testingtraining.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "hide": true
   },
   "source": [
    "# The Test set\n",
    "\n",
    "##### Keywords: empirical risk minimization, Hoeffding's inequality, hypothesis space,  training error, out-of-sample error, testing set, training set, test error, complexity parameter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Contents\n",
    "{:.no_toc}\n",
    "*  \n",
    "{: toc}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "hide": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import scipy as sp\n",
    "import matplotlib as mpl\n",
    "import matplotlib.cm as cm\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "pd.set_option('display.width', 500)\n",
    "pd.set_option('display.max_columns', 100)\n",
    "pd.set_option('display.notebook_repr_html', True)\n",
    "import seaborn as sns\n",
    "sns.set_style(\"whitegrid\")\n",
    "sns.set_context(\"poster\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "hide": true
   },
   "outputs": [],
   "source": [
    "def make_simple_plot():\n",
    "    fig, axes=plt.subplots(figsize=(12,5), nrows=1, ncols=2);\n",
    "    axes[0].set_ylabel(\"$y$\")\n",
    "    axes[0].set_xlabel(\"$x$\")\n",
    "    axes[1].set_xlabel(\"$x$\")\n",
    "    axes[1].set_yticklabels([])\n",
    "    axes[0].set_ylim([-2,2])\n",
    "    axes[1].set_ylim([-2,2])\n",
    "    plt.tight_layout();\n",
    "    return axes\n",
    "def make_plot():\n",
    "    fig, axes=plt.subplots(figsize=(20,8), nrows=1, ncols=2);\n",
    "    axes[0].set_ylabel(\"$p_R$\")\n",
    "    axes[0].set_xlabel(\"$x$\")\n",
    "    axes[1].set_xlabel(\"$x$\")\n",
    "    axes[1].set_yticklabels([])\n",
    "    axes[0].set_ylim([0,1])\n",
    "    axes[1].set_ylim([0,1])\n",
    "    axes[0].set_xlim([0,1])\n",
    "    axes[1].set_xlim([0,1])\n",
    "    plt.tight_layout();\n",
    "    return axes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Revisiting the model\n",
    "\n",
    "Let $x$ be the fraction of religious people in a county and $y$ be the probability of voting for Romney as a function of $x$. In other words $y_i$ is data that pollsters have taken which tells us their estimate of people voting for Romney and $x_i$ is the fraction of religious people in county $i$. Because poll samples are finite, there is a margin of error on each data point or county $i$, but we will ignore that for now."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us assume that we have a \"population\" of 200 counties $x$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>promney</th>\n",
       "      <th>rfrac</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.047790</td>\n",
       "      <td>0.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.051199</td>\n",
       "      <td>0.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.054799</td>\n",
       "      <td>0.02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.058596</td>\n",
       "      <td>0.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.062597</td>\n",
       "      <td>0.04</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    promney  rfrac\n",
       "0  0.047790   0.00\n",
       "1  0.051199   0.01\n",
       "2  0.054799   0.02\n",
       "3  0.058596   0.03\n",
       "4  0.062597   0.04"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dffull=pd.read_csv(\"data/religion.csv\")\n",
    "dffull.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets suppose now that the Lord came by and told us that the points in the plot below captures $f(x)$ exactly. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10cd736a0>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x=dffull.rfrac.values\n",
    "f=dffull.promney.values\n",
    "plt.plot(x,f,'.', alpha=0.3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that our sampling of $x$ is not quite uniform: there are more points around $x$ of 0.7.\n",
    "\n",
    "Now, in real life we are only given a sample of points. Lets assume that out of this population of 200 points we are given a sample $\\cal{D}$ of 30 data points. Such data is called **in-sample data**. Contrastingly, the entire population of data points is also called **out-of-sample data**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>f</th>\n",
       "      <th>i</th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.075881</td>\n",
       "      <td>7</td>\n",
       "      <td>0.07</td>\n",
       "      <td>0.138973</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.085865</td>\n",
       "      <td>9</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.050510</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.096800</td>\n",
       "      <td>11</td>\n",
       "      <td>0.11</td>\n",
       "      <td>0.183821</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.184060</td>\n",
       "      <td>23</td>\n",
       "      <td>0.23</td>\n",
       "      <td>0.057621</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.285470</td>\n",
       "      <td>33</td>\n",
       "      <td>0.33</td>\n",
       "      <td>0.358174</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          f   i     x         y\n",
       "0  0.075881   7  0.07  0.138973\n",
       "1  0.085865   9  0.09  0.050510\n",
       "2  0.096800  11  0.11  0.183821\n",
       "3  0.184060  23  0.23  0.057621\n",
       "4  0.285470  33  0.33  0.358174"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv(\"data/noisysample.csv\")\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "figure_type": "w"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x576 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "axes=make_plot()\n",
    "axes[0].plot(x,f, 'k-', alpha=0.4, label=\"f (from the Lord)\");\n",
    "axes[0].plot(x,f, 'r.', alpha=0.2, label=\"population\");\n",
    "axes[1].plot(df.x,df.f, 'o', alpha=0.6, label=\"in-sample noiseless data $\\cal{D}$\");\n",
    "axes[1].plot(df.x,df.y, 's', alpha=0.6, label=\"in-sample noisy data $\\cal{D}$\");\n",
    "axes[0].legend(loc=4);\n",
    "axes[1].legend(loc=4);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Testing and Training Sets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The process of learning has two parts:\n",
    "\n",
    "1. Fit for a model by minimizing the in-sample risk\n",
    "2. Hope that the in-sample risk approximates the out-of-sample risk well.\n",
    "\n",
    "Mathematically, we are saying that:\n",
    "\n",
    "$$\n",
    "\\begin{eqnarray*}\n",
    "A &:& R_{\\cal{D}}(g) \\,\\,smallest\\,on\\,\\cal{H}\\\\\n",
    "B &:& R_{out \\,of \\,sample} (g) \\approx R_{\\cal{D}}(g)\n",
    "\\end{eqnarray*}\n",
    "$$\n",
    "\n",
    "Hoping does not befit us as scientists. How can we test that the in-sample risk approximates the out-of-sample risk well?\n",
    "\n",
    "The \"aha\" moment comes when we realize that we can hold back some of our sample, and test the performance of our learner by trying it out on this held back part! Perhaps we can compute the error or risk on the held-out part, or \"test\" part of our sample, and have something to say about the out-of-sample error."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us introduce some new terminology. We take the sample of data $\\cal{D}$ that we have been given (our in-sample set) and split it into two parts:\n",
    "\n",
    "1. The **training set**, which is the part of the data we use to fit a model\n",
    "2. The **testing set**, a smaller part of the data set which we use to see how good our fit was.\n",
    "\n",
    "This split is done by choosing points at random into these two sets. Typically we might take 80% of our data and put it in the training set, with the remaining amount going into the test set. This can be carried out in python using the `train_test_split` function from `sklearn.cross_validation`.\n",
    "\n",
    "The split is shown in the diagram below:\n",
    "\n",
    "![m:caption](images/train-test.png)\n",
    "\n",
    "We ARE taking a hit on the amount of data we have to train our model. The more data we have, the better we can do for our fits. But, you cannot figure out the generalization ability of a learner by looking at the same data it was trained on: there is nothing to generalize to, and as we know we can fit very complex models to training data which have no hope of generalizing (like an interpolator). Thus, to estimate the **out-of-sample error or risk**, we must leave data over to make this estimation. \n",
    "\n",
    "At this point you are thinking: the test set is just another sample of the population, just like the training set. What guarantee do we have that it approximates the out-of-sample error well? And furthermore, if we pick 6 out of 30 points as a test set, why would you expect the estimate to be any good?\n",
    "\n",
    "We will kind-of hand wavingly show later that the test set error is a good estimate of the out of sample error, especially for larger and larger test sets. You are right to worry that 6 points is perhaps too few, but thats what we have for now, and we shall work with them.\n",
    "\n",
    "We are **using the training set then, as our in-sample set, and the test set as a proxy for out-of-sample.**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "//anaconda/envs/py3l/lib/python3.6/site-packages/sklearn/cross_validation.py:44: DeprecationWarning: This module was deprecated in version 0.18 in favor of the model_selection module into which all the refactored classes and functions are moved. Also note that the interface of the new CV iterators are different from that of this module. This module will be removed in 0.20.\n",
      "  \"This module will be removed in 0.20.\", DeprecationWarning)\n"
     ]
    }
   ],
   "source": [
    "from sklearn.cross_validation import train_test_split\n",
    "datasize=df.shape[0]\n",
    "#split dataset using the index, as we have x,f, and y that we want to split.\n",
    "itrain,itest = train_test_split(range(30),train_size=24, test_size=6)\n",
    "xtrain= df.x[itrain].values\n",
    "ftrain = df.f[itrain].values\n",
    "ytrain = df.y[itrain].values\n",
    "xtest= df.x[itest].values\n",
    "ftest = df.f[itest].values\n",
    "ytest = df.y[itest].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1a1a8c3128>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1440x576 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "axes=make_plot()\n",
    "axes[0].plot(df.x,df.f, 'k-', alpha=0.6, label=\"f (from the Lord)\");\n",
    "axes[0].plot(df.x,df.y, 'o',alpha=0.6, label=\"$\\cal{D}$\");\n",
    "axes[1].plot(df.x,df.f, 'k-', alpha=0.6, label=\"f (from the Lord)\");\n",
    "axes[1].plot(xtrain, ytrain, 's', label=\"training\")\n",
    "axes[1].plot(xtest, ytest, 's', label=\"testing\")\n",
    "axes[0].legend(loc=\"lower right\")\n",
    "axes[1].legend(loc=\"lower right\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A digression about scikit-learn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Scikit-learn is the main python machine learning library. It consists of many learners which can learn models from data, as well as a lot of utility functions such as `train_test_split`. It can be used in python by the incantation `import sklearn`.\n",
    "\n",
    "The library has a very well defined interface. This makes the library a joy to use, and surely contributes to its popularity. As the [scikit-learn API paper](http://arxiv.org/pdf/1309.0238v1.pdf) [Buitinck, Lars, et al. \"API design for machine learning software: experiences from the scikit-learn project.\" arXiv preprint arXiv:1309.0238 (2013).] says:\n",
    "\n",
    ">All objects within scikit-learn share a uniform common basic API consisting of three complementary interfaces: **an estimator interface for building and ﬁtting models, a predictor interface for making predictions and a transformer interface for converting data**. The estimator interface is at the core of the library. It deﬁnes instantiation mechanisms of objects and exposes a `fit` method for learning a model from training data. All supervised and unsupervised learning algorithms (e.g., for classiﬁcation, regression or clustering) are oﬀered as objects implementing this interface. Machine learning tasks like feature extraction, feature selection or dimensionality reduction are also provided as estimators.\n",
    "\n",
    "Earlier we fit `y` using the python function `polyfit`. To get you familiarized with scikit-learn, we'll use the \"estimator\" interface here, specifically the estimator `PolynomialFeatures`. The API paper again:\n",
    "\n",
    ">Since it is common to modify or ﬁlter data before feeding it to a learning algorithm, some estimators in the library implement a transformer interface which deﬁnes a transform method. It takes as input some new data X and yields as output a transformed version of X. Preprocessing, feature selection, feature extraction and dimensionality reduction algorithms are all provided as transformers within the library.\n",
    "\n",
    "To start with we have one **feature** `x`, the fraction of religious people in a county, which we want to use to predict `y`, the fraction of people voting for Romney in that county. What we will do is the transformation:\n",
    "\n",
    "$$ x \\rightarrow 1, x, x^2, x^3, ..., x^d $$\n",
    "\n",
    "for some power $d$. Our job then is to **fit** for the coefficients of these features in the polynomial\n",
    "\n",
    "$$ a_0 + a_1 x + a_2 x^2 + ... + a_d x^d. $$\n",
    "\n",
    "### Transformers in  sklearn\n",
    "\n",
    "In other words, we have transformed a function of one feature, into a (rather simple) **linear** function of many features. To do this we first construct the estimator as `PolynomialFeatures(d)`, and then transform these features into a d-dimensional space using the method `fit_transform`.\n",
    "\n",
    "![fit_transform](images/sklearntrans.jpg)\n",
    "\n",
    "Here is an example. The reason for using `[[1],[2],[3]]` as opposed to `[1,2,3]` is that scikit-learn expects data to be stored in a two-dimensional array or matrix with size `[n_samples, n_features]`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  1.,  1.,  1.],\n",
       "       [ 1.,  2.,  4.,  8.],\n",
       "       [ 1.,  3.,  9., 27.]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "PolynomialFeatures(3).fit_transform([[1],[2], [3]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To transform `[1,2,3]` into [[1],[2],[3]] we need to do a reshape.\n",
    "\n",
    "![reshape](images/reshape.jpg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1],\n",
       "       [2],\n",
       "       [3]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array([1,2,3]).reshape(-1,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So now we are in the recatangular, rows=samples, columns=features form expected by `scikit-learn`. Ok, so lets see the process to transform our 1-D dataset `x` into a d-dimensional one. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.54      , 0.71829603, 0.70533267, 0.43754875, 0.56      ,\n",
       "       0.94      , 0.66      , 0.33      , 0.91      , 0.75841654,\n",
       "       0.34      , 0.09      , 0.76      , 0.75868254, 0.67      ,\n",
       "       0.46      , 0.82850909, 0.6       , 0.63633949, 0.64832591,\n",
       "       0.63071361, 0.07      , 0.53596824, 0.52      ])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xtrain"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.54      ],\n",
       "       [0.71829603],\n",
       "       [0.70533267],\n",
       "       [0.43754875],\n",
       "       [0.56      ],\n",
       "       [0.94      ],\n",
       "       [0.66      ],\n",
       "       [0.33      ],\n",
       "       [0.91      ],\n",
       "       [0.75841654],\n",
       "       [0.34      ],\n",
       "       [0.09      ],\n",
       "       [0.76      ],\n",
       "       [0.75868254],\n",
       "       [0.67      ],\n",
       "       [0.46      ],\n",
       "       [0.82850909],\n",
       "       [0.6       ],\n",
       "       [0.63633949],\n",
       "       [0.64832591],\n",
       "       [0.63071361],\n",
       "       [0.07      ],\n",
       "       [0.53596824],\n",
       "       [0.52      ]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xtrain.reshape(-1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.        , 0.54      , 0.2916    ],\n",
       "       [1.        , 0.71829603, 0.51594919],\n",
       "       [1.        , 0.70533267, 0.49749418],\n",
       "       [1.        , 0.43754875, 0.1914489 ],\n",
       "       [1.        , 0.56      , 0.3136    ],\n",
       "       [1.        , 0.94      , 0.8836    ],\n",
       "       [1.        , 0.66      , 0.4356    ],\n",
       "       [1.        , 0.33      , 0.1089    ],\n",
       "       [1.        , 0.91      , 0.8281    ],\n",
       "       [1.        , 0.75841654, 0.57519565],\n",
       "       [1.        , 0.34      , 0.1156    ],\n",
       "       [1.        , 0.09      , 0.0081    ],\n",
       "       [1.        , 0.76      , 0.5776    ],\n",
       "       [1.        , 0.75868254, 0.5755992 ],\n",
       "       [1.        , 0.67      , 0.4489    ],\n",
       "       [1.        , 0.46      , 0.2116    ],\n",
       "       [1.        , 0.82850909, 0.68642731],\n",
       "       [1.        , 0.6       , 0.36      ],\n",
       "       [1.        , 0.63633949, 0.40492794],\n",
       "       [1.        , 0.64832591, 0.42032648],\n",
       "       [1.        , 0.63071361, 0.39779966],\n",
       "       [1.        , 0.07      , 0.0049    ],\n",
       "       [1.        , 0.53596824, 0.28726196],\n",
       "       [1.        , 0.52      , 0.2704    ]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "PolynomialFeatures(2).fit_transform(xtrain.reshape(-1,1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fitting in sklearn\n",
    "\n",
    "Once again, lets see the structure of scikit-learn needed to make these fits. `.fit` always takes two arguments:\n",
    "\n",
    "`estimator.fit(Xtrain, ytrain)`.\n",
    "\n",
    "Here `Xtrain` must be in the form of an array of arrays, with the inner array each corresponding to one sample, and whose elements correspond to the feature values for that sample. (This means that the 4th element for each of these arrays, in our polynomial example, corresponds to the valueof $x^3$ for each \"sample\" $x$). The `ytrain` is a simple array of responses..continuous for regression problems, and categorical values or 1-0's for classification problems.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![reshape](images/sklearn2.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The test set `Xtest` has the same structure, and is used in the `.predict` interface. Once we have fit the estimator, we predict the results on the test set by:\n",
    "\n",
    "`estimator.predict(Xtest)`.\n",
    "\n",
    "The results of this are a simple array of predictions, of the same form and shape as `ytest`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A summary of the scikit-learn interface can be found here:\n",
    "\n",
    "http://nbviewer.jupyter.org/github/jakevdp/sklearn_pycon2015/blob/master/notebooks/02.2-Basic-Principles.ipynb#Recap:-Scikit-learn's-estimator-interface"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets put this alltogether. Below we write a function to create multiple datasets, one for each polynomial degree:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def make_features(train_set, test_set, degrees):\n",
    "    traintestlist=[]\n",
    "    for d in degrees:\n",
    "        traintestdict={}\n",
    "        traintestdict['train'] = PolynomialFeatures(d).fit_transform(train_set.reshape(-1,1))\n",
    "        traintestdict['test'] = PolynomialFeatures(d).fit_transform(test_set.reshape(-1,1))\n",
    "        traintestlist.append(traintestdict)\n",
    "    return traintestlist"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## How do training and testing error change with complexity?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You will recall that the big question we were left with earlier is: what order of polynomial should we use to fit the data? Which order is too biased? Which one has too much variance and is too complex? Let us try and answer this question.\n",
    "\n",
    "We do this by fitting many different models (remember the fit is made by minimizing the empirical risk on the training set), each with increasing dimension `d`, and looking at the training-error and the test-error in each of these models. So we first try $\\cal{H}_0$, then $\\cal{H}_1$, then $\\cal{H}_2$, and so on.\n",
    "\n",
    "Since we use `PolynomialFeatures` above, each increasing dimension gives us an additional feature. $\\cal{H}_5$ has 6 features, a constant and the 5 powers of `x`. What we want to do is to find the coefficients of the 5-th order polynomial that best fits the data. Since the polynomial is **linear** in the coefficients (we multiply coefficients by powers-of-x features and sum it up), we use a learner called a `LinearRegression` model (remember that the \"linear\" in the regression refers to linearity in co-efficients). The scikit-learn interface to make such a fit is also very simple, the function `fit`. And once we have learned a model, we can predict using the function `predict`. The API paper again:\n",
    "\n",
    ">The predictor interface extends the notion of an estimator by adding a predict method that takes an array X_test and produces predictions for X_test, based on the learned parameters of the estimator.\n",
    "\n",
    "So, for increasing polynomial degree, and thus feature dimension `d`, we fit a `LinearRegression` model on the traing set. We then use scikit-learn again to calculate the error or risk. We calculate the `mean_squared_error` between the model's predictions and the data, BOTH on the training set and test set. We plot this error as a function of the defree of the polynomial `d`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.metrics import mean_squared_error\n",
    "\n",
    "degrees=range(21)\n",
    "error_train=np.empty(len(degrees))\n",
    "error_test=np.empty(len(degrees))\n",
    "\n",
    "traintestlists=make_features(xtrain, xtest, degrees)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[1.00000000e+00, 5.40000000e-01, 2.91600000e-01, 1.57464000e-01],\n",
       "        [1.00000000e+00, 7.18296032e-01, 5.15949190e-01, 3.70604256e-01],\n",
       "        [1.00000000e+00, 7.05332672e-01, 4.97494178e-01, 3.50898898e-01],\n",
       "        [1.00000000e+00, 4.37548746e-01, 1.91448905e-01, 8.37682282e-02],\n",
       "        [1.00000000e+00, 5.60000000e-01, 3.13600000e-01, 1.75616000e-01],\n",
       "        [1.00000000e+00, 9.40000000e-01, 8.83600000e-01, 8.30584000e-01],\n",
       "        [1.00000000e+00, 6.60000000e-01, 4.35600000e-01, 2.87496000e-01],\n",
       "        [1.00000000e+00, 3.30000000e-01, 1.08900000e-01, 3.59370000e-02],\n",
       "        [1.00000000e+00, 9.10000000e-01, 8.28100000e-01, 7.53571000e-01],\n",
       "        [1.00000000e+00, 7.58416542e-01, 5.75195651e-01, 4.36237897e-01],\n",
       "        [1.00000000e+00, 3.40000000e-01, 1.15600000e-01, 3.93040000e-02],\n",
       "        [1.00000000e+00, 9.00000000e-02, 8.10000000e-03, 7.29000000e-04],\n",
       "        [1.00000000e+00, 7.60000000e-01, 5.77600000e-01, 4.38976000e-01],\n",
       "        [1.00000000e+00, 7.58682543e-01, 5.75599200e-01, 4.36697065e-01],\n",
       "        [1.00000000e+00, 6.70000000e-01, 4.48900000e-01, 3.00763000e-01],\n",
       "        [1.00000000e+00, 4.60000000e-01, 2.11600000e-01, 9.73360000e-02],\n",
       "        [1.00000000e+00, 8.28509091e-01, 6.86427314e-01, 5.68711270e-01],\n",
       "        [1.00000000e+00, 6.00000000e-01, 3.60000000e-01, 2.16000000e-01],\n",
       "        [1.00000000e+00, 6.36339486e-01, 4.04927942e-01, 2.57671638e-01],\n",
       "        [1.00000000e+00, 6.48325909e-01, 4.20326484e-01, 2.72508550e-01],\n",
       "        [1.00000000e+00, 6.30713611e-01, 3.97799659e-01, 2.50897660e-01],\n",
       "        [1.00000000e+00, 7.00000000e-02, 4.90000000e-03, 3.43000000e-04],\n",
       "        [1.00000000e+00, 5.35968243e-01, 2.87261957e-01, 1.53963286e-01],\n",
       "        [1.00000000e+00, 5.20000000e-01, 2.70400000e-01, 1.40608000e-01]]),\n",
       " array([0.61984169, 0.81167767, 0.64431987, 0.49208494, 0.58004131,\n",
       "        0.93613422, 0.60311145, 0.35817449, 0.91261385, 0.81232659,\n",
       "        0.23599998, 0.05051023, 0.7612565 , 0.64634662, 0.89700996,\n",
       "        0.52531463, 0.76638914, 0.60188686, 0.71040586, 0.72006043,\n",
       "        0.65597413, 0.13897264, 0.53688748, 0.47094573]))"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "traintestlists[3]['train'], ytrain"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[1.        , 0.74990267, 0.56235401, 0.42171077],\n",
       "        [1.        , 0.79      , 0.6241    , 0.493039  ],\n",
       "        [1.        , 0.11      , 0.0121    , 0.001331  ],\n",
       "        [1.        , 0.23      , 0.0529    , 0.012167  ],\n",
       "        [1.        , 0.80965752, 0.65554529, 0.53076717],\n",
       "        [1.        , 0.96      , 0.9216    , 0.884736  ]]),\n",
       " array([0.74855785, 0.80195369, 0.18382092, 0.05762073, 0.79714359,\n",
       "        0.87217807]))"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "traintestlists[3]['test'], ytest"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Estimating the out-of-sample error\n",
    "\n",
    "We can then use `mean_squared_error` from `sklearn` to calculate the error between the predictions and actual `ytest` values. Below we calculate this error on both the training set (which we already fit on) and the test set (which we hadnt seen before), and plot how these errors change with the degree of the polynomial."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "est3 = LinearRegression()\n",
    "est3.fit(traintestlists[3]['train'], ytrain)\n",
    "pred_on_train3=est3.predict(traintestlists[3]['train'])\n",
    "pred_on_test3=est3.predict(traintestlists[3]['test'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "errtrain 0.0049921493087190716\n",
      "errtest 0.005959322409058766\n"
     ]
    }
   ],
   "source": [
    "print(\"errtrain\",mean_squared_error(ytrain, pred_on_train3))\n",
    "print(\"errtest\",mean_squared_error(ytest, pred_on_test3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us now do this for a polynomial of degree 19"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "errtrain 0.0029515851142934645\n",
      "errtest 389559.5217397779\n"
     ]
    }
   ],
   "source": [
    "est19 = LinearRegression()\n",
    "est19.fit(traintestlists[19]['train'], ytrain)\n",
    "pred_on_train19=est19.predict(traintestlists[19]['train'])\n",
    "pred_on_test19=est19.predict(traintestlists[19]['test'])\n",
    "print(\"errtrain\",mean_squared_error(ytrain, pred_on_train19))\n",
    "print(\"errtest\",mean_squared_error(ytest, pred_on_test19))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can see that the test set error is larger, corresponding to an overfit model thats doing very well on some points and awful on other.\n",
    "\n",
    "\n",
    "### Finding the appropriate complexity\n",
    "\n",
    "Lets now carry out this minimization systematically for each polynomial degree d."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "for d in degrees:#for increasing polynomial degrees 0,1,2...\n",
    "    Xtrain = traintestlists[d]['train']\n",
    "    Xtest = traintestlists[d]['test']\n",
    "    #set up model\n",
    "    #fit\n",
    "    #predict\n",
    "    #calculate mean squared error\n",
    "    #set up model\n",
    "    est = LinearRegression()\n",
    "    #fit\n",
    "    est.fit(Xtrain, ytrain)\n",
    "    #predict\n",
    "    prediction_on_training = est.predict(Xtrain)\n",
    "    prediction_on_test = est.predict(Xtest)\n",
    "    #calculate mean squared error\n",
    "    error_train[d] = mean_squared_error(ytrain, prediction_on_training)\n",
    "    error_test[d] = mean_squared_error(ytest, prediction_on_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(degrees, error_train, marker='o', label='train (in-sample)')\n",
    "plt.plot(degrees, error_test, marker='o', label='test')\n",
    "plt.axvline(np.argmin(error_test), 0,0.5, color='r', label=\"min test error at d=%d\"%np.argmin(error_test), alpha=0.3)\n",
    "plt.ylabel('mean squared error')\n",
    "plt.xlabel('degree')\n",
    "plt.legend(loc='upper left')\n",
    "plt.yscale(\"log\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The graph shows a very interesting structure. The training error decreases with increasing degree of the polynomial. This ought to make sense given what you know now: one can construct an arbitrarily complex polynomial to fit all the training data: indeed one could construct an order 24 polynomial which perfectly interpolates the 24 data points in the training set. You also know that this would do very badly on the test set as it would wiggle like mad to capture all the data points. And this is indeed what we see in the test set error. \n",
    "\n",
    "For extremely low degree polynomials like $d=0$ a flat line capturing the mean value of the data or $d=1$ a straight line fitting the data, the polynomial is not curvy enough to capturve the conbtours of the data. We are in the bias/deterministic error regime, where we will always have some difference between the data and the fit since the hypothesis is too simple. But, for degrees higher than 5 or so, the polynomial starts to wiggle too much to capture the training data. The test set error increases as the predictive power of the polynomial goes down thanks to the contortions it must endure to fit the training data.\n",
    "\n",
    "Thus the test set error first decreases as the model get more expressive, and then, once we exceed a certain level of complexity (here indexed by $d$), it increases. This idea can be used to identify just the right amount of complexity in the model by picking as **the best hypothesis as the one that minimizes test set error** or risk. In our case this happens around $d=4$. (This exact number will depend on the random points chosen into the training and test sets) For complexity lower than this critical value, identified by the red vertical line in the diagram, the hypotheses underfit; for complexity higher, they overfit.\n",
    "\n",
    "![m:caption](images/complexity-error-plot.png)\n",
    "\n",
    "Keep in mind that as you see in the plot above this minimum can be shallow: in this case any of the low order polynomials would be \"good enough\"."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Is this still a test set?\n",
    "\n",
    "But something should be troubling you about this discussion. We have made no discussion on the error bars on our error estimates, primarily because we have not carried out any resampling to make this possible. \n",
    "\n",
    "But secondly we seem to be \"visually fitting\" a value of $d$. It cant be kosher to use as a test set something you did some fitting on...\n",
    "\n",
    "We have contaminated our test set. The moment we **use it in the learning process, it is not a test set**.\n",
    "\n",
    "The answer to the second question is to use a validation set, and leave a separate test set aside. The answer to the first is to use cross-validation, which is a kind of resampling method that uses multiple validation sets!"
   ]
  }
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