notebooks/analyze.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from __future__ import division, print_function\n",
    "from IPython.display import display\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import os\n",
    "import sys\n",
    "sys.path.append('..')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from pummeler.data import election_data, centroids_cartesian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn import cross_validation as cv, linear_model, metrics\n",
    "import scipy.stats\n",
    "import GPy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**NOTE**: as of early September 2016, the release version of GPy doesn't actually support Laplace inference with binomial likelihoods, but it works on the `devel` branch. You can get it with e.g.\n",
    "\n",
    "    pip install 'git+https://github.com/SheffieldML/GPy.git@devel'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Load data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The embeddings:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['emb_lin', 'freqs', 'bandwidth', 'emb_rff', 'region_names', 'feature_names']"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "SORT_DIR = '../SORT_DIR'\n",
    "with np.load(os.path.join(SORT_DIR, 'embeddings.npz') as d:\n",
    "    display(d.keys())\n",
    "    locals().update(**d)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The centroids, which we load in 3d Cartesian coordinates (in units of km) so that distances are accurate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "centroids = np.asarray(centroids_cartesian('00').loc[region_names])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The paper reported the learned lengthscale in some weird units, so let's start it at \"a little more than half the median distance between locations\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.metrics.pairwise import euclidean_distances"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1090.2906089823362"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D2 = euclidean_distances(centroids, squared=True)\n",
    "np.sqrt(np.median(D2[np.triu_indices_from(D2, k=1)]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "election = election_data().loc[region_names]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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>votes_D</th>\n",
       "      <th>votes_G</th>\n",
       "      <th>votes_L</th>\n",
       "      <th>votes_R</th>\n",
       "      <th>votes_oth</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>region</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>AK_00_01</th>\n",
       "      <td>122640</td>\n",
       "      <td>2917</td>\n",
       "      <td>7392</td>\n",
       "      <td>164676</td>\n",
       "      <td>2870</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AL_00_01</th>\n",
       "      <td>18424</td>\n",
       "      <td>169</td>\n",
       "      <td>607</td>\n",
       "      <td>66016</td>\n",
       "      <td>275</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AL_00_02</th>\n",
       "      <td>75150</td>\n",
       "      <td>116</td>\n",
       "      <td>301</td>\n",
       "      <td>62561</td>\n",
       "      <td>227</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AL_00_03</th>\n",
       "      <td>15328</td>\n",
       "      <td>175</td>\n",
       "      <td>536</td>\n",
       "      <td>71439</td>\n",
       "      <td>402</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AL_00_04</th>\n",
       "      <td>37374</td>\n",
       "      <td>211</td>\n",
       "      <td>631</td>\n",
       "      <td>74343</td>\n",
       "      <td>432</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          votes_D  votes_G  votes_L  votes_R  votes_oth\n",
       "region                                                 \n",
       "AK_00_01   122640     2917     7392   164676       2870\n",
       "AL_00_01    18424      169      607    66016        275\n",
       "AL_00_02    75150      116      301    62561        227\n",
       "AL_00_03    15328      175      536    71439        402\n",
       "AL_00_04    37374      211      631    74343        432"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "election.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ignore third-party votes; `n` is number of votes, `y` is number Democratic."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "n = np.asarray(election.votes_D + election.votes_R)\n",
    "y = np.asarray(election.votes_D)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X_lin = np.hstack([emb_lin, centroids])\n",
    "X_rff = np.hstack([emb_rff, centroids])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n_regions = len(region_names)\n",
    "n_feats = len(feature_names)\n",
    "n_rff = emb_rff.shape[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Try out the model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just do a single train/test split for right now."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "train, test = next(iter(cv.ShuffleSplit(\n",
    "            n_regions, test_size=.1, random_state=10)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear embeddings"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's the model using linear embeddings (i.e. feature means), along with the Matérn kernel on centroids, with hyperparameters more or less what the paper said worked well:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " /usr/local/anaconda/lib/python2.7/site-packages/GPy-1.0.9-py2.7-macosx-10.6-x86_64.egg/GPy/inference/latent_function_inference/laplace.py:225: UserWarning:Not perfect mode found (f_hat). difference: 207.929438715, iteration: 30 out of max 30\n"
     ]
    }
   ],
   "source": [
    "m_lin = GPy.core.GP(\n",
    "    X_lin[train], y[train, np.newaxis],\n",
    "    kernel=\n",
    "        GPy.kern.Linear(\n",
    "            n_feats, variances=4.56,\n",
    "            active_dims=range(0, n_feats))\n",
    "        + GPy.kern.Matern32(\n",
    "            3, variance=0.18, lengthscale=560,\n",
    "            active_dims=range(n_feats, n_feats + 3)),\n",
    "    likelihood=GPy.likelihoods.Binomial(),\n",
    "    Y_metadata={'trials': n[train, np.newaxis]},\n",
    "    inference_method=GPy.inference.latent_function_inference.Laplace(),\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "}\n",
       "</style>\n",
       "\n",
       "<p class=pd>\n",
       "<b>Model</b>: gp<br>\n",
       "<b>Objective</b>: 24446.7904359<br>\n",
       "<b>Number of Parameters</b>: 3<br>\n",
       "<b>Number of Optimization Parameters</b>: 3<br>\n",
       "<b>Updates</b>: True<br>\n",
       "</p>\n",
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       "</style>\n",
       "<table class=\"tg\"><tr><th><b>  gp.                  </b></th><th><b>value</b></th><th><b>constraints</b></th><th><b>priors</b></th></tr>\n",
       "<tr><td class=tg-left>  sum.linear.variances </td><td class=tg-right> 4.56</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  sum.Mat32.variance   </td><td class=tg-right> 0.18</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  sum.Mat32.lengthscale</td><td class=tg-right>560.0</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<GPy.core.gp.GP at 0x12908c090>"
      ]
     },
     "execution_count": 16,
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   "source": [
    "m_lin"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def eval_preds(phat):\n",
    "    plt.plot([0, 1], [0, 1], color='r')\n",
    "    plt.scatter(y[test] / n[test], phat.squeeze())\n",
    "    plt.xlim(0, 1)\n",
    "    plt.ylim(0, 1)\n",
    "\n",
    "    return metrics.explained_variance_score(y[test] / n[test], phat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
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BACEs6jpn4jcBAKEuejpn4jcBAGEiKjpn4jcBAOEk4osz8ZsAgHAT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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11f7e7a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, fstd = m_lin._raw_predict(X_lin[test])\n",
    "phat = scipy.stats.norm.cdf(f.squeeze())\n",
    "eval_preds(phat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Predictions are pretty good. We can try optimizing it, see if that helps at all:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " /usr/local/anaconda/lib/python2.7/site-packages/GPy-1.0.9-py2.7-macosx-10.6-x86_64.egg/GPy/inference/latent_function_inference/laplace.py:229: UserWarning:f_hat now fine again. difference: 5.05701755174e-05, iteration: 4 out of max 30\n",
      " /usr/local/anaconda/lib/python2.7/site-packages/GPy-1.0.9-py2.7-macosx-10.6-x86_64.egg/GPy/inference/latent_function_inference/laplace.py:225: UserWarning:Not perfect mode found (f_hat). difference: 2.07836337076, iteration: 30 out of max 30\n",
      " /usr/local/anaconda/lib/python2.7/site-packages/GPy-1.0.9-py2.7-macosx-10.6-x86_64.egg/GPy/inference/latent_function_inference/laplace.py:229: UserWarning:f_hat now fine again. difference: 2.15533873416e-07, iteration: 14 out of max 30\n",
      " /usr/local/anaconda/lib/python2.7/site-packages/GPy-1.0.9-py2.7-macosx-10.6-x86_64.egg/GPy/inference/latent_function_inference/laplace.py:225: UserWarning:Not perfect mode found (f_hat). difference: 0.00392608354468, iteration: 30 out of max 30\n",
      " /usr/local/anaconda/lib/python2.7/site-packages/GPy-1.0.9-py2.7-macosx-10.6-x86_64.egg/GPy/inference/latent_function_inference/laplace.py:229: UserWarning:f_hat now fine again. difference: 3.26903927999e-05, iteration: 17 out of max 30\n",
      " /usr/local/anaconda/lib/python2.7/site-packages/GPy-1.0.9-py2.7-macosx-10.6-x86_64.egg/GPy/inference/latent_function_inference/laplace.py:229: UserWarning:f_hat now fine again. difference: 3.12667725666e-05, iteration: 17 out of max 30\n",
      " /usr/local/anaconda/lib/python2.7/site-packages/GPy-1.0.9-py2.7-macosx-10.6-x86_64.egg/GPy/inference/latent_function_inference/laplace.py:225: UserWarning:Not perfect mode found (f_hat). difference: 10.651530114, iteration: 30 out of max 30\n"
     ]
    }
   ],
   "source": [
    "m_lin.optimize()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       ".pd{\n",
       "    font-family: \"Courier New\", Courier, monospace !important;\n",
       "    width: 100%;\n",
       "    padding: 3px;\n",
       "}\n",
       "</style>\n",
       "\n",
       "<p class=pd>\n",
       "<b>Model</b>: gp<br>\n",
       "<b>Objective</b>: 7965.33062611<br>\n",
       "<b>Number of Parameters</b>: 3<br>\n",
       "<b>Number of Optimization Parameters</b>: 3<br>\n",
       "<b>Updates</b>: True<br>\n",
       "</p>\n",
       "<style type=\"text/css\">\n",
       ".tg  {font-family:\"Courier New\", Courier, monospace !important;padding:2px 3px;word-break:normal;border-collapse:collapse;border-spacing:0;border-color:#DCDCDC;margin:0px auto;width:100%;}\n",
       ".tg td{font-family:\"Courier New\", Courier, monospace !important;font-weight:bold;color:#444;background-color:#F7FDFA;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:#DCDCDC;}\n",
       ".tg th{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;color:#fff;background-color:#26ADE4;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:#DCDCDC;}\n",
       ".tg .tg-left{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;text-align:left;}\n",
       ".tg .tg-center{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;text-align:center;}\n",
       ".tg .tg-right{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;text-align:right;}\n",
       "</style>\n",
       "<table class=\"tg\"><tr><th><b>  gp.                  </b></th><th><b>         value</b></th><th><b>constraints</b></th><th><b>priors</b></th></tr>\n",
       "<tr><td class=tg-left>  sum.linear.variances </td><td class=tg-right> 3.62253710608</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  sum.Mat32.variance   </td><td class=tg-right>0.136401266784</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  sum.Mat32.lengthscale</td><td class=tg-right>  560.00075348</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<GPy.core.gp.GP at 0x12908c090>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m_lin"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.88431398469567279"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ftw1tvVas/X+Ntd83FJjj8OT2OucdO3Zoz549WrJkiQ4ePKjVq1drzZo1F/1c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\nd8OhAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116ea1fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, fstd = m_lin._raw_predict(X_lin[test])\n",
    "phat = scipy.stats.norm.cdf(f.squeeze())\n",
    "eval_preds(phat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "...the same."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ridge regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Of course, linear-kernel GPs are just ridge regression. If we drop the spatial kernel, we can investigate the importance of different features:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.84915614480653812"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Xss6/uExVtw4L8UgBRBuvxTkpKUnl5eUNX9cXZkl6++23VVxcrIceekhfffWV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\nwsz/B4i0/07dFr+dAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x123a28750>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ridge = linear_model.RidgeCV()\n",
    "ridge.fit(X_lin[train], y[train] / n[train])\n",
    "ridge_phat = ridge.predict(X_lin[test])\n",
    "eval_preds(ridge_phat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         RELP_0   0.279\n",
      "          MAR_1  -0.242\n",
      "         HISP_1  -0.2247\n",
      "          MAR_5   0.2217\n",
      "        MSP_6.0   0.2217\n",
      "        POBP_19   0.2188\n",
      " POWPUMA_6500.0   0.2176\n",
      "        MSP_1.0  -0.2102\n",
      "       ANC1P_32  -0.1976\n",
      "      POWSP_2.0  -0.1975\n",
      "       ANC1P_82   0.1959\n",
      "       ANC1P_21  -0.1936\n",
      " MIGPUMA_2090.0  -0.1905\n",
      "      POWSP_6.0   0.1896\n",
      "      SCHL_14.0   0.1727\n",
      "        POBP_24  -0.1667\n",
      "     LANP_625.0   0.1655\n",
      "        GCL_2.0   0.1647\n",
      "        HISP_24   0.1645\n"
     ]
    }
   ],
   "source": [
    "w = np.abs(ridge.coef_).argsort()[:-20:-1]\n",
    "for f, wt in zip(feature_names[w], ridge.coef_[w]):\n",
    "    print('{:>15}  {: .4}'.format(f, wt))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- `RELP_0` shouldn't happen according to [the documentation](http://www2.census.gov/programs-surveys/acs/tech_docs/pums/data_dict/PUMS_Data_Dictionary_2006-2010.pdf). Dunno what that means.\n",
    "- `MAR_1` means \"married.\"\n",
    "- `HISP_1` means \"not Hispanic.\"\n",
    "- `MAR_5` means \"never married.\"\n",
    "- `MSP_6.0` also means \"never married.\"\n",
    "- `POBP_19` means \"born in Iowa.\"\n",
    "- `POWPUMA_6500.0` means you work in either a specific place in California or a specific place in Texas....\n",
    "- `MSP_1.0` means \"now married, spouse present.\"\n",
    "- `ANC1P_32` means German ancestry, listed first.\n",
    "- `POWSP_2.0` means \"works in Alaska\".\n",
    "- `ANC1P_82` means Norwegian ancestry, listed first.\n",
    "- `ANC1P_21` is Dutch."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Avoiding referencing specific locations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that several of those refer to specific places (`POWPUMA` refers to working in a specific area; `POWSP_6.0` refers to a person who works in California; etc). We might try to avoid that:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that we could have done this in the embedding step by telling `pummel featurize` to ignore these features:\n",
    "\n",
    "    --skip-feats POBP RELP POWPUMA POWSP MIGSP MIGPUMA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.81360980824944207"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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AElVSFmfiNwEAiSy52kjiNwEASSBpOmfiNwEAySLxO2fiNwEASSah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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x136bb11d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "no_us_places = np.array([\n",
    "    not (s.startswith('POBP_') or s.startswith('RELP_')\n",
    "         or s.startswith('POWPUMA_') or s.startswith('POWSP')\n",
    "         or s.startswith('MIGSP_') or s.startswith('MIGPUMA_'))\n",
    "    for s in feature_names\n",
    "])\n",
    "ridge2 = linear_model.RidgeCV()\n",
    "ridge2.fit(X_lin[np.ix_(train, no_us_places)], y[train] / n[train])\n",
    "ridge2_phat = ridge2.predict(X_lin[np.ix_(test, no_us_places)])\n",
    "eval_preds(ridge2_phat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hurts a little, but not much."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        GCL_2.0   0.491\n",
      "           WKHP  -0.4464\n",
      "        GCL_nan  -0.3558\n",
      "       SCHG_4.0  -0.3353\n",
      "     LANP_966.0   0.3153\n",
      "          MAR_5   0.3153\n",
      "        ANC1P_5  -0.2868\n",
      "          MAR_1  -0.2656\n",
      "       SCHG_7.0   0.2326\n",
      "      ANC1P_904   0.2236\n",
      "     LANP_864.0  -0.2198\n",
      "       ANC1P_12   0.216\n",
      "        RELP_13  -0.2109\n",
      "       SCHG_5.0   0.2087\n",
      "      ANC2P_822  -0.2054\n",
      "      ANC1P_899  -0.1942\n",
      " naicsp02_32621  -0.1866\n",
      "    indp02_9780  -0.1866\n",
      "     indp07_nan   0.1842\n"
     ]
    }
   ],
   "source": [
    "w = np.abs(ridge2.coef_).argsort()[:-20:-1]\n",
    "for f, wt in zip(feature_names[w], ridge2.coef_[w]):\n",
    "    print('{:>15}  {: .4}'.format(f, wt))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- `GCL_2.0` indicates that the person is not a grandparent living with their grandchildren.\n",
    "- `WKHP` is the number of hours worked per week over the last year.\n",
    "- `GCL_nan` that either the person being referenced is under 30 or the household is an institution of some kind.\n",
    "- `SCHG_4.0` indicates that the person is currently in middle school. (Remember that people under 18 are not in this dataset, so this is a rare feature.)\n",
    "- `LANP_966.0` means that an American Indian language (other than Apache, \"Navaho\", Dakota, Keres, Cherokee, or Zuni) is spoken at home.\n",
    "- `MAR_5` means \"never married\".\n",
    "- `ANC1P_5` refers to Basque ancestry.\n",
    "- `MAR_1` means \"married\".\n",
    "- `SCHG_7.0` is people currently in graduate or professional school.\n",
    "- `ANC1P_904` is \"Negro\" ancestry. (Note that \"Afro American\", \"Afro\", \"African American\", \"Black\" are also options.)\n",
    "- `LANP_864.0` means \"Navaho\" is spoken at home.\n",
    "- `ANC1P_12` is \"British Isles\" ancestry (\"British\" is also an option)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Random Fourier feature embeddings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " /usr/local/anaconda/lib/python2.7/site-packages/GPy-1.0.9-py2.7-macosx-10.6-x86_64.egg/GPy/inference/latent_function_inference/laplace.py:225: UserWarning:Not perfect mode found (f_hat). difference: 0.000293246681395, iteration: 30 out of max 30\n"
     ]
    }
   ],
   "source": [
    "m_rff = GPy.core.GP(\n",
    "    X_rff[train], y[train, np.newaxis],\n",
    "    kernel=\n",
    "        GPy.kern.Linear(\n",
    "            n_rff, variances=4.56,\n",
    "            active_dims=range(0, n_rff))\n",
    "        + GPy.kern.Matern32(\n",
    "            3, variance=0.18, lengthscale=560,\n",
    "            active_dims=range(n_rff, n_rff + 3)),\n",
    "    likelihood=GPy.likelihoods.Binomial(),\n",
    "    Y_metadata={'trials': n[train, np.newaxis]},\n",
    "    inference_method=GPy.inference.latent_function_inference.Laplace(),\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "m_rff.optimize()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       ".pd{\n",
       "    font-family: \"Courier New\", Courier, monospace !important;\n",
       "    width: 100%;\n",
       "    padding: 3px;\n",
       "}\n",
       "</style>\n",
       "\n",
       "<p class=pd>\n",
       "<b>Model</b>: gp<br>\n",
       "<b>Objective</b>: 10014.7173089<br>\n",
       "<b>Number of Parameters</b>: 3<br>\n",
       "<b>Number of Optimization Parameters</b>: 3<br>\n",
       "<b>Updates</b>: True<br>\n",
       "</p>\n",
       "<style type=\"text/css\">\n",
       ".tg  {font-family:\"Courier New\", Courier, monospace !important;padding:2px 3px;word-break:normal;border-collapse:collapse;border-spacing:0;border-color:#DCDCDC;margin:0px auto;width:100%;}\n",
       ".tg td{font-family:\"Courier New\", Courier, monospace !important;font-weight:bold;color:#444;background-color:#F7FDFA;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:#DCDCDC;}\n",
       ".tg th{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;color:#fff;background-color:#26ADE4;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:#DCDCDC;}\n",
       ".tg .tg-left{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;text-align:left;}\n",
       ".tg .tg-center{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;text-align:center;}\n",
       ".tg .tg-right{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;text-align:right;}\n",
       "</style>\n",
       "<table class=\"tg\"><tr><th><b>  gp.                  </b></th><th><b>value</b></th><th><b>constraints</b></th><th><b>priors</b></th></tr>\n",
       "<tr><td class=tg-left>  sum.linear.variances </td><td class=tg-right> 4.56</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  sum.Mat32.variance   </td><td class=tg-right> 0.18</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  sum.Mat32.lengthscale</td><td class=tg-right>560.0</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<GPy.core.gp.GP at 0x12908c850>"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m_rff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.85751220633828462"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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JPltDZVY27seXYDg6hmj0IpLofBbnyspK0tLS6h8nJSXh9XqxWq18/fXX5OXl\nkZeXx1/+8hfTByoSTo277+HD72Ds2Lf4V8mNFPAzUvkrtV27Uv7UMjy3D27wu40L+7XXfoHF8jx7\n9owHAltmF5HE4rM4p6Wl4XK56h/XFWaALVu2UFZWxgMPPMC3336L2+3m+9//PsOHD/d5wECu9xL/\naZ5DwcH06SMBeO7ZjfygBLZwFQ4qeY1h/PtXI3ggJ6vZ39ux4z4KCrYBMG7cuXPN3z2+T+eb20if\nY/NpjqOTzxCSrVu3snPnThYtWsTBgwdZvnw5K1eubPK69evXc+zYsTZtCNMF7+ZTsEBoWUpLKRuV\nRa8jByinI5NYxouMpmfPxygunq5CaxJ9js2nOQ6PQL4A+bzOeeDAgaSkpOB0OsnNzWX27Nls3LiR\nl19+uclrLRaL3wcXiXYpG96gy4Br6XXkANu5nB+xnxfJAv7M8eOPBnT9tIhIa3wua1ssFn772982\n+FnPnj2bvG7ECJ0/k/jSOH5z+7DxDHpjEAYfAkeAbJThIyJmUQiJhEw0ZUEHM5bm4jd7d+/BNV+9\nzN697YD7ALjuuj/hdI40Y/gikuB044s4FInzSI0TtTIyIhe0EfBYqqpIWzCX1OdXYiQnUzV1JlVT\npkJycv37FhZu53//70+56aYfMXz4DUH/90XTF5poo/Oh5tMch4fuSiVAZP7BFRRsZcaModQFbYCH\nJUsiE7ThaywtFcPk/ftwTHqwPn6zIm8lZ/v0bfEYoZjjaPpCE41UOMynOQ6PkG8IE4kndcWwwQ0r\nTp+mfe4C0u8cSNKxz6iaOImybbt8FuZQCdUNOkQk/qg4S0g4nf3JyMgHPIDnfNBG/xZf39Idn8wc\nS+NiWF5yDSn9M+nw1O/wfu8Syl/biGv+45CaGtLxiIj4SxvCJCT8ybNuvJz72mvPM2RIJ2y2lDad\nd23tPG1rY7FSyy95moXMwf5lNWeyc3AtWBT2+M3vksScwA569tzD8OEPh3UMIhKddM45DkX7eaTm\nzgnDW8DgVs+7BnOe1u1288thq/jFe5sZwF85aXNQ+2weDPWdateclubY3w1ep06d4rbb1nD8+CN+\n//fEu2j/HMcDzXF46JyzxLBk2nLeNeDztIZB+rqXeeXo4wzgrxy98hrO/G1vQIW5Jc2e025lyf71\n1/92vjDrvLOIfEfFWcKu8TlhWA3cYtrxLKWldMzJwvGrSWBN4vSyFXR+exsp37skpMfRBi8RCRUV\nZwm7unOz5JuWAAARAklEQVTCS5ZsYOHC17j22mrOfRRb30jm78azuvjNdls348m8kbLiEqpHj4Eo\niZv1979HRBKDzjnHoVg7j+Tvedq2vL5x/Gbl3Pm4x08Aa2i+jzY3x9+dDx8HnLs1ZFvOHyuIpHmx\n9jmORZrj8FAIiQCJ9Q+uucLWXPxmba8rQnrcUG0Ik5Yl0uc4UjTH4RFIcdalVBKzGu/c/surK3jz\nhwdxFDyPkZyMa+acBvGb4WC32yOSiiYi8UXFWdokGjvCCzdgXcNenvvbH3D87ZM2xW+KiEQzbQiT\nVgVyiVC42PAwn8d4l+vpxafsyxzCVxu38sf3vjElfUxEJBxUnKVV0XqJ0L19L+aDDj/gMf4//kl3\nJv/wV6Q/n8fosZvD9kXCzBhSEUlcKs4Se2prSV2+lP+4ayC9Xf/k/R/fzBvzFzBr8yxef/1vYfsi\nEc0rCiIS21ScpVXRdC2u9cQ/6HT3XaTNm4Ph6Ej56iL+x6bXyZ44POznwaN1RUFEYp82hEmr/Lmp\nhWkMA/uaQjo8Ogurq5LqwUOoeOIZjK5dG7zsu5tJjAM4/0ViRMiGUbcxzuGwU1NTE7L3FRG5kK5z\njkPxdu2ipbQUx9TJtNu6Ga+jI5WLfkf1Pc4WU77M2lne+NKta69dicWSxJ4944G2h45I28Tb5zga\naY7DQyEkAkT3P7jmCqevYpqy4Q0c06dgPXkST+aNVDyTh/eS7hEZe3N301q4cB02WwoQPZeYxYto\n/hzHC81xeCiERKJa485z/fp8XnjhDsaOfavBz9auHUFqtbtB/GbF40tCGr/Z1vFe+KWhOTZbikJH\nRCTkVJwlbBpuoIKSknHMnLmYkpJZDX5WsmAhIzc9b2r8Zmta+iJh5vlsEZE6Ks4SNVKpYjHTGL3q\n2bDEb/paTm/ui8Trr2+o3xjncNi5806dXxYRc6g4S0AC2XTV3E7qxYvH8dVX+dSW/JDVjKc3n1Bz\n+RVUPrvK1PjN5jrjtmzmqsvO1rk6ETGTirP4LZjC1uSSLKuVt358BMeen2PBoOJnE3E/+ltITfVr\nPP5+UWiuMy4q2lB//tjsS7JERHxRcRa/tVbYGmtcPOtel/TxR6Q99DNSDn9AeeduVD+3EstNt/g1\nlkC/KLQmKq7tFpGEpYQwMVWzEZcuF6nLl9J5YH9SDn/A84yje9lHDH/6a7/jLwNN6WpL6lndEva4\ncYNUmEUkrNQ5i9/8WfJt3GX/q2QA3HwLacf/jiutE2Oq17CBu4HWO/BQUmcsItFMxVn8FlhhMxjP\nn3iaX+I4fi5+M//q4WyYPySosQRzbriuMxYRiTYqzhKQthY2p7M/xWuf5sH97zCEv1CZZOffTyzD\nm53DsOpq1mwLftPVXXd15D/+YzFXX305OTnqgEUk9qk4i6k6btvCG8dySeIkJy7/EbbCF7B9/3Ig\n+KXlxpvBvvoqn5yc0P83iIiEm4qzmMJSfqpJ/Gb7ZuI3g1la9nfXuIhIrFBxlpCzFe/EMeWhiMZv\ngnl3pxIRMZsupZLQqaoibfY00u8ZhvXrUlwz53Bq03bTCrOvy6GavYTLz8u0REQiRZ2z1Aum00ze\nvw/HpAdJ/uxTzl7Rm4q8labGb4Lvc9Za8haRWKbinMAuLMbDh1/T7K0bWy3QHg/tn1pM+6efBMOg\nauIkXLMf8yt+Mxi6HEpE4pGWtRNU42Xf225bQ0nJGPxJ2kr6+CPS77iFDk/9Du/3LqH8tY245j8e\ntsLsS1sSwEREopU65wTVeNn3+PFfAW8Bw1r/5dpaUlcsp8Oi+ViqqzmTnYNrwSIMR0czh+wXJYCJ\nSCxTcZZ6PXuWcPz4HUDLgSDWE//A8Yufk1KyG2/XbpxetRTP7YPDPdQ20ZK3iMQqFecE1Vzs5Qsv\nPMzrr7fQaRoG9jWFdHh0FlbXufjNiieewejaNQKjFxGJbyrOCaqlZd/mOk1LaSmOqZNpt3UzXkdH\nTi9bQfU9TrBYwj1sEZGEoOKcwNqy7Juy4Q0c06dgPXkST+aNVDyTh/eS7mEaoYhIYlJxlmY1F7/p\nbiZ+U0REQk/FWZqIlvhNEZFEpeIs36mqIm3BXFKfX4mRnIxr5hyqpkyFZN8fE2VYi4iEloqzAIHH\nbza+bWPjZDEVbhER/+kEYqLzeGifu4D0OweSdOwzqiZOomzbrjbnYjcMM2mYLKabT4iIBEbFOYGZ\nHb/pq3CLiEjLVJwTUW0tqcuX0nlgf2wfHOJMdg5l77xLzQ2Zfr+VMqxFREJP55wTTKjjN31lWDeX\nQtZcJKiIiDRkMQzDCOcBv/mmIpyHS0jdujmaznOE4jfjdUNYs3MsIaU5Np/mODy6dXP4/TvqnBNA\nJOM3dfMJERH/qTjHOcVviojEHp/F2ev1Mm/ePI4ePYrNZmPhwoX06NGj/vmNGzeyevVqkpKSuOKK\nK5g3bx4W3QwhKih+U0Qkdvn8S719+3ZqamooKipi2rRp5Obm1j/ndrt55plnKCws5KWXXqKyspKd\nO3eaPmBpg+3b6TwgA/ura6np24+yt/8b988mqjCLiMQIn3+tDxw4QGbmuctr+vTpw+HDh+ufa9eu\nHWvXrqVdu3YAnD17Nm42+8SsqirSZk+DgQOxfl2Ka+YcTm3arlxsEZEY43NZu7KykrS0tPrHSUlJ\neL1erFYrFouFLl26AFBYWMiZM2e4/vrrWz1gILvWpA327oX77oOjR+EHP8BSWEiHq66iQ6THFcf0\nWTaf5th8muPo5LM4p6Wl4XK56h/XFeYLH//ud7/jxIkTLF26tE0H1Lb9EPN4aP/UYto//SQYBmcm\nTqL9U0v4pvIsaK5No0tQzKc5Np/mODwC+QLkc1m7X79+7Np17hrVgwcP0rt37wbPz507F4/HQ15e\nXv3ytgTP7XZTULCVgoKtPrOozY7fFBGRyPAZQmIYBvPmzePIkSMALFq0iA8//JCqqiquvPJKRo4c\nydVXX13/+rFjx3Lrrbf6PKC+pfnW+C5PGRkN7/IEnIvfXLGcDovmY6mu5kx2Dq4FizAcHQF9Gw4H\nzbH5NMfm0xyHRyCdsxLCokxBwVZmzBjKuZtFAHhYsmRDfZBH4/jNiqeaxm/qH5z5NMfm0xybT3Mc\nHiFf1pYoYhjY/7yazjdeT0rJbqoHD+Hkrr1B5WKLiEh0UnGOMs3d5Sn75t50zMnC8atJYLVyetkK\nTue/aHoutoiIRIbiO6NM47s8/bRjMl0GDVD8pohIAlFxjkJ2u52fjrhG8ZsiIglKxTkK2Yp34pjy\nEElffkFN335ULFuplC8RkQSiNiyanI/fTL9nmOI3RUQSmDrnKJG8fx+OSQ+S/NmnnL2iNxV5Kznb\np2+khyUiIhGgzjnSPB7a5y4g/c6BJB37jKqJkyjbtkuFWUQkgalzjqCkjz/C8fAEbB8corZ7Dyr+\n8Cw1N2RGelgiIhJh6pwjobaW1OVL6TywP7YPDnEmO4eyd95VYRYREUCdc9g1jt88vapp/KaIiCQ2\ndc7hovhNERFpI3XOYWApLcUxdTLttm7G6+jI6WUrqL7HCRZLpIcmIiJRSMXZZCkb3sAxfYriN0VE\npM1UnE1iKT+l+E0REQmIirMJFL8pIiLBUBsXSorfFBGREFDnHCKK3xQRkVBR5xwsxW+KiEiIqXMO\nguI3RUTEDOqcA6H4TRERMZE6Zz8pflNERMymzrmtFL8pIiJhos65DRS/KSIi4aTi3ArFb4qISLip\nOLdA8ZsiIhIpKs7NUPymiIhEktrACyl+U0REooA65/MUvykiItFCnbPiN0VEJMokdOes+E0REYlG\nidk5K35TRESiWMJ1zorfFBGRaJc4nbPiN0VEJEYkROes+E0REYklcV+cFb8pIiKxJm6Ls+I3RUQk\nVsVlcVb8poiIxLL4aiMVvykiInEgbjpnxW+KiEi8iP3OWfGbIiISZ2K6c1b8poiIxKPY7JwVvyki\nInEs5jpnxW+KiEi8i53OWfGbIiKSIGKic1b8poiIJJKoL86K3xQRkUQTtcVZ8ZsiIpKoorI4K35T\nREQSWXS1oYrfFBERiZ7OWfGbIiIi50S+c1b8poiISAMR7ZwVvykiItKUz87Z6/Uyd+5cnE4nOTk5\nfP755w2e37FjB6NGjcLpdPLKK6+0/aiK3xQREWmRz855+/bt1NTUUFRUxKFDh8jNzWX58uUA1NTU\nkJuby7p167Db7YwZM4abb76Ziy66yOcBFb8pIiLim8/O+cCBA2Rmnutm+/Tpw+HDh+uf++yzz+jR\nowcOhwObzcZVV13Fvn37fB/t+ecVvykiItIKn51zZWUlaWlp9Y+TkpLwer1YrVYqKytxOBz1z3Xo\n0IGKigrfR/vZz0DxmyIiIj75LM5paWm4XK76x3WFGcDhcDR4zuVy0alTJ99HMwysQMfAxytt1K2b\no/UXSVA0x+bTHJtPcxydfC5r9+vXj127dgFw8OBBevfuXf/cZZddxokTJygvL8fj8bBv3z7+67/+\ny9zRioiIJACLYRhGS08ahsG8efM4cuQIAIsWLeLDDz+kqqqK0aNHs3PnTvLy8vB6vYwaNYrs7Oyw\nDVxERCRe+SzOIiIiEn6RTwgTERGRBlScRUREooyKs4iISJRRcRYREYkyphRn0zK5pV5rc7xx40ZG\njx7NmDFj+M1vfoP2/fmvtTmu89hjj/Hkk0+GeXTxo7V5fv/99/nJT35CdnY2v/jFL/B4PBEaaexq\nbY7ffPNN7r77bkaNGsVLL70UoVHGh0OHDpGTk9Pk537XPcMEW7ZsMWbNmmUYhmEcPHjQ+PnPf17/\nnMfjMQYOHGicPn3a8Hg8xsiRI41vv/3WjGHENV9zfObMGePWW2813G63YRiG8cgjjxhvv/12RMYZ\ny3zNcZ2XXnrJyMrKMp588slwDy9u+Jpnr9drDBs2zPj8888NwzCMl19+2Th27FhExhnLWvss33DD\nDUZ5eXmDv8/iv5UrVxp33XWXkZWV1eDngdQ9UzrnkGdySxO+5rhdu3asXbuWdu3aAXD27FnsdntE\nxhnLfM1x3fPvv/8+WVlZWpkIgq95Pn78OOnp6eTn55OTk0N5eTk9e/aM1FBjVmuf5d69e3P69Gmq\nq6sxDAOLopUDcumll7Js2bImfw8CqXumFOeWMrnrnvM7k1ua8DXHFouFLl26AFBYWMiZM2e4/vrr\nIzLOWOZrjr/++mvy8vKYO3euCnOQfM1zWVkZ7733Hvfeey/5+fmUlJSwZ8+eSA01ZvmaY4BevXox\ncuRI7rrrLm666aYGr5W2GzRoEElJSU1+HkjdM6U4hzyTW5rwNcd1jxcvXkxJSQlLly6NxBBjnq85\n3rJlC2VlZTzwwAOsWrWKjRs38vrrr0dqqDHN1zynp6fTo0cPLrvsMpKTk8nMzGzS9UnrfM3xxx9/\nTHFxMTt27GDHjh38+9//ZvPmzZEaalwKpO6ZUpyVyW0+X3MMMHfuXDweD3l5efXL2+IfX3Ock5PD\na6+9RmFhIRMmTOCuu+5i+PDhkRpqTPM1z927d6eqqqp+A9P+/fvp1atXRMYZy3zNscPhwG63k5KS\ngtVqpUuXLlrNDLFA6p7Pu1IFauDAgezevRun0wmcy+TeuHFjfSb3rFmzuP/+++szuS+++GIzhhHX\nfM3xlVdeybp167j66qu57777ABg7diy33nprJIccc1r7HF9I5+gC19o8L1y4kKlTp2IYBv369WPA\ngAERHnHsaW2Os7KyyM7OxmazcemllzJixIgIjzi21f09CKbuKVtbREQkyiiEREREJMqoOIuIiEQZ\nFWcREZEoo+IsIiISZVScRUREooyKs4iISJRRcRYREYky/z8qUzhl6aH0MAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x136f268d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, fstd = m_rff._raw_predict(X_rff[test])\n",
    "phat = scipy.stats.norm.cdf(f.squeeze())\n",
    "eval_preds(phat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "About the same as, maybe slightly worse than, the straight linear embeddings..."
   ]
  }
 ],
 "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": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}