot. Here,\n",
    "- `x-axis` spans over 104 data points, but only first 50 data point are shown. It corresponds to the `coeff_` or` weight` of `n`th feature/ dimension\n",
    "- `y-axis` shows the numeric (magnitude) values of the corresponding values of the coefficients.\n",
    "    <p style=\"color:blue\"> &#9632; Coefficients of Ridge model with alpha=1. <font color=\"black\">Here, the coefficients are somewhat larger than range of -3 to 3</font></p>\n",
    "    <p style=\"color:orange\"> &#9650; Coefficients of Ridge model with alpha=10. <font color=\"black\">Here, the coefficients are mostly between -3 to 3</font></p>\n",
    "    <p style=\"color:green\"> &#9660; Coefficients of Ridge model with alpha=0.1. <font color=\"black\">Here, the coefficients have large magnitude</font></p>\n",
    "    <p style=\"color:red\"> &#9679; Coefficients of Linear model (no alpha parameter involved). <font color=\"black\">Here, the coefficients are so large that many of them are outside the chart range</font></p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Training size - insight"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another way to understand the effect of regularization is to fix `alpha` but vary the **size of training data**.\n",
    "In the figure below, the `boston housing` dataset is subsampled & evaluated on `LinearRegression` and `Ridge(alpha=1)` with training subsets of increasing size."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-14T04:06:17.945884Z",
     "start_time": "2018-09-14T04:06:14.305961Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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VmTF2aXEQdwU88MADZ4YPHx5rG8zeOH3ixIllERERxqioqMSBAwfGJiUlVV2u\nsoSFhZlfe+21nHHjxsXEx8cb8vPzNRqNRti3QjgyYMCA6nHjxhUvXLiwycUHH3/88dF33323S0xM\nTMJrr70WmJiYWGmf9tZbbwXq9XrDyy+/HBgTE1Pt4+NjAYAvvvgiOzMz01mv1xv0er1h8uTJ3QsL\nCzttENeRz4WNGzd6BQYGJtkejzzySHBr8xo7dmzFM888c+rGG2+Mjo2NNej1+oSvv/7aGwCee+65\n3BUrVgTo9XrDs88+G9y3b98m3ZAt+ec//3lq1apVfjk5OdpZs2YVTZ48uTA5OTlWr9cbkpKSDBs3\nbnQHgH/84x+n8/PzNVFRUQnjxo3rnpSUVOnl5dVs86VWq8WaNWsOr1q1ylev1xuio6MTZs6cGW40\nGlW7du1y6du3b1xsbKyhd+/e8XPmzDkTGRlpWrlypU9sbGxCfHy8Ye7cueGLFi1qchX3Y489lp+Q\nkFCdmJhoSExMNCQkJFTPmzcv/3z2lzHGbHiKkatQcXGxysfHxwoAixcv9luxYoX/rl27Lnk3oU1p\naanKw8PDqlKpsGvXLudRo0bFZmVlHQgICHDc/8euiCt9LrQlo9FIFosFrq6uoqioSDVw4MC4RYsW\nnbj55pvPK2hsazzFCGPMptO2eDDH/vGPf3RZvXq1r8ViIS8vL/P777+fcznz+/nnn92feuqpUNs/\nDEuWLMnhAK59uNLnQlsqKChQX3/99TEWi4WMRiNNnDixqKMFcIwxZo9b4hhjrAPhljjGmA2PiWOM\nMcYY64A4iGOMMcYY64A4iGOMMcYY64A4iGOMMcYY64A4iGOMMcYY64A4iLsC5s2bF1xTU3NRtzk6\n1zaIqI9erzcoE6kaPv30Uy9b2qJFiwIc3dx8yZIlfmPGjOnWXBq79K7UuVBaWtrksx0XF2eoqKi4\nLLfbas68efOCfX19e8bFxRmioqISbrzxxqiysrJ2+51z7Ngx7YABA/RtXQ7GGGutdvuF2pm8/vrr\nXY1G40X9eLZmGzt27MjMyspKf/HFF0/ef//93UwmEwDgiSeeyF+wYEHexeTPLo0rdS40JzMzM93d\n3f2KzClku+fnpEmTCjMzM9MzMjLSc3NznV5++eVm/5m4ULZz/FKIjIw0/f777wcv2QYZY+wy6/ST\n/f7fV6lhB8+Uu16ObeuDPKr+OanniZbWmTZtWjgA9OvXL06lUmHLli1ZKpVKzJw5Myw9Pd3VaDRS\ncnJy+fuVRdI5AAAgAElEQVTvv39Co9Hgscce6/rNN9/46nQ6QUTYvHlz1qOPPhrSeBv+/v4OJ8u9\n4YYbyquqqlT5+fma4OBg87x584IrKipU77333smamhq65557wrdu3erh4+NjTkxMrLutU01NDd19\n993h27dv9/Dz8zMlJCRU5+XladatW5cNAE8//XTQmjVrfCwWC4KCgkzLly8/Fh4e3nHu0P3trDDk\npV+WcwFdDFW4+a12dy7YI6I+JSUle7y8vKwhISE9Jk+eXLhhwwbP/Px87axZs8785S9/yQeA1NRU\n3ezZs8OLioo0JpOJHnroobOPPPJIIQBMmDAhKjs727m2tpYiIiKM//73v48FBARY1q5d6zFv3ryw\npKSkqgMHDrguWLDglH3ezs7Oon///hXHjx93si375Zdf3J566qmQiooKNQA8++yzuXfccUcpAPzt\nb38LWLp0aaCHh4dl1KhRpcuXLw8oLi5OzcrKcho4cGD85MmTC7ds2eIxY8aMgjlz5hQ88sgjIdu2\nbfOora2l+Pj46o8//jjHy8vL+sorr/i//fbbgU5OTsJqteKLL77ITkpKqvnTn/4UvnXrVg8nJyfh\n5uZm3b17d6Zt28XFxakA8NVXX3k+++yzoRaLBX5+fub3338/JzEx0bh27VqPxx9/PKx3796VO3fu\ndCMifPbZZ9m9e/euae3pwhhjlwK3xF1mn3zyyXFAtpJlZmam+/v7W2bOnBk2dOjQ8v3792dkZGSk\nFxQUaBYvXux/9uxZ9XvvvRe4f//+9MzMzPRt27Zlenl5WZrbRkt5rly50mfgwIHlwcHBTQKsV199\nNSAnJ8fp4MGDaZs3bz64d+9eN/u0kydPOh06dOjA5s2bD6amptYFPG+//bZvdna2bu/evRnp6ekZ\no0ePLn344YfDLl1NdX5tcS60pKqqSrV3797MX375JevFF18MLS0tVZlMJkydOrXb4sWLTxw4cCDj\nt99+y3z99de77tmzxxkAli5deuLAgQMZBw8eTI+Pj69esGBB3X10jxw54vLggw/mZ2Zmpk+ZMqXU\nPq/i4mLVtm3bPCZPnlwMyLsnzJo1K+LLL788mpaWlvHdd98dfuSRRyIKCgrUv//+u8sbb7zRdfv2\n7ZkHDhzIKCkpaXCP2ZKSEk2/fv0q09PTM5544on85557LsjLy8uyf//+jKysrPSuXbvWPvPMM10B\nYOHChaG//vrrwczMzPTU1NSM6Ojo2t9++81l27ZtHocPH07LyspKX79+/aHGdXPq1CnNfffdF7Vy\n5crsgwcPpt92221FU6dOjbKlHz582HnWrFl5Bw8eTL/55puLnn/++a4XehwYY+xCdfqWuHO1lLWF\nH3/80XvPnj1ub775ZhAA1NTUqIKDg01+fn6WiIgI4+TJk6Ouu+66skmTJpXa7mvZGv369YurrKxU\nFxYWateuXdvs/S83btzocddddxXqdDqh0+nEbbfdVrht2zZ3W9rUqVMLtVottFqtmDRpUtHWrVvd\nAWDt2rXe+/btc0tISDAAgMViIQ8Pj45166xztJS1hct1LrTGXXfdVQQAsbGxtZ6enpbs7Gwnq9WK\n7Oxs5ylTptSNkzSZTLR//37nXr161SxdutRv1apVviaTiaqqqtRRUVF1rU/h4eE11113XaV9Hl99\n9ZXfxo0bPY8fP64bPHhw2fjx48sBeSu2kydPOo0ePTrGti4RIT09Xbdp0yb3ESNGlNr+Cbn//vsL\nvv32W1/bejqdTvz5z38utr3+/vvvvSsqKlRr1qzxAYDa2loyGAzVADBw4MDyqVOnRt5www2lt9xy\nS4nBYKiNi4urNZvNdPvtt0cOHz687LbbbmsQcALAxo0b3eLj46v79OlTAwBz5swpePLJJ8OLi4tV\nABAVFWVMTk6uBoBBgwZVrlu3zvtijgVjjF2ITh/EtUdCCHz77beHDQZDbeO0PXv2ZPzwww/uP/30\nk2e/fv3i//vf/x4aMGBAdWu2u2PHjkwvLy/rc889Fzh9+vRuhw8fPuDq6npJxkAJIfD444/nzp07\nt/BSbI9Jl+tcaA0XF5e6oFCtVguz2Qwigre3tzkzMzO98frr1q1z/+ijjwK2b9+eGRwcbH733Xd9\nly1bFmBLd3NzaxJkTpo0qfC99947efz4cc3gwYPjFi1aFDB//vx8IQRiY2Ord+7c2eSfjU2bNrmf\no9wWlaq+E0EIgcWLFx+fMGFCk/ugrl+//sjGjRtdf/zxR8/rrrsu9o033si57bbbyrKystK+++47\njx9++MFz4cKFoTt37myyvy3R6XT2dQeLxXLFLhhhjDEb7k69Atzc3KxFRUV1XUKjRo0qeeGFF7ra\nBn+fPn1ak5mZ6VRcXKzKzc3Vjhs3ruL111/PjYmJqd6zZ49Lc9toyfPPP3/Wz8/P/MorrwQ0TktJ\nSSn797//7WcymVBRUUGrVq3ys6UNHTq0/PPPP/c1mUyoqqqib775pq71Y/z48SUffPBBl/z8fDUA\nVFdX0/bt210uuFKuUlf6XDhfPXv2rHF2dra+9dZbdcd+z549zkVFRaqioiK1h4eHJTAw0FxdXU0r\nVqzwb+12w8PDzYsWLTrx6quvdq2oqKCRI0dW5OTk6P773/962NbZuHGjq9VqxciRI8t//fVXr9On\nT2sA4MMPP/RzvGVg7NixJa+//nqg7crb4uJi1e7du51NJhMyMjJ0w4cPr/rb3/52ZujQoWW7d+92\nzc3N1VRUVKgmTpxY9tZbb510d3e3ZGVl6ey3mZKSUpmRkeFi60b+17/+5RcfH191qVtDGWPsYnAQ\ndwU88MADZ4YPHx4bFxdnKCgoUC9duvSESqUS8fHxCXq93jBq1KiYnJwcp6KiIvWNN97YXa/XG2Ji\nYhK6dOlimj59enFz22gpP5VKhUWLFp3417/+FdR4Sol58+YVhIaG1kZHRycOHjw49pprrqnr/nr8\n8cfzAwMDTTExMYnJycmxMTEx1Z6enhYAmDVrVtHkyZMLk5OTY/V6vSEpKcmwcePGFltMWFNX6lyI\niYlJDAwMTAoMDEyKjIxMbG35tFot1qxZc3jVqlW+er3eEB0dnTBz5sxwo9GomjhxYllERIQxKioq\nceDAgbFJSUlV595ivTvuuKO0e/fuNa+99lpAQECA5auvvjr8wgsvBMfGxhq6deuWsGDBgmAhBK69\n9trq2bNnnxk4cGBcQkJCvEajgbu7u8Ou+xdffPFMYmJida9evQx6vd4wcODAuP379zubzWaaPn16\npG3qnbNnz2rnzp2bn52d7ZSSkqKPjY01xMXFJYwYMaJ0xIgRDbqBg4ODze+///7RO++8M0qv1xs+\n//xzv08//fTo+ewvY4xdbiTEFZlx4IpKTU091rNnz4K2LkdHVFxcrPLx8bFWV1fTqFGjom+99dbi\nefPmcV2yK8p2HgJyvrkjR47oVq9ezUEUgNTUVP+ePXtGtnU5GGNtj8fEsQaGDRumr62tVRmNRhoy\nZEj57NmzOYBjV9ycOXNCd+zY4W4ymSg8PNz40Ucf5bR1mRhjrL3hII41sG/fvsy2LgNjtqlUGGOM\nOdZZx8RZrVYrXy3GGOtUlO81vriCMQag8wZxB/Lz8704kGOMdRZWq5Xy8/O9ABxo67IwxtqHTtmd\najab7z1z5swHZ86cSUTnDVQZY1cXK4ADZrP53rYuCGOsfeiUV6cyxhhjjHV23ErFGGOMMdYBcRDH\nGGOMMdYBcRDHGGOMMdYBcRDHGGOMMdYBcRDHGGOMMdYBcRDHGGOMMdYBcRDHGGOMMdYBcRDHGGOM\nMdYBcRDHGGOMMdYBcRDHGGOMMdYBcRDHGGOMMdYBcRDHGGOMMdYBcRDHGGOMMdYBcRDHGGOMMdYB\ncRDHGGOMMdYBadq6AJeDv7+/iIyMbOtidDqVlZVwc3Nr62KwS4iPaefEx7Xz4WPaOdmO665duwqE\nEAHn+/42DeKIaBmA8QDyhBCJzaQTgMUAbgBQBWCGEGL3ubYbGRmJnTt3XuriXvU2bNiAlJSUti4G\nu4T4mHZOfFw7Hz6mnZPtuBJRzoW8v627U5cDGNNC+lgAMcrjfgDvXIEyMcYYY4y1e23aEieE2ERE\nkS2schOAFUIIAeA3IvImoq5CiNNXpICO1JQBy5qJPfvfC/S9Byg/C3xyS9P05EeAnrcDRUeBz+9s\nmp4yHzBMAM6mAV/fJ5epNYDGBdA6A0MeB6KGAPkHgd/eBjTOcrnGBdDoAMNNgG8UUJYLnNxRv1zr\nItf16w44uQFmI2CplcvU2ktbN4wxxhi7Itr7mLgQACfsXp9UljUJ4ojofsjWOgQGBmLDhg2XrVAq\nSw3irR5Nludln0Z+xQZoa8ugbyb9zKEcFBZvgK6mANHNpOdmZqM4bwNcqnLRzeoBQEBltkBVXQWV\ntRhH9+5BSY4FXiUHkJD2DVRWE1TWWqiEGQCQmmdFsW9v+OdvQ2Lay022v7vXP1DmFY/AM78gPnMx\nIHOARe0Eq0qH1J5/RaV7JLxK0uFbtBtGnR+MOl8YdX6odfJDRa36stYru/IqKir4mHZCfFw7Hz6m\nndPFHleSjVxtR2mJW+tgTNxaAP8QQmxRXv8M4EkhRIsD3vr27SuuqjFxVgtgrgHUTrJlraYMKDku\nl5lrAFMNYK4GIpIBV18gLwM49KNskTNXy7+mKmD4M4CbH7D9beCHZwBhaZDNtms/wqDRtwJ7PgUO\nrQc8QwCProBnsHyEDQBU6jaqBHYheJxN58THtfPhY9o52Y2J2yWE6Hu+72/vLXGnAITZvQ5VljF7\nKrXsJrVx9gSCmsTE9brEy4cj1z4EDHgAqMgDynOBstNAWS5qq7xkek0JcDYdOPQTYKpUyqABnsmT\nz394BjiyAfDsWh/keYcD10yV6aZq2ZVLdMG7zBhjjF3t2nsQtwbAw0T0OYABAErbfDzc1UKllkGY\nZ1fZgQ0Atibfa2fJhxCAsUwGeZX59a1w3hGAV4gcm5e7R6Z52QVxX9wFZG8E3Pzlw9UfCEwARr8k\n0w+uB6xmwC0AcPWTf3Ue7S/oE0K2dNZWynGHTm6AxQRUFcm6IJUMblVqGbRyKyVjjLFLqK2nGPkM\nQAoAfyI6CWABAC0ACCHeBfAd5PQihyGnGLm7bUrKmkUEOHvJB+Lql/e/Tz5szLVAdXH966TbgcBE\noKoAqFQepXZDH39aCOSlNcwrahjwpzXy+eqHZRewW4Ds/nX1ly2LYf1lem0loHVtGPQJIV9brUBR\nNlBbIderrZTP/WOAoB6yK3rrG/XLbetcMxVIuAUoPAIsH1efLqxy+zcuBvrMAM4eAN5LaVpXt34A\nJE0Gjm0BPp4gAzqVBiA1oFIBk5YB0dcBR34F1syRy+rSNcBNbwIhfYDDPwMbFynBoS1I1ABj/iEv\nXMneAOz+pH65LZ+U+YB7F+DYVuDwj3XpEceOA5t3A/3vB3TuwMldwOk9du9XypBws+yqz8sASk7U\nb9eWR9gAWb9lubIOVWq7dbTynwEAqK0CIOz2Td3+gnPGGOsg2vrq1CnnSBcAZl2h4rDLReMEeATW\nv066reX17/oKqDgLVBbKVryqAsDd7v1lp4DCwzLd1p3bY3J9EPeKXraIufrKv7WVQJ8/AWNfBixG\n4F99muY5eJ4M4iwmYMsbMqBxcpeta05uclwhIAPWmFEyTeuqpLvLIAYAPEOBca/JcYrCIv9azXLb\ngBxHOPhRuawu3QJ4BMt0V18gMtnu/Wb5XOsq01VqWZ9WqwyORXX9OoAMiHP31C+zbWPQbJmeuwfY\n/paSvxVRAHAMwDV3yn0+uA7YtKhp/cTdIIO43SvkldGNLSiRfzf8Xa5jz8kD+MtJ+Xz1LCDtm4bp\nnqHAPCVo/+YBIGebvKpa4yz/+nYDJr4v0zcukld3a53r073D5VXhAJC+RgbX9u936wJ0TZLpxccA\nkAy+bcfGyQ3wVkZtnNql1Kut7s2Ae1D98IT01fIcsa9b/1ggfABgMQO/v2v3XqvMJ3wg0G2Y/Mcj\n9TNArZN1qdHJ5/4x8qpycy2Qn6ksd5IPjU62Qmt0TeucMXbVa/MLGy6Hq+7ChiukXQ6sra2SQR6p\nAK9Q2eK27U0Z/FUXyR9CJzcgfJAMRIQA9q+qD85sgZp7oAygbJ+Hq6F1yGrFxg2/YNiQwTJIIKpv\nebQFMBaTDER8u8uWv9KTcgodW7rtET1SbjN3jwyUrHZBEKnqu9Kz1gEFB+uDTKsZcHKV0+8AwG/v\nAKdTlYtyjPKvexBwizJF5KoZwMmdDdO79gTu/Ummv30tkJfecD+7pQDTV8vnb/SQF/3Yi78RuH2l\nfP5yZMNWYwDoObU+/xcC5PQ89vrdB4x7RQZhLzYz4fqQx4CRz8kA+5/dm6aPfE6uU3wMWNyzafrY\nRXKM6tk0YOkwJbhzkgGgxgm4/iU5NdGZA8DauQCpUVJWAW9fX9namTJfBpKnU4HNr9a37tpaS6+d\nDXSJA07vk0Gm/TAAlQboPV1+ts6mAUd+kS2rdVMX6YDuI+Q/NxV5QPnpplMbObnLc4ddlHb5/csu\nWme/sIGxljm5Ak7h9a+JgOQ5jtcnarkl8GoI3mxUKgiVRrZq2diCW0e8QuXDkeBe8uFI7Bj5cGTg\nTMdpADB5edNl9v+ITl8jW2dNNfWBnpNrffrovwE1pfVduSq1bAms2/7HsiXNvivZ3S4we2BTw/eS\nWraUAbJ1bf7xht3g9ueTiw/waLoMAi21ynyNpvquZld/GUzalluMMjCMGKS831e2qNa9V1nPvYtM\nJ5Usi1VOOdSgRREAjBVAXmbDFmBhAa65S6aX5MiuePsWYGEBYkbLY35yp7xoqbFZf8ggbv8qYP1f\nmqY/mibfv+UNYNsSpYXUuT7Im/6tLHfqF7Krvy5NJ1ughz0p6zp3L1B+pr6VXOcB6DwbHh/GrjIc\nxDHGOjb7QMk9AEALP+rxN7a8rW7DWk5v6apu2xhRR1RqecGPIzr3lsvn2RW4boHj9EADMO0/AIC9\nzbXaRCYDD//h+P3xNzbN3z5Ato0LtZqVqYuU6Yl8ImV67A3yuanaLr1GBq8A0MUAGG5u+F5ztWzZ\nA+QwibpWVmVqJKsJSHlKpu94H9izsmH57Lvq18wGDv+iBHdKoOcdBkx4U6bv+1LmYQsAndxlAGwb\nhmG7IEnrJidZZ6wD4DOVMcZY8+wDZLW25Tu8+EbJhyP66+XDkSHz5MOe1VpfhuFPy7GPxgrAWC7H\nPtpaGQHZAmwxA7Xlcp3aCnnlvM2elcDRjQ23H5gIzNwqn386SY6JBOqHYUQkA3d8Kpd9+5AcpmEb\nC6t1lWNd+/xJpu9bJYceOLnJ1l+tmxwLbAtyjRWyhZGvUmeXEAdxjDHG2if7sXS2ScUd6XtP/QUu\nzZm+WrYA1ipBoLG8YZA6aDZQekpOfF5bKf962U1Taq6RQVxtpRyLW1sBVObVB3Hr5svxufZ6TAYm\nfiCfv6KXXf0aZxno6TzkeMuUJ2WL5zfKFeI6D+XhJa9ID+0DWC3wKDsEFITWp2tdrq7hH6xZHMQx\nxhjr/IiUMbSu9eMI7SU0c79re5OWtZz+4BYl+FOCPFOlHOdoM/wp2RpnUi4eMlbUj4c018j7XduC\nS4tRLh/6fzKIqypCn92PA7vt90cNjFoog8+y0/Kin7oAUHkk3AKE9pVX8h/8XgZ+Wtf6h193eUGX\nuVYGrVpX2drKwWGHwUEcY4wxdrFsAZkjtml+mqN1AR7ZW//abJRBnm1sns4d+xOfQQ99pJxg3Vgm\ng73g3jLdapYXglQVyqucbcFgQKwM4oqPyul9Gpv4IdBjEnDiN+BjZTwkqZUgz0VO7dMtBcjZDvzy\nojKpuWt9+rUPy0AwL1Neuax1llcn2/5GDJJ3EKoqkq2Y9he0aJw5YLwEOIhjjDHG2hONruHcgFoX\nFPr3A5JSml/fO6x+MvTmBCUBc/fL7mRTVf3fQGX+Q58oYPTf7dKUdNv8nMICQMju4lK7bfSaJtNP\n7gDWP9U035nbAWeDvKhk3ZNN0x9JlWMGf3tXTg1lPzWN1kWOR3T2AtL+Iyc6bxwADnlMjjE8thUo\nyJJjGVXK2E2Ns5xWCgDyD8qpg9Sa+nU0uvoxnMZy2aWt1irpHWfcIgdxjDHGWGemcZKTYjviHSbv\nme1I5GDg7u8cp/e8A4gbV3/FsW2KH1uQFDNK3mLR/spjc7W8rSIgA7luwxqmmY1ymh5A3inn8E/1\nVzyblcnXhzwu/+7/Eti1vGGZtK7A08qFLZsWySlw7Ll1Af7vkHz+zf1Alt3+kQrw1wOzfne8z+0E\nB3GMMcYYu3BqrRxb54hfd/lw5FzzRw59XD5shJDzGNoufBn1AjBsvpySxmKScyna7mIDyBa7nlOU\nu60o6Sq78KfXNHklsqW2fh2dZ8v73E5wEMcYY4yxjoOo4Vx+zp7y4UiX+JbneLR1u3ZAfC8Uxhhj\njLEOiFviGGPsErFaBcprzCiuqkVJtQlOahUMwbKFIC23FCoiOGlUcFKr4KRRwdVJDQ9nOYGuEALE\nV+oxxs4DB3GMMdaIEAIVRjNqTFYEeMirBH/JPIuTxdUoqTIpj1qE+7li7nV6AMDo1zfhYF55gztV\njU0Mwjt39QEATHnvN5TVmBvkM6lPKF6ZLG96r3/mexAIWrUM9LRqFe7oH455o/SoNVsx6d1t0Kpl\nAKhVAsHxSV1xc68QVBrNeOm7DKgIUBHh1CkjNpSlYZQhEMnR/iiurMXbGw6DiECA/EvAKEMgeof7\nIK+sBit/y6lbrlLWG5UQiLggT+SWVGP13lwlDdCoZBlS9AEI83VFXnkNdh4rhkZF0GpU0KpU0KgJ\n8V094eWiRVmNCWdLa6BVy+VatQoaFcHLRQuNWgWhVBoHsYydHw7iGGOdksUqUG2ywF0nv+YO55Uj\nt6SmrqWstNoEtYrw4DA54PrZbw9g25EClFbLIM1sFUgI9sT/5gwBALzx0yHsO1kKAHDXaeDlom0Q\ndIxP6opaSyC8XZ3g7aKFj5sW4b5udemLp/RCTa0FtRYras1W1FqsiPKvT5+ZEg2Tkmb72z1ApluF\ngJ+bE2otVpjMAlXVJpjMVpRWmwAAVbUWrD9wBgIyAK01mbEj7yQi/FyRHO2P8hozVv52HAICQqBu\nvRBvFxnElRux5JfDTeowxMcFcUGeOFFUhZfXZTZJf29aH4T5uuLAqVI89OnuJun/vncABkX7Y2NW\nPmZ/tqdJ+rezknFNmDe+2HEC87/ZD62aoFECQCe1CqsevBbdAtxhsQqoVRzgMdYYB3GMsXbFZLGi\nosaMCqMZ5TVmxAV5QKUi7DtZgv2nShukVdWa8fLEJBARlvx8CKv3nkKF0YyKGjMqay3wcNZg//Oj\nAQCv/3QI/9t3ukFeYb4udUGct6sWsUEe9UGYqxNCfFzq1n3nrj5wUqvg7aqFVt10OPHskTEt7tfw\n2GbuEmBn3ii9wzRnrRof3d3fYXqAhw67nh1V93rDhg1ISUmpex3u54qMFxxf/ZcY4oVj/xgHIeqD\nPKsQUCtBat9IX2T8dQwEBKwCMFtkEOqpdAX3j/LDurlDYLYI1FqsMFsEzBZrXVdy7wgfvDmlF0xK\nmskq/4Yq9ZsQ7IU5I6Jhssr3mSwCJou1rqt50bpM/JZdiFt7h+LGnsHwdXNqsS4Zu1pwEMcYu6Qs\nVoHyGhNKq+UjposHXJzUSM8tw8aD+SitNqFMSS+rNuH126+Bv7sO7206gld/OAij2dpge6nPXQ8v\nVy2+238G7248AkBenOau08BDp4HJIuCkIfi6OSEuyBPuOg3cnTVw12ng6VJ/w/Y5I2JwT3Ik3HVa\neLtq4eWihbO2flLPx66PbXG/QrxdWkzvDGzdqQCgRn3Ll1pFcHFyPAGqu06DuCDHVweGeLu0WH89\nQr3QI9TLYXr3Lu7YfKgAC9ak4YW16UiJDcDt/cIxyhDYwt4w1vlxEMcYa5bJYkVuSTV83Jzg6azF\nqZJq/JxxFmXV9QFaabUJj47SIy7IE9/vP40nvtqHcmPDcV//fXgweoR6Ye+JEry8LhNatRwL5eki\nA6kak5zPKSHYCzMGRTYIwjycNdBpZavXA0O74e5kme7qpG4yfuqugRG4a2CEw/2JDfK4xDXErpTb\n+obhtr5hyDxThv/sPoX/7DkFd11uXRC3/2QpEkM8eUwdu+pwEMfYVUwI2W2lVatwurQay7YcxdGC\nSmTnV+J4URXMVoG3pvbGuKSuOJpfiedWpwEAnLUqGYg5a1GhDNYP83XFxD6h8FKCM9sj3NcVAHBr\n7xDc3CsYLtqmARgAJEf7Iznav8lyGx/uQrvqxQV54qkbPPHEmDiU18jxgJlnynDjv7Yg3NcVt/QK\nwa29QxDh53aOLTHWOXAQx9hVosZkwfq0M8jOr8TRAvk4dKYKj2uO4d4h3WAyC6zYnoMofzfEBnlg\nTGIQIv3dcE24NwCgb6QP/nh6JLxctNBpmnatJYZ4ITHEcZeYfdclYxdDrSJ4u8qgPszHFa9O7olv\n9pzEkl8OYfHPh9AnwgeLJiWhe4B7G5eUscuLgzjGLkBVrRnZ+ZU4lFeOYwVVmHtdDIgIP6SdwZ4T\nJfBw1sDDWQtPZ9klODy2C4gIpdUmOZ7LSQPVZbjaLju/oq4lLbugEkcLKpDc3b9u0P3cL/YCkGOU\novzdMDhEg4RgGXiF+bog469jHJbLWavmQIy1O246DSb2CcXEPqE4XVqNb/fk4vsDpxHo6QwA+DUz\nDyaLFSmxXeCk4fntz0dZjQk1JguMJiuMZgtqTFa46TR1V1X/lH4WFUYzjGYLzFYBjYoQ5e+O/lHy\nFlw/Z5wFKVPS2KaWCfJ0RpivK4QQOJJfAbVKTjdjm37GzUkDFyc1hJAX0fBVyS3jII6xFpRWmXA4\nvxwJwV5w1qrx5c4TWPzTIZwqqa5bR6MiTLs2Av7uOuw4VoSPth6D2Vo/WZiTWoWDL40FAPz1v+n4\netZfWhEAACAASURBVPfJukDOw1mDYG8XfDVzEADgo61HcTivAh7OWng4a+DprEGAhzPGJAYBAE4U\nVcEqBE6X1igtahXwc9fVXWE5+d3tKKysBQD4uGrRLcAdbsoUG85aNX58dBhCfVzqgrENGzbg2u7y\nJtT2g9oZ64i6erlgZkp3zEypv0/nsq1HsflQAXxctZjQMxi39g5FUqhXhx0/Z7ZYoVGujj5RVIWC\nCiOqai2oNJpRVWuBVq3CuKSuAIDlW48iu6BSBmJmK4wmK0J9XPDMeAMAYNa/dyPrTDmMZhmo1Zgs\n6Bvpi2Uz+gEAxi3ZjBNF1Q3yv94QiPem9wUAPPn1vrrvG5tbe4XUBXEzV+5GraXhhUrTBkbghZsT\nYbYKXPfapib79+Cw7pg/Ng5l1Wb0/OsPIAK0KhXUKoJGTXhkZAzuHdINeWU1uOP93+CkVkGnkZNn\nO2lUmH5tJEYnBOFMaQ3+uT4LThq7dLUKYxKDkBjihfxyI9annalLt83BmBTqhS6eziivMSGnsArd\nA9xbvKinrXEQx656tmkVVCpC5pkyfPrbcRzOq8ChvAoUVBgBAKtnJaNnmDcC3HXoE+GD2/uFIaaL\nO6K7uCPCz63uP/ynxxnwlxviUWOyorzGhLIaM6pr62/EfEuvEMQFedSlldeY4aSp/zFJyy3DL5l5\nKK8xwWSRgWD3ALe6IO6xL1Pxx7GiuvV1GhVGxtdPXfHK5J7wdNGim79bs2PIortw9xK7uiyb0Q+b\nD+Xj692n8NmOE/h4ew4m9g7Fq7f1vOx5my1WVJksqDJaUFlrRqXRjEqjBQO7+YKI8Ht2IfafKpVB\nmJJusQr8/dYkAMCrP2ThhzTZ2lVaWY3aH7+Ht6sWfzx9HQBgwZo0/JKZ1yDPCD/XuiBuw8F8pJ4o\ngU6jhk4rgxXbhUIAEOTpDAgoy9XQaVTobvcd8chIPapNFjjbpXf1cq5L//z+gVCrCDqtGhoVwWwV\n0Nm1dn7z0CCY7aaNMVutMk/ICaWXTOkFi1VJU9ITlGlpnDQqPHqdHmYl3baePlBeoKRSycmkjSar\nMveiBdW1FpiV780Kowm/ZRfCaJZptvkZo/zd5JQ6hZV45tsDTY7Zu3f1xpjErtiZU4y7P9pRN5dh\ne0XCfnrxTqJv375i586dbV2MTqfx3FMdUaXRjD+OFilBWnldsPbPST0xJjEI244U4IFPdiG6izui\nA2SQFt3FHf2ifOvmxLoShBAwmq0oU4I52/QMWw4V4HRpNYK8nBHl74ZgL5eL6pbtDMeUNcXHtXml\n1SZ8v/80gryckRLbBfnlRjzy+R7cfE0IrlOudK00mtHFUwedRo2TxVVIyy1DVa1s5bIFY3cPioKX\nqxbr087g610n64IwW/r/Zg+Bl6sWL6/LxDsbjjQpR9aLY6DTqPH8mjQs33YMgAyk3JQrsjc8ngIi\nwgebs7HzWDFcdWqUFJyFPioCPq5aPKC0vO/KKUZZtQmuTmq46TRw08mrum13GWFN2W5vV2u2oqSq\nVgZ5dpNsh/u6wtvVCfnlRuw+XoyBUX7wcr183/22zyoR7RJC9D3f93NLHGuXhBCwWAXMVnn1pFpF\ncHWSp+uJoqq6CUVNFvnB83PTIdzPFVarwIaDeTBZZBCUU1CJw/kVGGUIxPikYJwtq8Hdy3cAAPzd\nnRDdxR03XROMYG/53+HAKD/sW3B9m3e1EFGzY9AGxzi+epMx1jIvFy3u6B9e9/pkcRVOl9bgia/3\nAV/Xr7d29mAkhnhh08EC/OU/+5tsZ3xSMLxctSitNuF4UVVd8BTo4QxXXf1ndnhsF/i5OcFNmRbH\nzUkDV526bhLlx67X49FRerg6qZudQPreId1wr7xhiPJjH9cgvU+Ez8VUx1XJ9t3upFGhi6ezw/UC\nPHQYnRB0pYp1wTiI66RqTBYUVdaiqLIWxVW1qDT+f3t3Hh9XXe9//PWZmSxtk7ZJm6b7Rhf20oWW\nnZaqLLKJG7IqYkHB5V6vV73en97rcq/36lURUQREQNSqIIKAgixlUcrSsnRJd6ArJN2bpM02n98f\nZ5KmadqkzZw5mcn7+XjkcWbOOTPzSb6UvPM95/v9NnLOsUEX+73z3+aFNVvY1up4QSLOs/86C4Br\n736FZ1dU7V1D0eCIsiK+eFzw3tfc9TKvrt2WOhYcP2ZoX+5KzSj/8V++xMp3q4nF9q7BOGVkCT/4\n6Aktx9elpq9oDmKnjy9rubwx47+e4N2ddft8Px+YPIwfpl4/+wfPUN9mQtgrThrJty8+jqQ719y1\nby/ssP69mJzqDh9Z2ps/XH8y48qK2r3cGMZgAxHpniaPLOGpL57Jq+u289KbWylMxOhdkGi5ZPi+\nY8o5fni/oJcrP07vggS98uItN9s3z193INPHlLb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ub+JT97zCnoYmfvOpGZT0yQ/187JO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\nQgpxIiIiIlno/wPbEv5uz4F0+gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x19e933e8c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,6))\n",
    "mglearn.plots.plot_ridge_n_samples()\n",
    "plt.title('Learning curves for ridge regression and linear regression \\n on Boston housing dataset', y=1.2)\n",
    "plt.grid()\n",
    "plt.ylim([-0.5,1.02])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the above learning curve, we can deduce that\n",
    "- Training score is higher than test score for different training set size, for both linear and ridge regression.\n",
    "- As ridge is regularized (as weights are constrained), the training score of ridge is always lower than linear regression. \n",
    "- However, the test score for ridge is better, especially for smaller training dataset.\n",
    "\n",
    "As more and more data becomes available for training the model, both models improve, and linear regression catches up with ridge. The lesson here is that with enough training data, regularization becomes less important. Another interesting aspect is the decrease of training set preformance when more data is added. This implies that, with more data, it becomes harder for the model to overfit or memorize the data crudely."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-14T03:49:13.842928Z",
     "start_time": "2018-09-14T03:49:13.464375Z"
    }
   },
   "source": [
    "## Lasso"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- An alternative to `Ridge` for  regularizing and to restrict the weight/ slope coefficients close to zero, but in a slightly different way.\n",
    "\n",
    "- The lasso regression is also known as `L1 regularization`, penalizes the sum of absolute value of the `w`\n",
    "<p><img src=\"https://prasanth-ntu.github.io/html/ML-Course/Intro-to-ML-with-Python/images/Cost_function_3_Lasso.png\" alt=\"Cost function - Lasso\" title=\"Cost function - Lasso\" style=\"max-width:320px;\"></p>\n",
    "\n",
    "- The ridge regression is also known as `L2 regularization`, penalizes the Euclidean length of `w`\n",
    "<p><img src=\"https://prasanth-ntu.github.io/html/ML-Course/Intro-to-ML-with-Python/images/Cost_function_3_RR.png\" alt=\"Cost function - Ridge Regression\" title=\"Cost function - Ridge Regression\" style=\"max-width:280px;\"></p>\n",
    "\n",
    "\n",
    "<p style=\"color:red; font-size:110%;  border-left: 5px solid blue; padding-left: 10px;\">The consequence of <code>L1 regularization</code> is that when using lasso, some coefficients are <i>exactly zero</i></p>\n",
    "\n",
    "<p style=\"color:green; font-size:110%;  border-left: 5px solid blue; padding-left: 10px;\">This can be seen as <b>automatic feature selection</b>, where having some coefficients as 0 reveals the most important features of the model, thereby making it easier to interpret it</i></p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### boston housing: *n*-D dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-14T04:47:30.200863Z",
     "start_time": "2018-09-14T04:47:30.165390Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of training set: (379, 104)\n",
      "Shape of test set    : (127, 104)\n",
      "\n",
      "Lasso details: Lasso(alpha=1.0, copy_X=True, fit_intercept=True, max_iter=1000,\n",
      "   normalize=False, positive=False, precompute=False, random_state=None,\n",
      "   selection='cyclic', tol=0.0001, warm_start=False)\n",
      "\n",
      "Number of features used: 4 out of 104\n",
      "Training set score: 0.29\n",
      "Test set score: 0.21\n"
     ]
    }
   ],
   "source": [
    "import mglearn\n",
    "from sklearn.linear_model import Lasso\n",
    "from sklearn.model_selection import train_test_split\n",
    "import numpy as np\n",
    "\n",
    "X,y = mglearn.datasets.load_extended_boston()\n",
    "X_train, X_test, y_train, y_test = train_test_split(X,y, random_state=0)\n",
    "print (\"Shape of training set: {}\".format(X_train.shape))\n",
    "print (\"Shape of test set    : {}\".format(X_test.shape))\n",
    "\n",
    "lasso = Lasso().fit(X_train, y_train)\n",
    "print (\"\\n\" + 'Lasso details:', lasso)\n",
    "print (\"\\nNumber of features used: {} out of {}\".format(np.sum(lasso.coef_ != 0), X.shape[1]))\n",
    "\n",
    "print(\"Training set score: {:.2f}\".format(lasso.score(X_train, y_train)))\n",
    "print(\"Test set score: {:.2f}\".format(lasso.score(X_test, y_test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `alpha`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- We can see that Lasso does quite badly on both training (`0.29`) and testing (`0.21`) whereas *Ridge scored `0.77` on test set*. \n",
    "-  A low training and test score indicates **underfitting** and it's obvious that the **model only used `4` out of `104` input features**\n",
    "- Similar to `Ridge`, we can control the regularization strength using `alpha` parameter. \n",
    "- To resovle underfitting issue, let's reduce the `alpha` from `default value (1.0)` to `0.01`, thereby reducing the regularization strength.   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-14T04:54:10.228671Z",
     "start_time": "2018-09-14T04:54:10.152718Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Lasso details: Lasso(alpha=0.01, copy_X=True, fit_intercept=True, max_iter=100000,\n",
      "   normalize=False, positive=False, precompute=False, random_state=None,\n",
      "   selection='cyclic', tol=0.0001, warm_start=False)\n",
      "\n",
      "Number of features used: 33 out of 104\n",
      "Training set score: 0.90\n",
      "Test set score: 0.77\n"
     ]
    }
   ],
   "source": [
    "lasso = Lasso(alpha=.01, max_iter=100000).fit(X_train, y_train)\n",
    "print (\"\\n\" + 'Lasso details:', lasso)\n",
    "print (\"\\nNumber of features used: {} out of {}\".format(np.sum(lasso.coef_ != 0), X.shape[1]))\n",
    "\n",
    "print(\"Training set score: {:.2f}\".format(lasso.score(X_train, y_train)))\n",
    "print(\"Test set score: {:.2f}\".format(lasso.score(X_test, y_test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-14T04:40:13.969734Z",
     "start_time": "2018-09-14T04:40:13.957757Z"
    }
   },
   "source": [
    "- It's evident that lower `alpha` allows us to fit a more complex model, thereby improving the score. \n",
    "- The performance on test data is `0.77` and is slightly better than `Ridge` as we are using only **33 out of 104** features. \n",
    "- If we set the `alpha` too low, we again remove the effect of regularization and end up overfitting, similar to `LinearRegression`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-14T04:57:21.957624Z",
     "start_time": "2018-09-14T04:57:19.358120Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Lasso details: Lasso(alpha=0.0001, copy_X=True, fit_intercept=True, max_iter=100000,\n",
      "   normalize=False, positive=False, precompute=False, random_state=None,\n",
      "   selection='cyclic', tol=0.0001, warm_start=False)\n",
      "\n",
      "Number of features used: 94 out of 104\n",
      "Training set score: 0.95\n",
      "Test set score: 0.64\n"
     ]
    }
   ],
   "source": [
    "lasso = Lasso(alpha=.0001, max_iter=100000).fit(X_train, y_train)\n",
    "print (\"\\n\" + 'Lasso details:', lasso)\n",
    "print (\"\\nNumber of features used: {} out of {}\".format(np.sum(lasso.coef_ != 0), X.shape[1]))\n",
    "\n",
    "print(\"Training set score: {:.2f}\".format(lasso.score(X_train, y_train)))\n",
    "print(\"Test set score: {:.2f}\".format(lasso.score(X_test, y_test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- It's evident that a very low `alpha` (close to 0) causes overfitting, thereby failing to generalize well on test set. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### alpha - Qualitative insight"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-14T05:05:22.984114Z",
     "start_time": "2018-09-14T05:05:19.997135Z"
    }
   },
   "outputs": [
    {
     "data": {
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52dva2qIOAwAAVLhUgpDekKHV1nJTFBVn7YyZQaKbobqxUccsuzuCiICBMbOV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\nEnT+P2H1yqucySzAAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x19e92e45710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "No of features used by Lasso(alpha=1)     = 4\n",
      "No of features used by Lasso(alpha=0.01)  = 33\n",
      "No of features used by Lasso(alpha=0.0001 = 94\n",
      "No of features used by Ridge(alpha=0.1)   = 104\n"
     ]
    }
   ],
   "source": [
    "lasso1 = Lasso(alpha=1).fit(X_train, y_train)\n",
    "lasso0_01 = Lasso(alpha=0.01, max_iter=100000).fit(X_train, y_train)\n",
    "lasso0_0001 = Lasso(alpha=0.0001, max_iter=100000).fit(X_train, y_train)\n",
    "ridge0_1= Ridge(alpha=0.1).fit(X_train, y_train)\n",
    "\n",
    "plt.figure(figsize=(16,6))\n",
    "plt.title('Comparing coefcient magnitudes for lasso regression with different values of alpha and for ridge regression')\n",
    "plt.plot(lasso1.coef_, 's', label=\"Lasso alpha=1\")\n",
    "plt.plot(lasso0_01.coef_, '^', label=\"Lasso alpha=0.01\")\n",
    "plt.plot(lasso0_0001.coef_, 'v', label=\"Lasso alpha=0.0001\")\n",
    "plt.plot(ridge0_1.coef_, 'o', label=\"Ridge alpha=0.1\")\n",
    "plt.xlabel(\"Coefficient index\")\n",
    "plt.ylabel(\"Coefficient magnitude\")\n",
    "plt.hlines(0, 0, len(ridge0_1.coef_))\n",
    "plt.xlim(0,50)\n",
    "plt.ylim(-25,25)\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "print (\"No of features used by Lasso(alpha=1)     = {}\".format(np.sum(lasso1.coef_ != 0)))\n",
    "print (\"No of features used by Lasso(alpha=0.01)  = {}\".format(np.sum(lasso0_01.coef_ != 0)))\n",
    "print (\"No of features used by Lasso(alpha=0.0001 = {}\".format(np.sum(lasso0_0001.coef_ != 0)))\n",
    "print (\"No of features used by Ridge(alpha=0.1)   = {}\".format(len(ridge0_1.coef_)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p style=\"color:green; font-size:110%;  border-left: 5px solid blue; padding-left: 10px;\"> A higher <code>alpha</code> means a more restricted model (more penalty), so we execpt a lot of <code>losso coef_</code> (weights) to have zero magnitude for a higher value of <code>alpha</code>.</p>\n",
    "\n",
    "This is confirmed by the above plot. Here,\n",
    "- `x-axis` spans over 104 data points, but only first 50 data point are shown. It corresponds to the `coeff_` or` weight` of `n`th feature/ dimension\n",
    "- `y-axis` shows the numeric (magnitude) values of the corresponding values of the coefficients.\n",
    "    <p style=\"color:blue\"> &#9632; Coefficients of <code style=\"color:blue\">Losso model with alpha=1</code>: <font color=\"black\">Here, the majority of the coefficients are zero and the remaining 4 features are also small in magnitude</font></p>\n",
    "    <p style=\"color:orange\"> &#9650; Coefficients of <code style=\"color:orange\">Losso model with alpha=0.01</code>: <font color=\"black\">Here, most of the features are still zero, but the remaining 33 features are slightly less restricted than when alpha=1</font></p>\n",
    "    <p style=\"color:green\"> &#9660; Coefficients of <code style=\"color:green\">Losso model with alpha=0.0001</code>: <font color=\"black\">Heremodel is slightly unregularized, woith most coefficients non-zero and large magnitude</font></p>\n",
    "    <p style=\"color:red\"> &#9679; Coefficients of <code style=\"color:red\">Ridge model with alpha=0.1</code>: <font color=\"black\">Here, all the coefficients are non-zero though the test results are similar to Lasso model with alpha=0.01</font></p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-14T12:12:55.088600Z",
     "start_time": "2018-09-14T12:12:55.083622Z"
    }
   },
   "source": [
    "#  Miscallaneous"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Additional Datasets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dataset 1: 1-D"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You are the CEO  of a restaurant franchise and are considering different cities for opening a new outlet. The chain  already has trucks in various cities and you have data for profits and population from cities.\n",
    "\n",
    "You would like to use this data to help you select which city to expand next based solely on the city population.\n",
    "\n",
    "- The first column is the population of city and \n",
    "- the second column is the profit of a good truck in that city. The -ve value for profit indicates a loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 339,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-14T12:29:32.600819Z",
     "start_time": "2018-09-14T12:29:32.590823Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "File already exists: data\\ex1data1.txt\n"
     ]
    }
   ],
   "source": [
    "# This block of code downloads the data file from GitHub incase if it doesn't exist in the computer\n",
    "import urllib\n",
    "import os\n",
    "\n",
    "url = '''https://prasanth-ntu.github.io/html/ML-Course/Intro-to-ML-with-Python/data/ex1data1.txt'''\n",
    "\n",
    "path =  os.path.join(url.split(\"/\")[-2], url.split(\"/\")[-1])\n",
    "\n",
    "if not os.path.exists(path):\n",
    "    path_out, message = urllib.request.urlretrieve(url, path)\n",
    "    print (\"File downloaded to:\", path)\n",
    "else:\n",
    "    print (\"File already exists:\", path)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 290,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-14T11:50:33.084074Z",
     "start_time": "2018-09-14T11:50:33.076100Z"
    }
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "data = pd.read_csv(path, header=None, names=['Population in 10,000s', 'Profit in $10,000s'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 291,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-14T11:50:34.342092Z",
     "start_time": "2018-09-14T11:50:34.327102Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
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       "        text-align: right;\n",
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       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Population in 10,000s</th>\n",
       "      <th>Profit in $10,000s</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>6.1101</td>\n",
       "      <td>17.5920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.5277</td>\n",
       "      <td>9.1302</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>8.5186</td>\n",
       "      <td>13.6620</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>7.0032</td>\n",
       "      <td>11.8540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.8598</td>\n",
       "      <td>6.8233</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Population in 10,000s  Profit in $10,000s\n",
       "0                 6.1101             17.5920\n",
       "1                 5.5277              9.1302\n",
       "2                 8.5186             13.6620\n",
       "3                 7.0032             11.8540\n",
       "4                 5.8598              6.8233"
      ]
     },
     "execution_count": 291,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()           # displays the first 5 rows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 292,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-14T11:50:35.022069Z",
     "start_time": "2018-09-14T11:50:34.997082Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Population in 10,000s</th>\n",
       "      <th>Profit in $10,000s</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>97.000000</td>\n",
       "      <td>97.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>8.159800</td>\n",
       "      <td>5.839135</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>3.869884</td>\n",
       "      <td>5.510262</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>5.026900</td>\n",
       "      <td>-2.680700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>5.707700</td>\n",
       "      <td>1.986900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>6.589400</td>\n",
       "      <td>4.562300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>8.578100</td>\n",
       "      <td>7.046700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>22.203000</td>\n",
       "      <td>24.147000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Population in 10,000s  Profit in $10,000s\n",
       "count              97.000000           97.000000\n",
       "mean                8.159800            5.839135\n",
       "std                 3.869884            5.510262\n",
       "min                 5.026900           -2.680700\n",
       "25%                 5.707700            1.986900\n",
       "50%                 6.589400            4.562300\n",
       "75%                 8.578100            7.046700\n",
       "max                22.203000           24.147000"
      ]
     },
     "execution_count": 292,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.describe()   # displays the basic stats of each column"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 297,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-14T11:52:02.642434Z",
     "start_time": "2018-09-14T11:52:02.297649Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Size of dataset: (97, 2)\n"
     ]
    },
    {
     "data": {
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J0x4CRlc60My+Bvwf8Ndm9qCZvRtYYmbrzGwt0At8eBhpFmkM9fiRLlGtRHAJsNrMlgMP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\naZ0LbjAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x19e930cf198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "fname = path\n",
    "data = np.genfromtxt(fname, delimiter=',')\n",
    "print (\"Size of dataset:\", data.shape)\n",
    "\n",
    "X = data[:,0:1]   # input feature - city population\n",
    "y = data[:,-1]    # output  - profit\n",
    "\n",
    "plt.plot(X,y, 'rx')\n",
    "plt.xlabel('Population in 10,000s')\n",
    "plt.ylabel('Profit in $10,000s')\n",
    "plt.title('Scatter plot of entire data')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dataset 2: 2-D"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose we are selling our hoeu and we want to know what a good market price would be. One way to do this is to first collect information on recent houses sold in the neighourhood and make a model of housing prices.\n",
    "\n",
    "- The first column in the size of the house (in sq feet)\n",
    "- the second column in the number of bedrooms\n",
    "- the third column is the price of the house"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 340,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-14T12:29:38.201795Z",
     "start_time": "2018-09-14T12:29:38.187822Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "File already exists: data\\ex1data2.txt\n"
     ]
    }
   ],
   "source": [
    "# This block of code downloads the data file from GitHub incase if it doesn't exist in the computer\n",
    "import urllib\n",
    "import os\n",
    "\n",
    "url = '''https://prasanth-ntu.github.io/html/ML-Course/Intro-to-ML-with-Python/data/ex1data2.txt'''\n",
    "\n",
    "path =  os.path.join(url.split(\"/\")[-2], url.split(\"/\")[-1])\n",
    "\n",
    "if not os.path.exists(path):\n",
    "    path_out, message = urllib.request.urlretrieve(url, path)\n",
    "    print (\"File downloaded to:\", path)\n",
    "else:\n",
    "    print (\"File already exists:\", path)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 319,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-14T12:07:06.835608Z",
     "start_time": "2018-09-14T12:07:06.824634Z"
    }
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "data = pd.read_csv(path, header=None, names=['House size (in sq ft)','No of bedrooms','House price'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 320,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-14T12:07:07.322330Z",
     "start_time": "2018-09-14T12:07:07.301362Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>House size (in sq ft)</th>\n",
       "      <th>No of bedrooms</th>\n",
       "      <th>House price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2104</td>\n",
       "      <td>3</td>\n",
       "      <td>399900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1600</td>\n",
       "      <td>3</td>\n",
       "      <td>329900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2400</td>\n",
       "      <td>3</td>\n",
       "      <td>369000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1416</td>\n",
       "      <td>2</td>\n",
       "      <td>232000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3000</td>\n",
       "      <td>4</td>\n",
       "      <td>539900</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   House size (in sq ft)  No of bedrooms  House price\n",
       "0                   2104               3       399900\n",
       "1                   1600               3       329900\n",
       "2                   2400               3       369000\n",
       "3                   1416               2       232000\n",
       "4                   3000               4       539900"
      ]
     },
     "execution_count": 320,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()           # displays the first 5 rows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 321,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-14T12:07:10.102931Z",
     "start_time": "2018-09-14T12:07:10.066947Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>House size (in sq ft)</th>\n",
       "      <th>No of bedrooms</th>\n",
       "      <th>House price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>47.000000</td>\n",
       "      <td>47.000000</td>\n",
       "      <td>47.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>2000.680851</td>\n",
       "      <td>3.170213</td>\n",
       "      <td>340412.659574</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>794.702354</td>\n",
       "      <td>0.760982</td>\n",
       "      <td>125039.899586</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>852.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>169900.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>1432.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>249900.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>1888.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>299900.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>2269.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>384450.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>4478.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>699900.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       House size (in sq ft)  No of bedrooms    House price\n",
       "count              47.000000       47.000000      47.000000\n",
       "mean             2000.680851        3.170213  340412.659574\n",
       "std               794.702354        0.760982  125039.899586\n",
       "min               852.000000        1.000000  169900.000000\n",
       "25%              1432.000000        3.000000  249900.000000\n",
       "50%              1888.000000        3.000000  299900.000000\n",
       "75%              2269.000000        4.000000  384450.000000\n",
       "max              4478.000000        5.000000  699900.000000"
      ]
     },
     "execution_count": 321,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.describe()   # displays the basic stats of each column"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 327,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-14T12:09:55.374873Z",
     "start_time": "2018-09-14T12:09:54.947119Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Size of entire dataset: (47, 3)\n"
     ]
    },
    {
     "data": {
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shmg0CsZYxiI2HYnV2bkCNxKJIBKJSI/NFbckcAmCIJY2ZDMgCEJWUlkKUrGQzSBXxOPZ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ktLS8SdwyRXjQFFzJYCipgtEeSqjkjVTSsej6O/vz/FEzo+Pi5LBZVkz6xQjWUYRjwOc3Nzkotv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\nZGRk2LVqThYKRJCx2d0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0Wi2dOnUCoGfPngBcvHiRkydPEhwcjE6nY9SoUbRr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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x19e96386ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "fname = path\n",
    "data = np.genfromtxt(fname, delimiter=',')\n",
    "print (\"Size of entire dataset:\", data.shape)\n",
    "\n",
    "X = data[:,0:2]   # input features\n",
    "y = data[:,-1]    # output  - \n",
    "\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "fig = plt.figure(figsize=(12,10))\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "ax.scatter(X[:,0], X[:,1], y)\n",
    "\n",
    "ax.set_xlabel('House size (in sq ft)')\n",
    "ax.set_ylabel('No of bedrooms')\n",
    "ax.set_zlabel('House Price'); \n",
    "\n",
    "plt.title(\"3D Scatter plot of entire data\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-14T12:17:26.659431Z",
     "start_time": "2018-09-14T12:17:26.654415Z"
    }
   },
   "source": [
    "### Dataset 3: *n*-D"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The code below will generate some sparse data to play with. \n",
    "To generate more features per input sample, change the `n_features` variable and to generate more data samples, increase the `n_samples` variable in the code below. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 336,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-14T12:22:23.431989Z",
     "start_time": "2018-09-14T12:22:23.414002Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dataset size: (50, 200) (50,)\n"
     ]
    }
   ],
   "source": [
    "n_samples, n_features = 50, 200\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from sklearn.metrics import r2_score\n",
    "\n",
    "# #############################################################################\n",
    "# Generate some sparse data to play with\n",
    "np.random.seed(42)\n",
    "\n",
    "X = np.random.randn(n_samples, n_features)\n",
    "coef = 3 * np.random.randn(n_features)\n",
    "inds = np.arange(n_features)\n",
    "np.random.shuffle(inds)\n",
    "coef[inds[10:]] = 0  # sparsify coef  => Makes most of the coef as zero\n",
    "y = np.dot(X, coef)\n",
    "\n",
    "# add noise\n",
    "y += 0.01 * np.random.normal(size=n_samples)\n",
    "\n",
    "print (\"Dataset size:\", X.shape, y.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ElasticNet"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-14T12:13:57.945025Z",
     "start_time": "2018-09-14T12:13:57.936024Z"
    }
   },
   "source": [
    "**ElasticNet**\n",
    "- A linear regresion model that combines the penalaties of `Lasso` and `Ridge`\n",
    "- This combination works best in practice, though at the price of haign two parameters to adjust\n",
    "    - one for L1 regularization\n",
    "    - one for L2 regularization\n",
    "    \n",
    "Refer http://scikit-learn.org/stable/modules/linear_model.html#elastic-net for more details on it as it's out of scope for this post."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-14T05:25:31.752025Z",
     "start_time": "2018-09-14T05:25:31.746030Z"
    }
   },
   "outputs": [],
   "source": [
    "import mglearn\n",
    "from sklearn.linear_model import ElasticNet\n",
    "from sklearn.model_selection import train_test_split\n",
    "import numpy as np\n",
    "\n",
    "X,y = mglearn.datasets.load_extended_boston()\n",
    "X_train, X_test, y_train, y_test = train_test_split(X,y, random_state=0)\n",
    "print (\"Shape of training set: {}\".format(X_train.shape))\n",
    "print (\"Shape of test set    : {}\".format(X_test.shape))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-14T05:40:16.397142Z",
     "start_time": "2018-09-14T05:40:08.438314Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "alpha:   0.0010 | l1_ratio:   0.1000 | Training score: 0.9114 | Test score: 0.7719\n",
      "alpha:   0.0010 | l1_ratio:   0.2000 | Training score: 0.9132 | Test score: 0.7728\n",
      "alpha:   0.0010 | l1_ratio:   0.3000 | Training score: 0.9150 | Test score: 0.7737\n",
      "alpha:   0.0010 | l1_ratio:   0.4000 | Training score: 0.9170 | Test score: 0.7746\n",
      "alpha:   0.0010 | l1_ratio:   0.5000 | Training score: 0.9191 | Test score: 0.7752\n",
      "alpha:   0.0010 | l1_ratio:   0.6000 | Training score: 0.9215 | Test score: 0.7758\n",
      "alpha:   0.0010 | l1_ratio:   0.7000 | Training score: 0.9242 | Test score: 0.7760\n",
      "alpha:   0.0010 | l1_ratio:   0.8000 | Training score: 0.9272 | Test score: 0.7755\n",
      "alpha:   0.0010 | l1_ratio:   0.9000 | Training score: 0.9312 | Test score: 0.7735\n",
      "alpha:   0.0010 | l1_ratio:   1.0000 | Training score: 0.9397 | Test score: 0.7397\n",
      "alpha:   0.0030 | l1_ratio:   0.1000 | Training score: 0.8847 | Test score: 0.7515\n",
      "alpha:   0.0030 | l1_ratio:   0.2000 | Training score: 0.8875 | Test score: 0.7542\n",
      "alpha:   0.0030 | l1_ratio:   0.3000 | Training score: 0.8904 | Test score: 0.7570\n",
      "alpha:   0.0030 | l1_ratio:   0.4000 | Training score: 0.8936 | Test score: 0.7597\n",
      "alpha:   0.0030 | l1_ratio:   0.5000 | Training score: 0.8971 | Test score: 0.7626\n",
      "alpha:   0.0030 | l1_ratio:   0.6000 | Training score: 0.9010 | Test score: 0.7655\n",
      "alpha:   0.0030 | l1_ratio:   0.7000 | Training score: 0.9054 | Test score: 0.7689\n",
      "alpha:   0.0030 | l1_ratio:   0.8000 | Training score: 0.9103 | Test score: 0.7730\n",
      "alpha:   0.0030 | l1_ratio:   0.9000 | Training score: 0.9161 | Test score: 0.7779\n",
      "alpha:   0.0030 | l1_ratio:   1.0000 | Training score: 0.9256 | Test score: 0.7806\n",
      "alpha:   0.0100 | l1_ratio:   0.1000 | Training score: 0.8386 | Test score: 0.7012\n",
      "alpha:   0.0100 | l1_ratio:   0.2000 | Training score: 0.8423 | Test score: 0.7055\n",
      "alpha:   0.0100 | l1_ratio:   0.3000 | Training score: 0.8462 | Test score: 0.7102\n",
      "alpha:   0.0100 | l1_ratio:   0.4000 | Training score: 0.8506 | Test score: 0.7153\n",
      "alpha:   0.0100 | l1_ratio:   0.5000 | Training score: 0.8555 | Test score: 0.7209\n",
      "alpha:   0.0100 | l1_ratio:   0.6000 | Training score: 0.8612 | Test score: 0.7270\n",
      "alpha:   0.0100 | l1_ratio:   0.7000 | Training score: 0.8678 | Test score: 0.7337\n",
      "alpha:   0.0100 | l1_ratio:   0.8000 | Training score: 0.8755 | Test score: 0.7415\n",
      "alpha:   0.0100 | l1_ratio:   0.9000 | Training score: 0.8848 | Test score: 0.7515\n",
      "alpha:   0.0100 | l1_ratio:   1.0000 | Training score: 0.8965 | Test score: 0.7656\n",
      "alpha:   0.0300 | l1_ratio:   0.1000 | Training score: 0.7843 | Test score: 0.6303\n",
      "alpha:   0.0300 | l1_ratio:   0.2000 | Training score: 0.7872 | Test score: 0.6342\n",
      "alpha:   0.0300 | l1_ratio:   0.3000 | Training score: 0.7904 | Test score: 0.6384\n",
      "alpha:   0.0300 | l1_ratio:   0.4000 | Training score: 0.7941 | Test score: 0.6433\n",
      "alpha:   0.0300 | l1_ratio:   0.5000 | Training score: 0.7986 | Test score: 0.6490\n",
      "alpha:   0.0300 | l1_ratio:   0.6000 | Training score: 0.8042 | Test score: 0.6557\n",
      "alpha:   0.0300 | l1_ratio:   0.7000 | Training score: 0.8109 | Test score: 0.6638\n",
      "alpha:   0.0300 | l1_ratio:   0.8000 | Training score: 0.8200 | Test score: 0.6750\n",
      "alpha:   0.0300 | l1_ratio:   0.9000 | Training score: 0.8328 | Test score: 0.6914\n",
      "alpha:   0.0300 | l1_ratio:   1.0000 | Training score: 0.8540 | Test score: 0.7208\n",
      "alpha:   0.1000 | l1_ratio:   0.1000 | Training score: 0.7030 | Test score: 0.5262\n",
      "alpha:   0.1000 | l1_ratio:   0.2000 | Training score: 0.7064 | Test score: 0.5307\n",
      "alpha:   0.1000 | l1_ratio:   0.3000 | Training score: 0.7100 | Test score: 0.5357\n",
      "alpha:   0.1000 | l1_ratio:   0.4000 | Training score: 0.7143 | Test score: 0.5414\n",
      "alpha:   0.1000 | l1_ratio:   0.5000 | Training score: 0.7192 | Test score: 0.5476\n",
      "alpha:   0.1000 | l1_ratio:   0.6000 | Training score: 0.7250 | Test score: 0.5549\n",
      "alpha:   0.1000 | l1_ratio:   0.7000 | Training score: 0.7320 | Test score: 0.5644\n",
      "alpha:   0.1000 | l1_ratio:   0.8000 | Training score: 0.7400 | Test score: 0.5768\n",
      "alpha:   0.1000 | l1_ratio:   0.9000 | Training score: 0.7497 | Test score: 0.5933\n",
      "alpha:   0.1000 | l1_ratio:   1.0000 | Training score: 0.7710 | Test score: 0.6302\n",
      "\n",
      "\n",
      "----------------- BEST on TEST set----------------\n",
      "Coefficients of the elastic model: [ -0.           0.          -0.           0.          -0.           0.          -0.\n",
      "  -0.          -0.          -0.          -6.94791033   0.         -15.73526712\n",
      "  -0.           0.          -0.           0.          -0.          -0.          -0.\n",
      "  -0.          -0.          -0.          -0.          -0.          -0.           0.\n",
      "  -0.           0.           0.           0.           0.          -0.           0.\n",
      "  -0.          -0.           0.          -0.          -0.           0.          -0.\n",
      "  -0.          -0.          -0.          -0.          -0.          -0.          -0.\n",
      "  -0.           0.           0.           0.           0.           0.           0.\n",
      "   0.           0.           1.57250048   0.          -0.06794425  -0.          -0.\n",
      "  -0.          -0.          -0.          -0.          -0.          -0.\n",
      "  19.43341184  -0.          -0.          -0.          -5.13377204  -0.\n",
      "   5.34522643  -0.          -0.          -0.          -0.          -0.          -0.\n",
      "   0.          -0.45788656  -0.          -0.          -0.          -0.          -0.\n",
      "  -0.          -0.          -0.          -0.           0.          -0.          -0.\n",
      "  -0.          -0.          -0.          -0.          -0.          -0.           0.\n",
      "  -0.           0.        ]\n"
     ]
    }
   ],
   "source": [
    "training_score_list = []\n",
    "test_score_list = []\n",
    "best_test_score = None\n",
    "best_alpha = 0; best_l1_ratio = 0\n",
    "\n",
    "alpha_settings = [0.001, 0.003, 0.01, 0.03, 0.1]\n",
    "l1_ratio_setting =  [0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1]\n",
    "for alpha in alpha_settings:\n",
    "    for l1_ratio in l1_ratio_setting:\n",
    "        elastic = ElasticNet(alpha=alpha,l1_ratio=l1_ratio, max_iter=100000, random_state=42).fit(X_train, y_train)\n",
    "        train_score, test_score = elastic.score(X_train, y_train), elastic.score(X_test, y_test)\n",
    "        training_score_list.append(train_score)\n",
    "        test_score_list.append(test_score)\n",
    "        print(\"alpha: {:8.4f} | l1_ratio: {:8.4f} | Training score: {:.4f} | Test score: {:.4f}\".format(alpha, l1_ratio, train_score, test_score))  \n",
    "        \n",
    "        if best_test_score is None or best_test_score < test_score:\n",
    "            best_test_score = test_score\n",
    "            best_alpha = alpha\n",
    "            best_l1_ratio = l1_ratio\n",
    "\n",
    "print (\"\\n\\n----------------- BEST on TEST set----------------\")          \n",
    "elastic = ElasticNet(alpha=alpha,l1_ratio=l1_ratio, max_iter=100000, random_state=42).fit(X_train, y_train)\n",
    "print (\"Coefficients of the elastic model:\", elastic.coef_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Summary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have covered about 3 most popular linear models for regression, namely\n",
    "- <p><code style=\"font-size:120%;color:green\">Linear Regression</code></p>\n",
    "- <p><code style=\"font-size:120%;color:green\">Ridge Regression</code></p>\n",
    "- <p><code style=\"font-size:120%;color:green\">Lasso</code></p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**General Practice**\n",
    "- `linear regression` is where people start with as it doesn't involve any tuning of parameters, like `alpha`. However, the LR model might easily overfit on the training set and fail to generalize on test set.\n",
    "- `ridge regression` is usually the first choice when compared to `Lasso`, especailly when we have fewer features\n",
    "\n",
    "**When is Lasso better?**\n",
    "- If we have large number of input features and expect only few of them to be important, `Lasso` is a better choice\n",
    "- If we would like to have a model that is easy to interpret, `Lasso` is better as it will select only a subset of features."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Now that we have covered Linear models for regression, let's explore Linear models for Classification in the next post."
   ]
  }
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