Supervised_Learning_Linear_Model.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Linear models make a prediction using a *linear function* of the input features."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear models for regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The general formula for a linear model is as below:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ŷ = w[0] * x[0] + w[1] * x[1] + ... + w[p] * x[p] + b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The simplest and most classic linear method is *ordinary least square*. In this method, linear regression finds the parameters *w* and *b* that minimize the *mean squared error* between predictions and the true regression targets,*y*, on the training set."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The *mean squared error* is the sum of the squared differences between the predictions and the true values. Linear regression has no parameters, which is a benefit, but it also has no way to control model complexity. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import mglearn\n",
    "import matplotlib \n",
    "import matplotlib.pylab as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.linear_model import LinearRegression\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=111)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "lr = LinearRegression().fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The *slope* parametrs *(w)* which is also called *weights* or *coefficients* are stored in the *coef_* attribute, while the offset or *intercept (b)* is stored in the *intercept_* attribute."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "lr.coef_: [ 0.44231285]\n",
      "lr.intercept_: -0.04949297304070671\n"
     ]
    }
   ],
   "source": [
    "print('lr.coef_: {}'.format(lr.coef_))\n",
    "print('lr.intercept_: {}'.format(lr.intercept_))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There will be alwasy one single *intercetp_* attribute while the *coef_* attribute is a Numpy array with one entry per input feature. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looking at training set and test set performance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training set score: 0.70\n",
      "Test set score: 0.56\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": [
    "An $R^2$ of around 0.56 is not very good, but we can see that the scores on the training\n",
    "and test sets are very close together. This means we are likely underfitting, not over‐\n",
    "fitting. **For this one-dimensional dataset, there is little danger of overfitting, as the\n",
    "model is very simple (or restricted). However, with higher-dimensional datasets\n",
    "(meaning datasets with a large number of features), linear models become more pow‐\n",
    "erful, and there is a higher chance of overfitting**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we look at how *LinearRegression* performs on a more complex dataset, like the Boston Housing dataset. This dataset has 506 samples and 105 features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X, y = mglearn.datasets.load_extended_boston()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=112)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "lr = LinearRegression().fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training score is: 0.93\n",
      "Test score is: 0.87\n"
     ]
    }
   ],
   "source": [
    "print('Training score is: {:.2f}'.format(lr.score(X_train, y_train)))\n",
    "print('Test score is: {:.2f}'.format(lr.score(X_test, y_test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another commonly used standard linear regression is ***Ridge regression*** which is explained as below:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Ridge regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Reidge regression is also a linear model for regression. It uses the same formula as the ordinary least squre regression model. In the ridge regression, though, the coefficients *(w)* are chosen not only so that they predict well on the training data, but also to fit an additional constraint. We also want the magnitude of the coefficients to as small as possible, in other words, all entries of *w* should be as close to zero. This means each feature should have a little effect on the outcome as possible (having a small slope), while still predicting well. This constraint is an example of what is called regularization. Regularization means explicitly restricting a model to avoid overfitting. The particular kind used by ridge regression is known as L2 regularization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training set score is: 0.84\n",
      "Test set score is: 0.89\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import Ridge\n",
    "ridge = Ridge().fit(X_train, y_train)\n",
    "print('Training set score is: {:.2f}'.format(ridge.score(X_train, y_train)))\n",
    "print('Test set score is: {:.2f}'.format(ridge.score(X_test, y_test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, the training set score of Ridge is lower than for LinearRegression, while the test set score is higher. This is consistent with our expectation. With linear regression, we were overfitting our data. Ridge is a more restricted model, so we are less likely to overfit. A less complex model means worse performance on the training set, but better generalization. As we are only interested in generalization performance, we should choose the Ridge model over the LinearRegression model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another important parameter in Ridge regression is called *alpha* which is by default set to 1. However, if one wants to force the coeffecients to move more toward zero, which decreases training set performance, you can set *alpha* to higher values. \n",
    "We can see more in the example below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training set score is: 0.74\n",
      "Test set score is: 0.79\n"
     ]
    }
   ],
   "source": [
    "ridge10 = Ridge(alpha=10).fit(X_train, y_train)\n",
    "print('Training set score is: {:.2f}'.format(ridge10.score(X_train, y_train)))\n",
    "print('Test set score is: {:.2f}'.format(ridge10.score(X_test, y_test)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training set score is: 0.90\n",
      "Test set score is: 0.91\n"
     ]
    }
   ],
   "source": [
    "ridge01 = Ridge(alpha=0.1).fit(X_train, y_train)\n",
    "print('Training set score is: {:.2f}'.format(ridge01.score(X_train, y_train)))\n",
    "print('Test set score is: {:.2f}'.format(ridge01.score(X_test, y_test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A higher alpha means a more restricted model, so we expect the entries of coef_ tohave smaller magnitude for a high value of alpha than for a low value of alpha ."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f54d61777f0>"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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H/0Lr5R3gsXNzOPdXyQ+xNCqimOuBi9dKW4V7rHujpksbw+/p2zMp69eWvoTn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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f54d61a9828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "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",
    "\n",
    "plt.plot(lr.coef_, 'o', label='Linear regression')\n",
    "plt.xlabel('coefficient index')\n",
    "plt.ylabel('coefficient magnitued')\n",
    "plt.hlines(0, 0, len(lr.coef_))\n",
    "plt.ylim(-25, 25)\n",
    "plt.legend(loc=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Comparing coefficient magnitudes for ridge regression with different values of alpha and linear regression*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another way to understand the impact of regularization is to fix a value of *alpha* and vary the amount of training data. For the figure below, the Boston housing dataset is subsampled and evaluated using *LinearRegression* and *Rdige(alpha=1)* on subsets of increasing size."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PFxYWKlatWuXU6zLYP+POEBMTY9q/f/9Jp52wl6FE0QGNLS1dXl4umTNnTrR9ae277747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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f54d6854160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mglearn.plots.plot_ridge_n_samples()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Figure above shows Learing curves for ridge regression and linear regression on the Boston Housing dataset*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As one would expect, the training score is higher than the test score for all dataset\n",
    "sizes, for both ridge and linear regression. Because ridge is regularized, the training\n",
    "score of ridge is lower than the training score for linear regression across the board.\n",
    "However, the test score for ridge is better, particularly for small subsets of the data.\n",
    "For less than 400 data points, linear regression is not able to learn anything. As more\n",
    "and more data becomes available to the model, both models improve, and linear\n",
    "regression catches up with ridge in the end. The lesson here is that with enough train‐\n",
    "ing data, regularization becomes less important, and given enough data, ridge and linear regression will have the same performance (the fact that this happens here\n",
    "when using the full dataset is just by chance)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Lasso"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An alternative to Ridge for regularizing linear regression is Lasso . As with ridge\n",
    "regression, using the lasso also restricts coefficients to be close to zero, but in a\n",
    "slightly different way, called L1 regularization. 8 The consequence of L1 regularization\n",
    "is that when using the lasso, some coefficients are exactly zero. This means some fea‐\n",
    "tures are entirely ignored by the model. This can be seen as a form of automatic fea‐\n",
    "ture selection. Having some coefficients be exactly zero often makes a model easier to\n",
    "interpret, and can reveal the most important features of your model."
   ]
  }
 ],
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  "anaconda-cloud": {},
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   "display_name": "Python [conda env:py3k]",
   "language": "python",
   "name": "conda-env-py3k-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
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   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.0"
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 },
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