notebooks/08_bias_variance.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exploring the Bias-Variance Tradeoff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# allow plots to appear in the notebook\n",
    "%matplotlib inline\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Brain and body weight"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a [dataset](http://people.sc.fsu.edu/~jburkardt/datasets/regression/x01.txt) of the average weight of the body and the brain for 62 mammal species. Let's read it into pandas and take a quick look:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>brain</th>\n",
       "      <th>body</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>id</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3.385</td>\n",
       "      <td>44.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.480</td>\n",
       "      <td>15.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.350</td>\n",
       "      <td>8.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>465.000</td>\n",
       "      <td>423.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>36.330</td>\n",
       "      <td>119.5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      brain   body\n",
       "id                \n",
       "1     3.385   44.5\n",
       "2     0.480   15.5\n",
       "3     1.350    8.1\n",
       "4   465.000  423.0\n",
       "5    36.330  119.5"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "url = 'http://people.sc.fsu.edu/~jburkardt/datasets/regression/x01.txt'\n",
    "col_names = ['id', 'brain', 'body']\n",
    "mammals = pd.read_table(url, sep='\\s+', skiprows=33, names=col_names, index_col='id')\n",
    "mammals.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>brain</th>\n",
       "      <th>body</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>62.000000</td>\n",
       "      <td>62.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>198.789984</td>\n",
       "      <td>283.134194</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>899.158011</td>\n",
       "      <td>930.278942</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.005000</td>\n",
       "      <td>0.140000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.600000</td>\n",
       "      <td>4.250000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>3.342500</td>\n",
       "      <td>17.250000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>48.202500</td>\n",
       "      <td>166.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>6654.000000</td>\n",
       "      <td>5712.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             brain         body\n",
       "count    62.000000    62.000000\n",
       "mean    198.789984   283.134194\n",
       "std     899.158011   930.278942\n",
       "min       0.005000     0.140000\n",
       "25%       0.600000     4.250000\n",
       "50%       3.342500    17.250000\n",
       "75%      48.202500   166.000000\n",
       "max    6654.000000  5712.000000"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mammals.describe()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We're going to focus on a smaller subset in which the body weight is less than 200:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>brain</th>\n",
       "      <th>body</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>51.000000</td>\n",
       "      <td>51.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>15.014098</td>\n",
       "      <td>40.810196</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>37.842178</td>\n",
       "      <td>58.105713</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.005000</td>\n",
       "      <td>0.140000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.352500</td>\n",
       "      <td>3.250000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>1.620000</td>\n",
       "      <td>12.100000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>4.261500</td>\n",
       "      <td>53.200000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>192.000000</td>\n",
       "      <td>180.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            brain        body\n",
       "count   51.000000   51.000000\n",
       "mean    15.014098   40.810196\n",
       "std     37.842178   58.105713\n",
       "min      0.005000    0.140000\n",
       "25%      0.352500    3.250000\n",
       "50%      1.620000   12.100000\n",
       "75%      4.261500   53.200000\n",
       "max    192.000000  180.000000"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# only keep rows in which the body weight is less than 200\n",
    "mammals = mammals[mammals.body < 200]\n",
    "mammals.shape\n",
    "mammals.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We're now going to pretend that there are only 51 mammal species in existence. In other words, we are pretending that this is the entire dataset of brain and body weights for **every known mammal species**.\n",
    "\n",
    "Let's create a scatterplot (using [Seaborn](http://stanford.edu/~mwaskom/software/seaborn/)) to visualize the relationship between brain and body weight:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-10, 250)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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HL5qO0xFSB/ijF03HEJY6wF/GaTpOR0gd4I9eNB1DWOoAf/Si6TgdIUkFGcKSVJAhLEkF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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1102e0410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.lmplot(x='body', y='brain', data=mammals, ci=None, fit_reg=False)\n",
    "sns.plt.xlim(-10, 200)\n",
    "sns.plt.ylim(-10, 250)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There appears to be a relationship between brain and body weight for mammals."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Making a prediction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's pretend that a **new mammal species** is discovered. We measure the body weight of every member of this species that we can find, and calculate an **average body weight of 100**. We want to **predict the average brain weight** of this species (rather than measuring it directly). How might we do this?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-10, 250)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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rNvj9WqWXicYlncZkbuVTCDcDHwSeMsbsBlqmu3NPz9B0u9MsX1rF+d7ZHwmX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\nr6ywAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1103732d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.lmplot(x='body', y='brain', data=mammals, ci=None)\n",
    "sns.plt.xlim(-10, 200)\n",
    "sns.plt.ylim(-10, 250)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We drew a straight line that appears to best capture the relationship between brain and body weight. So, we might predict that our new species has a brain weight of about 45, since that's the approximate y value when x=100.\n",
    "\n",
    "This is known as a \"linear model\" or a \"linear regression model\"."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Making a prediction from a sample"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Earlier, I said that this dataset contained every known mammal species. That's very convenient, but **in the real world, all you ever have is a sample of data**. A more realistic situation would be to only have brain and body weights for (let's say) half of the 51 known mammals.\n",
    "\n",
    "When that new mammal species (with a body weight of 100) is discovered, we still want to make an accurate prediction for the brain weight, but this task might be more difficult since we don't have all of the data that we would ideally like to have.\n",
    "\n",
    "Let's simulate this situation by assigning each of the 51 observations to **either universe 1 or universe 2**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>brain</th>\n",
       "      <th>body</th>\n",
       "      <th>universe</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>id</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3.385</td>\n",
       "      <td>44.5</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.480</td>\n",
       "      <td>15.5</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.350</td>\n",
       "      <td>8.1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>36.330</td>\n",
       "      <td>119.5</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>27.660</td>\n",
       "      <td>115.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     brain   body  universe\n",
       "id                         \n",
       "1    3.385   44.5         1\n",
       "2    0.480   15.5         2\n",
       "3    1.350    8.1         2\n",
       "5   36.330  119.5         2\n",
       "6   27.660  115.0         1"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# set a random seed for reproducibility\n",
    "np.random.seed(12345)\n",
    "\n",
    "# randomly assign every observation to either universe 1 or universe 2\n",
    "mammals['universe'] = np.random.randint(1, 3, len(mammals))\n",
    "mammals.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Important:** We only live in one of the two universes. Both universes have 51 known mammal species, but each universe knows the brain and body weight for different species.\n",
    "\n",
    "We can now tell Seaborn to create two plots, in which the left plot only uses the data from **universe 1** and the right plot only uses the data from **universe 2**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-10, 250)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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yOJ4uDvupOLfaT2dHrvDtw6f4hxdOcWKBM2p3t67hPXu38MQjW9i8TJaa+Z4q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\nJEuSJEkFDMmSJElSAUOyJEmSVOD/B4thWWhzFSoFAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11572d850>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# col='universe' subsets the data by universe and creates two separate plots\n",
    "sns.lmplot(x='body', y='brain', data=mammals, ci=None, col='universe')\n",
    "sns.plt.xlim(-10, 200)\n",
    "sns.plt.ylim(-10, 250)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The line looks pretty similar between the two plots, despite the fact that they used separate samples of data. In both cases, we would predict a brain weight of about 45.\n",
    "\n",
    "It's easier to see the degree of similarity by placing them on the same plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-10, 250)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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okUiEa4M3YpVhTzI6pzJsfmYedVX7aPDVsqFoHZNTYU5c7KGp4xJnrt5mTosJ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\nXOy9pJgKT/EP579Fe89ZJqY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      "text/plain": [
       "<matplotlib.figure.Figure at 0x115507b50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# hue='universe' subsets the data by universe and creates a single plot\n",
    "sns.lmplot(x='body', y='brain', data=mammals, ci=None, hue='universe')\n",
    "sns.plt.xlim(-10, 200)\n",
    "sns.plt.ylim(-10, 250)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What was the point of this exercise? This was a visual demonstration of a high bias, low variance model:\n",
    "\n",
    "- It's **high bias** because it doesn't fit the data particularly well.\n",
    "- It's **low variance** because it doesn't change much depending on which observations happen to be available in that universe."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Let's try something completely different"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What would a **low bias, high variance** model look like? Let's try polynomial regression, with an eighth order polynomial:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-10, 250)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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eTYObt9QhSAssllrA8rvAQ6ZpHi3lYURELq5yY5uXMr6FnKkOYJc7eNeXioSd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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11642ca90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.lmplot(x='body', y='brain', data=mammals, ci=None, col='universe', order=8)\n",
    "sns.plt.xlim(-10, 200)\n",
    "sns.plt.ylim(-10, 250)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- It's **low bias** because the models match the data quite well!\n",
    "- It's **high variance** because the models are widely different depending on which observations happen to be available in that universe. (For a body weight of 100, the brain weight prediction would be 40 in one universe and 0 in the other universe!)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Can we find a middle ground?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Perhaps we can create a model that has **less bias than the linear model**, and **less variance than the eighth order polynomial**?\n",
    "\n",
    "Let's try a second order polynomial instead:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-10, 250)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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mtnBcMawGEowxrwMRwF8Ba6212/uefxXYAigYZMYKBBze/LCC371bQo8vOFAt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\nFAwiIuKiYBARERcFg4iIuCgYRETE5f8HwSXHjtHgLmQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116438e90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.lmplot(x='body', y='brain', data=mammals, ci=None, hue='universe', order=3)\n",
    "sns.plt.xlim(-10, 200)\n",
    "sns.plt.ylim(-10, 250)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This seems better. In both the left and right plots, **it fits the data pretty well, but not too well**.\n",
    "\n",
    "This is the essence of the **bias-variance tradeoff**: You are seeking a model that appropriately balances bias and variance, and thus will generalize to new data (known as \"out-of-sample\" data)."
   ]
  }
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