2.2 Supervised Learning - Regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Regression\n",
    "==========\n",
    "In regression we try to predict a continuous output variable. This can be most easily visualized in one dimension.\n",
    "We will start with a very simple toy example. We will create a dataset out of a sinus curve with some noise:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-3.         -2.93939394 -2.87878788 -2.81818182 -2.75757576 -2.6969697\n",
      " -2.63636364 -2.57575758 -2.51515152 -2.45454545 -2.39393939 -2.33333333\n",
      " -2.27272727 -2.21212121 -2.15151515 -2.09090909 -2.03030303 -1.96969697\n",
      " -1.90909091 -1.84848485 -1.78787879 -1.72727273 -1.66666667 -1.60606061\n",
      " -1.54545455 -1.48484848 -1.42424242 -1.36363636 -1.3030303  -1.24242424\n",
      " -1.18181818 -1.12121212 -1.06060606 -1.         -0.93939394 -0.87878788\n",
      " -0.81818182 -0.75757576 -0.6969697  -0.63636364 -0.57575758 -0.51515152\n",
      " -0.45454545 -0.39393939 -0.33333333 -0.27272727 -0.21212121 -0.15151515\n",
      " -0.09090909 -0.03030303  0.03030303  0.09090909  0.15151515  0.21212121\n",
      "  0.27272727  0.33333333  0.39393939  0.45454545  0.51515152  0.57575758\n",
      "  0.63636364  0.6969697   0.75757576  0.81818182  0.87878788  0.93939394\n",
      "  1.          1.06060606  1.12121212  1.18181818  1.24242424  1.3030303\n",
      "  1.36363636  1.42424242  1.48484848  1.54545455  1.60606061  1.66666667\n",
      "  1.72727273  1.78787879  1.84848485  1.90909091  1.96969697  2.03030303\n",
      "  2.09090909  2.15151515  2.21212121  2.27272727  2.33333333  2.39393939\n",
      "  2.45454545  2.51515152  2.57575758  2.63636364  2.6969697   2.75757576\n",
      "  2.81818182  2.87878788  2.93939394  3.        ]\n"
     ]
    }
   ],
   "source": [
    "x = np.linspace(-3, 3, 100)\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "rng = np.random.RandomState(42)\n",
    "y = np.sin(4 * x) + x + rng.uniform(size=len(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f22b29c7690>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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9/e9/gauvXo+y4Wvz2pRIgYBIa1OjIolEo02J3Nyh1k4oPP8uqc6GV1MiEamm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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f22b4d86510>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y, 'o')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Linear Regression\n",
    "=================\n",
    "One of the simplest models again is a linear one, that simply tries to predict the data as lying on a line. One way to find such a line is LinearRegression (also known as ordinary least squares).\n",
    "The interface for LinearRegression is exactly the same as for the classifiers before, only that ``y`` now contains float values, instead of classes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To apply a scikit-learn model, we need to make X be a 2d-array:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(100,)\n",
      "(100, 1)\n"
     ]
    }
   ],
   "source": [
    "print(x.shape)\n",
    "X = x[:, np.newaxis]\n",
    "print(X.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We split our data in a training and a test set again:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.cross_validation import train_test_split\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we can built our regression model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "regressor = LinearRegression()\n",
    "regressor.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And predict. First let us try the training set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y_pred_train = regressor.predict(X_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f22a8314350>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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suC3wPLHbAsOX8tvf/DbiOrl+/fqUzy/TfQb+HtgCHMbpCvEZnB5J9Zl6z0QdmryHvHTX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\nkwEzM7OK+w8uxR/9p8YaogAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f22a87f7f50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X_train, y_train, 'o', label=\"data\")\n",
    "plt.plot(X_train, y_pred_train, 'o', label=\"prediction\")\n",
    "plt.legend(loc='best')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The line is able to capture the general slope of the data, but not many details."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's try the test set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y_pred_test = regressor.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f22a826ced0>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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S2Nh4xJ+3paWFP//5z2zatIlTTz0VgL/927/l9NNPZ9myZfz85z9P2X/mzJmsXbt2+PsD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\nIiIiJU7BgIiISIn7/7o1zmcIGJuXAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f22a83b3e90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X_test, y_test, 'o', label=\"data\")\n",
    "plt.plot(X_test, y_pred_test, 'o', label=\"prediction\")\n",
    "plt.legend(loc='best')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, scikit-learn provides an easy way to evaluate the prediction quantitatively using the ``score`` method. For regression tasks, this is the R2 score. Another popular way would be the mean squared error."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.79943214050796851"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "regressor.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "KNeighborsRegression\n",
    "=======================\n",
    "As for classification, we can also use a neighbor based method for regression. We can simply take the output of the nearest point, or we could average several nearest points. This method is less popular for regression than for classification, but still a good baseline."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, let us look at the behavior on training and test set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On the training set, we do a perfect job: each point is its own nearest neighbor!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On the test set, we also do a better job of capturing the variation, but our estimates look much more messy then before.\n",
    "Let us look at the R2 score:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# %load scripts/knn_regression.py\n",
    "from sklearn.neighbors import KNeighborsRegressor\n",
    "kneighbor_regression = KNeighborsRegressor(n_neighbors=1)\n",
    "kneighbor_regression.fit(X_train, y_train)\n",
    "\n",
    "y_pred_train = kneighbor_regression.predict(X_train)\n",
    "\n",
    "plt.plot(X_train, y_train, 'o', label=\"data\")\n",
    "plt.plot(X_train, y_pred_train, 'o', label=\"prediction\")\n",
    "plt.legend(loc='best')\n",
    "\n",
    "#y_pred_test = kneighbor_regression.predict(X_test)\n",
    "\n",
    "#plt.plot(X_test, y_test, 'o', label=\"data\")\n",
    "#plt.plot(X_test, y_pred_test, 'o', label=\"prediction\")\n",
    "#plt.legend(loc='best')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Random Forests"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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FOGEJAAnqup637YslTUXEFe2vPyopIuJPO8axmDcAFFTazRhsnyLpPyVdKukZSfdIen9E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\nDloWAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f719b570490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create some simple data\n",
    "import numpy as np\n",
    "np.random.seed(0)\n",
    "X = np.random.random(size=(20, 1))\n",
    "y = 3 * X.squeeze() + 2 + np.random.randn(20)\n",
    "\n",
    "plt.plot(X.squeeze(), y, 'o');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f719ab7a810>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Fit a Random Forest\n",
    "from sklearn.ensemble import RandomForestRegressor\n",
    "model = RandomForestRegressor()\n",
    "model.fit(X, y)\n",
    "\n",
    "# Plot the data and the model prediction\n",
    "X_fit = np.linspace(0, 1, 100)[:, np.newaxis]\n",
    "y_fit = model.predict(X_fit)\n",
    "\n",
    "plt.plot(X.squeeze(), y, 'o')\n",
    "plt.plot(X_fit.squeeze(), y_fit);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Much better then before! Here, the linear model was not a good fit for our problem."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Exercise\n",
    "=========\n",
    "Compare the KNeighborsRegressor and LinearRegression on the boston housing dataset. You can load the dataset using ``sklearn.datasets.load_boston``."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [default]",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}