Recidivism and GPs.ipynb

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   "cell_type": "markdown",
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   "source": [
    "Contributed by Sam Mason.  From his email:\n",
    "\n",
    "\"I've done a very naive thing in a gaussian process regression.  I use the GPy toolbox:\n",
    "  http://sheffieldml.github.io/GPy/ which is a reasonably nice library for doing this sort of thing.  GPs have n^2 complexity in the number of data points, so scaling beyond a few hundred points can be awkward but there are various sparse approximations (some included in GPy) should you want to play with much more data.\n",
    "The main thing to choose is the covariance function—i.e. how related are points should points be considered to be at a given distance.  The GPML book by Rasmussen and Williams is a good reference if you want to know more.\n",
    "\n",
    "\"The generally recommended kernel if you don't know much about the data is a Matern kernel and this ends up looking a bit like your quadratic fit (a squared exponential kernel is also commonly used, but tends to be too strong).  I'd agree with the GP model that the logistic regression is probably saying that those with high scores are too likely to recidivate.  Another kernel that looked like a good fit is the Exponential kernel.  This smooths the independent estimates a bit and says that the extreme rates (i.e. <=0 or >=7) are basically equal—which seems reasonable to me.\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy as sp\n",
    "import scipy.stats as sps\n",
    "\n",
    "import pandas as pd\n",
    "import GPy\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "    <tr style=\"text-align: right;\">\n",
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       "   score  rec\n",
       "0     -2    0\n",
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      ]
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     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "# load in data\n",
    "inp = pd.read_excel(\"DATABASE Helmus 10 yr fixed HR-HN 09-29-2012.xlsx\")\n",
    "# give columns nicer names\n",
    "inp.columns = [\"score\",\"rec\"]\n",
    "# drop the last row of totals\n",
    "inp = inp.iloc[:-1]\n",
    "# display a summary\n",
    "inp.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
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      "text/plain": [
       "rec     0   1\n",
       "score        \n",
       "-2      2   0\n",
       "-1     22   2\n",
       " 0     28   3\n",
       " 1     51   5\n",
       " 2     28  14\n",
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     "execution_count": 3,
     "metadata": {},
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   ],
   "source": [
    "# cross tabulate the data counting number of entries\n",
    "ct = pd.crosstab(inp.score,inp.rec)\n",
    "ct"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Name                              : gp_classification\n",
      "Log-likelihood                    : -1183.6563267719255\n",
      "Number of Parameters              : 2\n",
      "Number of Optimization Parameters : 2\n",
      "Updates                           : True\n",
      "Parameters:\n",
      "  gp_classification.       |      Value       |  Constraint  |  Prior  |  Tied to\n",
      "  \u001b[1mExponential.variance   \u001b[0;0m  |  0.784395048464  |     +ve      |         |         \n",
      "  \u001b[1mExponential.lengthscale\u001b[0;0m  |   16.1593223119  |     +ve      |         |         \n"
     ]
    }
   ],
   "source": [
    "# create our GP regression using an Exponential kernel\n",
    "me = GPy.models.GPClassification(inp[[\"score\"]].values, inp[[\"rec\"]].values,\n",
    "                                GPy.kern.Exponential(1))\n",
    "# optimize hyperparameters\n",
    "me.optimize()\n",
    "# display summary of model\n",
    "print(me)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Name                              : gp_classification\n",
      "Log-likelihood                    : -1182.2751029594572\n",
      "Number of Parameters              : 2\n",
      "Number of Optimization Parameters : 2\n",
      "Updates                           : True\n",
      "Parameters:\n",
      "  gp_classification.  |      Value      |  Constraint  |  Prior  |  Tied to\n",
      "  \u001b[1mMat52.variance    \u001b[0;0m  |  1.30463115832  |     +ve      |         |         \n",
      "  \u001b[1mMat52.lengthscale \u001b[0;0m  |   14.233401485  |     +ve      |         |         \n"
     ]
    }
   ],
   "source": [
    "# and again with a Matern covariance function\n",
    "mm = GPy.models.GPClassification(inp[[\"score\"]].values, inp[[\"rec\"]].values,\n",
    "                                GPy.kern.Matern52(1))\n",
    "# optimize hyperparameters\n",
    "mm.optimize()\n",
    "# display summary of model\n",
    "print(mm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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hRo4cyZ/+9KdYHV5RUcEDDzwQ209EpDVTS3oDMAzjqO7uR2Y8nT59Or/73e/o1KkTY8aM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\nAAAAAAAUCUI6AAAAAABF4v8BjqlBEulbIvsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109959f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# pull in CDF function so we can display confidence intervals\n",
    "from GPy.likelihoods.link_functions import std_norm_cdf\n",
    "\n",
    "# get to posteriour of independent estimates with beta(1,1) prior\n",
    "d = sps.beta(1+ct[1], 1+ct[0])\n",
    "\n",
    "# generate some points on which to estimate GP\n",
    "X = np.linspace(-2.5,11.5,101)\n",
    "\n",
    "# get some better colors\n",
    "pal = sns.color_palette()\n",
    "\n",
    "# to make the plots look nice\n",
    "with sns.axes_style(\"ticks\"):\n",
    "    fig,axs = plt.subplots(1,2,sharey=True,figsize=(14,5))\n",
    "\n",
    "# loop over our two GPs\n",
    "for i,(ax,m,kern) in enumerate(zip(axs,[mm,me],[\"Exp\",\"Matern\"])):\n",
    "    # get a prediction from the GP, Y is the mean, Yv is the variance\n",
    "    Y,Yv = m._raw_predict(X[:,None])\n",
    "    Y,Yv = m._raw_predict(X[:,None])\n",
    "\n",
    "    # draw the independent estimates with 95% CI\n",
    "    ax.scatter(ct.index, d.mean(), label=\"Independent Beta(1,1)\",\n",
    "               facecolor='k', edgecolor=None)\n",
    "    ax.vlines(ct.index, d.ppf(0.025), d.ppf(0.975), lw=1)\n",
    "\n",
    "    # draw the GP mean and 95% CI\n",
    "    ax.plot(X, std_norm_cdf(Y), color=pal[i], label=\"%s GP mean + 95%%CI\"%(kern,))\n",
    "    ax.fill_between(X,\n",
    "                    std_norm_cdf(Y - 2*np.sqrt(Yv))[:,0],\n",
    "                    std_norm_cdf(Y + 2*np.sqrt(Yv))[:,0],\n",
    "                    alpha=0.2, color=pal[i], zorder=0)\n",
    "\n",
    "    # add a figure legend\n",
    "    ax.legend(loc=\"upper left\")\n",
    "    # set the axes up nicely\n",
    "    ax.set_xlim(np.min(X), np.max(X))\n",
    "    ax.set_ylim(0,1)\n",
    "    ax.set_xlabel(\"score\")\n",
    "\n",
    "# just a single label on the y axis\n",
    "axs[0].set_ylabel(\"recidivism probability\")\n",
    "\n",
    "# remove lines on the top and right of plot and squeeze everything up nicely\n",
    "sns.despine()\n",
    "plt.tight_layout()"
   ]
  }
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