notebooks/08_bias_variance.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exploring the Bias-Variance Tradeoff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "\n",
    "# allow plots to appear in the notebook\n",
    "%matplotlib inline"
   ]
  },
  {
   "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": 2,
   "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": 2,
     "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": 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",
       "  </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": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mammals.describe()"
   ]
  },
  {
   "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": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(51, 2)"
      ]
     },
     "execution_count": 4,
     "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"
   ]
  },
  {
   "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": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-10, 250)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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GsNQiXhmnRhwTllrAC180E3vCUpN54YtmYwhLUkGGsNRkXhmn2TgmLLWAF75oJoaw1CKG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\nydvNAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x18acc2e8>"
      ]
     },
     "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": 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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hkYL8PLZvWMHpK7HhjhzYGhqOzHilTqq3KBWcIuktnUK4Cxh7ne6UAVxVVUph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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x18c38d68>"
      ]
     },
     "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\", which we will study in a future class."
   ]
  },
  {
   "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": 7,
   "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": 7,
     "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": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-10, 250)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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xxg9e99jXgWdijN8NIfx74KPAH61026TVKjN25Vot43fOXSm63tHWTE++ZJuF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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x190045f8>"
      ]
     },
     "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": 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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Td0l9A3iXRMeftdaOzVK/RGSWKSju2qe4/0+rHQQwxpSRCI/fc7JfxgNjcvm5tfYMifU0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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x18c59a20>"
      ]
     },
     "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": 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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EROaRzeUZnwhW4Nt+0RKLFd0tFfvej+4+xh5zAIDptN08F4QFFv4/oYiIiEidjU2kcapk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\nihwcAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x19011a90>"
      ]
     },
     "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": 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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wgZvmszoVjjV0DMmSMqIntXPFg8/spK0jNfc4P5cP3uLosTTcPfri3t6txdaE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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x18c59f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.lmplot(x='body', y='brain', data=mammals, ci=None, col='universe', order=2)\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)."
   ]
  }
 ],
 "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": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}