TrainTest.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Train / Test"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll start by creating some data set that we want to build a model for (in this case a polynomial regression):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x113d69dd0>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x105f1a550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "from pylab import *\n",
    "\n",
    "np.random.seed(2)\n",
    "\n",
    "pageSpeeds = np.random.normal(3.0, 1.0, 100)\n",
    "purchaseAmount = np.random.normal(50.0, 30.0, 100) / pageSpeeds\n",
    "\n",
    "\n",
    "scatter(pageSpeeds, purchaseAmount)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we'll split the data in two - 80% of it will be used for \"training\" our model, and the other 20% for testing it. This way we can avoid overfitting."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "trainX = pageSpeeds[:80]\n",
    "testX = pageSpeeds[80:]\n",
    "\n",
    "trainY = purchaseAmount[:80]\n",
    "testY = purchaseAmount[80:]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's our training dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x113f79b90>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x105efdbd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "scatter(trainX, trainY)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And our test dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x11422db10>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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4b25uL48++gfs27ev0rZKvldVx9o10f+64CHgzv72B4AHK2xLG2g2m+zbt2/qv4FVrnGW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\nFcyQl6SCGfKSVDBDXpIKZshLUsH+P74a2AaVZZ3hAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114035790>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "scatter(testX, testY)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we'll try to fit an 8th-degree polynomial to this data (which is almost certainly overfitting, given what we know about how it was generated!)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x = np.array(trainX)\n",
    "y = np.array(trainY)\n",
    "\n",
    "p4 = np.poly1d(np.polyfit(x, y, 4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot our polynomial against the training data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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TB48/rrr33m5su+mSJfdi0Nam2tCg+stfqh5/vGrfvm7ujW99S3XBAjf6Jkuz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11407f4d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "xp = np.linspace(0, 7, 100)\n",
    "axes = plt.axes()\n",
    "axes.set_xlim([0,7])\n",
    "axes.set_ylim([0, 200])\n",
    "plt.scatter(x, y)\n",
    "plt.plot(xp, p4(xp), c='r')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And against our test data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11602ab90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "testx = np.array(testX)\n",
    "testy = np.array(testY)\n",
    "\n",
    "axes = plt.axes()\n",
    "axes.set_xlim([0,7])\n",
    "axes.set_ylim([0, 200])\n",
    "plt.scatter(testx, testy)\n",
    "plt.plot(xp, p4(xp), c='r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Doesn't look that bad when you just eyeball it, but the r-squared score on the test data is kind of horrible! This tells us that our model isn't all that great..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.393626926099\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import r2_score\n",
    "\n",
    "r2 = r2_score(testy, p4(testx))\n",
    "\n",
    "print r2\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "...even though it fits the training data better:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.483122165597\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import r2_score\n",
    "\n",
    "r2 = r2_score(np.array(trainY), p4(np.array(trainX)))\n",
    "\n",
    "print r2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you're working with a Pandas DataFrame (using tabular, labeled data,) scikit-learn has built-in train_test_split functions to make this easy to do.\n",
    "\n",
    "Later we'll talk about even more robust forms of train/test, like K-fold cross-validation - where we try out multiple different splits of the data, to make sure we didn't just get lucky with where we split it."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Activity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Try measuring the error on the test data using different degree polynomial fits. What degree works best?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "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": "2.7.11"
  }
 },
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}