notebooks/06_bias_variance.ipynb

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  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Exploring the Bias-Variance Tradeoff"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "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"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "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",
     "collapsed": false,
     "input": [
      "df = pd.read_table('http://people.sc.fsu.edu/~jburkardt/datasets/regression/x01.txt', sep='\\s+', skiprows=33, names=['id','brain','body'], index_col='id')\n",
      "df.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\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>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 2,
       "text": [
        "      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"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "df.describe()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\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>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "             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"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "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",
     "collapsed": false,
     "input": [
      "# only keep rows in which the body weight is less than 200\n",
      "df = df[df.body < 200]\n",
      "df.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "(51, 2)"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We're actually 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",
     "collapsed": false,
     "input": [
      "sns.lmplot(x='body', y='brain', data=df, ci=None, fit_reg=False)\n",
      "sns.plt.xlim(-10, 200)\n",
      "sns.plt.ylim(-10, 250)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "(-10, 250)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x18dd5e10>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "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",
     "collapsed": false,
     "input": [
      "sns.lmplot(x='body', y='brain', data=df, ci=None)\n",
      "sns.plt.xlim(-10, 200)\n",
      "sns.plt.ylim(-10, 250)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "(-10, 250)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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hkYL8PLZvWMHpK7HhjhzYGhqOzHilTqq3KBWcIuktnUK4Cxh7ne6UAVxVVUph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\nRK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x18e50128>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "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 rows to **either sample 1 or sample 2**:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# set a random seed for reproducibility\n",
      "np.random.seed(12345)\n",
      "\n",
      "# randomly assign every row to either sample 1 or sample 2\n",
      "df['sample'] = np.random.randint(1, 3, len(df))\n",
      "df.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\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>sample</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>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "     brain   body  sample\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"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can now tell Seaborn to create two plots, in which the left plot only uses the data from **sample 1** and the right plot only uses the data from **sample 2**:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# col='sample' subsets the data by sample and creates two separate plots\n",
      "sns.lmplot(x='body', y='brain', data=df, ci=None, col='sample')\n",
      "sns.plt.xlim(-10, 200)\n",
      "sns.plt.ylim(-10, 250)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "(-10, 250)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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U+MOVbpu0WmXGLl+tZfzu2ctF1zvamunJl2yzkL2kapHNZjl+ZoK+9BAvHB7m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\nLEmSJBUwJEuSJEkF/n8O2KJLrDyPLwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x19175cf8>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "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",
     "collapsed": false,
     "input": [
      "# hue='sample' subsets the data by sample and creates a single plot\n",
      "sns.lmplot(x='body', y='brain', data=df, ci=None, hue='sample')\n",
      "sns.plt.xlim(-10, 200)\n",
      "sns.plt.ylim(-10, 250)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "(-10, 250)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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aoosRFN8Evm2MuX1P4mNAL/ANY0w2cBp4cRH6JTJv0WiUi4NXaAkGaOs+xcRs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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xac7a978>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "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 upon which points happen to be in the sample."
     ]
    },
    {
     "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",
     "collapsed": false,
     "input": [
      "sns.lmplot(x='body', y='brain', data=df, ci=None, col='sample', order=8)\n",
      "sns.plt.xlim(-10, 200)\n",
      "sns.plt.ylim(-10, 250)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "(-10, 250)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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XDss0zb+u3rFEJKyOeyc6LDHwbUnGaU7EmE7ntMTCQzW+IhcLw0QHgEgkQltL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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x194131d0>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "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 upon which points happen to be in the sample. (For a body weight of 100, the brain weight prediction would either be 40 or 0, depending upon which data happened to be in the sample.)"
     ]
    },
    {
     "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",
     "collapsed": false,
     "input": [
      "sns.lmplot(x='body', y='brain', data=df, ci=None, col='sample', order=2)\n",
      "sns.plt.xlim(-10, 200)\n",
      "sns.plt.ylim(-10, 250)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "(-10, 250)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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V9z27g5a27rnHudnce7Ojx9JQ98iLe3q2FlsZyrl79ZyM1mckO3C0kYdf2MOG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\nBWwGvhRjHLV7BoYQrgX+KsZ4awhhAf2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       "text": [
        "<matplotlib.figure.Figure at 0x18e48e80>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "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**: finding a model that appropriately balances bias and variance, and thus will generalize to new data (known as \"out of sample\" data)."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}