stat_model_pb_pred.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Statistical Modeling of Powerball data\n",
    "There are three main steps to Statistical modeling:\n",
    "- Write down the model\n",
    "  - Prior and likelihood functions\n",
    "- Compute the Posterior\n",
    "  - Sampling or Inference\n",
    "- Check the model\n",
    "  - Prior Sensitivity\n",
    "  - Reliability/accuracy in relation to observed data\n",
    "\n",
    "A powerball ticket has five distinct numbers drawn from 1 to 69, and a sixth \"powerball number\" drawn independently. Here we are going to model the distribution of the smallest number in the powerball lottery tickets. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import theano\n",
    "import pymc3 as pm\n",
    "import sklearn\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from warnings import filterwarnings\n",
    "filterwarnings('ignore')\n",
    "sns.set_style('white')\n",
    "from sklearn import datasets\n",
    "from sklearn.preprocessing import scale\n",
    "from sklearn.cross_validation import train_test_split\n",
    "from sklearn.datasets import make_moons\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load dataset\n",
    "Peek into the data - curiosity helps build intuition\n",
    "Intuition yields a prior (required for probabilistic modeling).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "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>x1</th>\n",
       "      <th>x2</th>\n",
       "      <th>x3</th>\n",
       "      <th>x4</th>\n",
       "      <th>x5</th>\n",
       "      <th>x6</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>16</td>\n",
       "      <td>30</td>\n",
       "      <td>41</td>\n",
       "      <td>48</td>\n",
       "      <td>53</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>26</td>\n",
       "      <td>41</td>\n",
       "      <td>50</td>\n",
       "      <td>57</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>23</td>\n",
       "      <td>33</td>\n",
       "      <td>42</td>\n",
       "      <td>46</td>\n",
       "      <td>59</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2</td>\n",
       "      <td>18</td>\n",
       "      <td>19</td>\n",
       "      <td>22</td>\n",
       "      <td>63</td>\n",
       "      <td>19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>10</td>\n",
       "      <td>16</td>\n",
       "      <td>40</td>\n",
       "      <td>52</td>\n",
       "      <td>55</td>\n",
       "      <td>17</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   x1  x2  x3  x4  x5  x6\n",
       "0  16  30  41  48  53  16\n",
       "1   1  26  41  50  57  11\n",
       "2  23  33  42  46  59   4\n",
       "3   2  18  19  22  63  19\n",
       "4  10  16  40  52  55  17"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_train = pd.read_csv('./pb/pb_asc_x1x5_x6.csv', header=None, names=['x1', 'x2', 'x3', 'x4', 'x5', 'x6'])\n",
    "df_train.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x119e9a410>"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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3nr1/ubcAAJ7iyhkAAMMQZwAADEOcAQAwDHEGAMAwxBkAAMMQZwAADEOcAQAwDHEGAMAw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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x119de7190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_train['x1'].hist()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 1 - Build the Model\n",
    "The likelihood function is assumed to be a Geometric here. How did we arrive that? First study a list of probability functions, wikipedia is a great starter source. Then notice that our model has a definite support. What does that mean? That means the variable X1 is defined in a specific range. Also, X1 is discrete. So now one keeps rummaging for distributions that appear to have similar profile as the data we like to model including support and type.\n",
    "In this case we find that Geometric distribution appears to fit the bill. It is definitely possible that one could other equally feasible probability distributions. In fact, that is part of the adventure of statistical modeling:\n",
    "- positing the modeling question in interesting ways\n",
    "- so as to find easily approximateable distributions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Assume a Geometric distribution for the lowest number, X1\n",
    "Use a Uniform Prior on the probability parameter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 2 - Compute the Posterior\n",
    "This is either done through sampling or inference. In case of MCMC family of sampling, the choices are - Metropolis, HMC, NUTS. \n",
    "Variational Inference converts the approximation problem into an optimization problem of minimizing KL Divergence between the posterior and a known suggested distribution _q_. Variational Inference, though was known for decades, recently got a boost from the recent techniques of Automatic Differentiation Variational Inference (ADVI). Variational Inferences are usually rapid, but suffer from accuracy.\n",
    "\n",
    "Here we use NUTS sampler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "100%|██████████| 5500/5500 [00:02<00:00, 2461.44it/s]\n"
     ]
    },
    {
     "data": {
      "image/png": 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RaAAAgPEINAAAwHgEGgAAYDwCDQAAMB6BBgAAGI9AAwAAjEegAQAAxiPQAAAA4xFoAACA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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1190dd410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "obs = df_train['x1']\n",
    "with pm.Model() as zmodel:\n",
    "    mu = pm.Uniform('mu', lower=0., upper=1.)\n",
    "    zp_poisson = pm.Geometric('zp', p=mu, observed=obs)\n",
    "    ztrace = pm.sample(5000)\n",
    "    pm.plot_posterior(ztrace)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot observed and simulated\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 5000/5000 [00:00<00:00, 15766.91it/s]\n"
     ]
    },
    {
     "data": {
      "image/png": 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zk1xR5zweGxde4CYYMtm2o71mwzC4OvsvSHdkU9r8ge4/i4gMEArnbjQeXYCk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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11a5981d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with zmodel:\n",
    "    ppc = pm.sample_ppc(ztrace, 5000)\n",
    "    sns.distplot(ppc['zp'], label='Simulated')\n",
    "    sns.distplot(obs, label='Real')\n",
    "    plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 3 - Check the Model\n",
    "- Use the Posterior Predictive Check, ppc\n",
    "- Plot observed and simulated\n",
    "- Check model sensitivity to prior\n",
    "\n",
    "### Prior sensitivity\n",
    "- Same model with different priors (note the use of Beta distribution)\n",
    "- Check the posterior with the previous posterior\n",
    "- Notice the Highest Posterior Density region of the parameters(HPD)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "100%|██████████| 5500/5500 [00:02<00:00, 2293.12it/s]\n"
     ]
    },
    {
     "data": {
      "image/png": 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VUFwRUPu05Cg9MO+MNh4VAIkQAwDNKiiuUF6RM9jDAPALTCcBAAAjEWIAAICRCDEAAMBI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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x115a17210>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with pm.Model() as zmodel:\n",
    "    mu = pm.Beta('mu', alpha=2, beta=2)\n",
    "    zp_poisson = pm.Geometric('zp', p=mu, observed=obs)\n",
    "    ztrace = pm.sample(5000)\n",
    "    pm.plot_posterior(ztrace)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**__That posterior is the same as the previous one (except for minor numerical precision differences)__**\n",
    "It further confirms / validates our model.\n",
    "Now, one could apply the same model for each of x2, x3, x4, and x5, with varying discrete intervals as support.\n",
    "For x6 we could consider a categorical distribution (or a similar BetaBinomial as for x1-x5)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 5000/5000 [00:00<00:00, 15101.64it/s]\n"
     ]
    },
    {
     "data": {
      "image/png": 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43SZTLnQRCFhs+ay1ffs/FcwjyzGM7b5P2OH7NIEViojIqdD0nXEc7Tm30gzA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\nnEVERJLM/wew4I16OIBevgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x119232090>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with zmodel:\n",
    "    ppc = pm.sample_ppc(ztrace, 5000)\n",
    "    sns.distplot(ppc['zp'], label='Simulated')\n",
    "    sns.distplot(obs, label='Real')\n",
    "    plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Divergences\n",
    "ztrace['diverging'].nonzero()[0].size * 1.0 / len(ztrace)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.0"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Posterior mean\n",
    "chosen_x1 = ppc['zp'].argsort()[::-1]\n",
    "ppc['zp'].mean().round()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bayesian Neural Network\n",
    "Now we shall use a neural network based regression model.\n",
    "The neural net will predict a value for 'X2' draw, given an 'X1'\n",
    "In order to check fitness and proximity to reality, we compare against a few held-off records (not that this is supposed to be useful in a generative narrative as this)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Prepare the data\n",
    "Training data consists of X1, X2 pairs\n",
    "Also split the data into train and test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.cross_validation import train_test_split\n",
    "def prepare_data(df):\n",
    "    X_data = df[['x1', 'x2']]\n",
    "    \n",
    "    #Shuffle\n",
    "    X_data = X_data.sample(frac=1).reset_index(drop=True)\n",
    "\n",
    "    #split - train, test\n",
    "    X_train, X_test, y_train, y_test = train_test_split(X_data['x1'], X_data['x2'], test_size=0.01)\n",
    "    X_train = np.reshape(X_train, (-1, 1))\n",
    "    X_test = np.reshape(X_test, (-1, 1))\n",
    "    y_train = np.reshape(y_train, (-1, 1))\n",
    "    y_test = np.reshape(y_test, (-1, 1))\n",
    "    return X_train, X_test, y_train, y_test\n",
    "\n",
    "X_train, X_test, y_train, y_test = prepare_data(df_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[10],\n",
       "       [ 8],\n",
       "       [ 9],\n",
       "       [18],\n",
       "       [10],\n",
       "       [12],\n",
       "       [ 6],\n",
       "       [36],\n",
       "       [ 3],\n",
       "       [ 8],\n",
       "       [17],\n",
       "       [ 1],\n",
       "       [13],\n",
       "       [ 9],\n",
       "       [ 6],\n",
       "       [13],\n",
       "       [ 5],\n",
       "       [ 8],\n",
       "       [ 1],\n",
       "       [ 2],\n",
       "       [ 3]])"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot the training data (X2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x119d81f50>"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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GyXWZslnmnEXPR5H58MbrETkFBDyCIMTI+dh8y5YteN/73odHHnkE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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x119d89310>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.scatter(X_train, y_train, color='g', alpha=0.3)\n",
    "plt.xlabel('X1'); plt.ylabel('X2')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_This makes sense of course, since X2 >= X1_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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1NCLyEjxyJpfzjWa0tHcjLSEYOj/+aPRm+rg41Jos+L/9lThR2YxakwUzJiYgOkwvdTQi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\nRCQzLGciIiKZ+f8PC1EEjH1wFQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11a69d710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(y_train)\n",
    "plt.legend()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,\n",
       "       18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34,\n",
       "       35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48])"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xrange = np.arange(X_train.min(), X_train.max() + 1)\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(X_train[arange])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define a model for X2\n",
    "Assuming BetaBinomial, discrete distribution with support over positive integers\n",
    "The model for X2 will be a Bayesian Neural Net conditioned on the value of X1\n",
    "The prior for the X2's support \\{0..n\\}  and it's alpha and beta are dependent on X1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "ntrain = len(X_train)\n",
    "\n",
    "#Construct the NN\n",
    "def construct_nn(nn_in, nn_out):\n",
    "    n_hidden = 5\n",
    "    init_1 = np.random.randn(1, n_hidden).astype(theano.config.floatX)\n",
    "    init_2 = np.random.randn(n_hidden, n_hidden).astype(theano.config.floatX)\n",
    "    init_3 = np.random.randn(n_hidden, 1).astype(theano.config.floatX)\n",
    "    \n",
    "    with pm.Model() as bnn:\n",
    "        a = pm.Uniform('a', lower=0.4, upper=5.)\n",
    "        b = pm.Uniform('b', lower=2., upper=8.)\n",
    "        c = pm.Uniform('c', lower=1., upper=60.)\n",
    "        \n",
    "        weights_1 = pm.Normal('w_1', mu=0, sd=1, shape=(1, n_hidden), testval=init_1)\n",
    "        weights_2 = pm.Normal('w_2', mu=0, sd=1, shape=(n_hidden, n_hidden), testval=init_2)\n",
    "        weights_3 = pm.Normal('w_3', mu=0, sd=1, shape=(n_hidden, 1), testval=init_3)\n",
    "        \n",
    "        #Activations\n",
    "        act_1 = pm.math.tanh(pm.math.dot(nn_in, weights_1))\n",
    "        act_2 = pm.math.tanh(pm.math.dot(act_1, weights_2))\n",
    "        act_3 = pm.math.sigmoid(pm.math.dot(act_2, weights_3))\n",
    "        \n",
    "        print(\"{}, {}, {},\".format(act_3.tag.test_value.shape, act_3.shape, type(act_3)))\n",
    "        print(\"{}\".format(act_3.tag.test_value[:,0].mean()))\n",
    "#         print(\"{}\".format(act_3.tag.test_value[:,1].mean()))\n",
    "#         print(\"{}\".format(act_3.tag.test_value[:,2].mean()))\n",
    "#         a = pm.Deterministic('a', act_3.tag.test_value[:,0].mean())\n",
    "#         b = pm.Deterministic('b', act_3.tag.test_value[:,1].mean())\n",
    "#         c = pm.Deterministic('c', act_3.tag.test_value[:,2].mean())\n",
    "        out = pm.BetaBinomial('x2pred', \n",
    "                              alpha=a, \n",
    "                              beta=b,\n",
    "                              n=tt.round(c),\n",
    "                              observed=nn_out, \n",
    "                              total_size=ntrain)\n",
    "        \n",
    "    return bnn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fit the model to data (Inference)\n",
    "Uses ADVI to compute the posterior distribution of parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2001, 1), Shape.0, <class 'theano.tensor.var.TensorVariable'>,\n",
      "0.282729815524\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|          | 0/1500 [00:00<?, ?it/s]\n"
     ]
    },
    {
     "ename": "ValueError",
     "evalue": "Bad initial energy: inf. The model might be misspecified.",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m\u001b[0m",
      "\u001b[0;31mValueError\u001b[0mTraceback (most recent call last)",
      "\u001b[0;32m<ipython-input-208-f00922bc0b51>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0;32mwith\u001b[0m \u001b[0mbnn\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m     \u001b[0;31m# inference = pm.ADVI()\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 6\u001b[0;31m     \u001b[0mapprox\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msample\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1000\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m/Users/vmullachery/anaconda/envs/dl2.7/lib/python2.7/site-packages/pymc3/sampling.pyc\u001b[0m in \u001b[0;36msample\u001b[0;34m(draws, step, init, n_init, start, trace, chain, njobs, tune, nuts_kwargs, step_kwargs, progressbar, model, random_seed, live_plot, discard_tuned_samples, live_plot_kwargs, **kwargs)\u001b[0m\n\u001b[1;32m    284\u001b[0m     \u001b[0mdiscard\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtune\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mdiscard_tuned_samples\u001b[0m \u001b[0;32melse\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    285\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 286\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0msample_func\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0msample_args\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mdiscard\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    287\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    288\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/vmullachery/anaconda/envs/dl2.7/lib/python2.7/site-packages/pymc3/sampling.pyc\u001b[0m in \u001b[0;36m_sample\u001b[0;34m(draws, step, start, trace, chain, tune, progressbar, model, random_seed, live_plot, live_plot_kwargs, **kwargs)\u001b[0m\n\u001b[1;32m    331\u001b[0m     \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    332\u001b[0m         \u001b[0mstrace\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 333\u001b[0;31m         \u001b[0;32mfor\u001b[0m \u001b[0mit\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstrace\u001b[0m \u001b[0;32min\u001b[0m \u001b[0menumerate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msampling\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    334\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mlive_plot\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    335\u001b[0m                 \u001b[0;32mif\u001b[0m \u001b[0mlive_plot_kwargs\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/vmullachery/anaconda/envs/dl2.7/lib/python2.7/site-packages/tqdm/_tqdm.pyc\u001b[0m in \u001b[0;36m__iter__\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    870\u001b[0m \"\"\", fp_write=getattr(self.fp, 'write', sys.stderr.write))\n\u001b[1;32m    871\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 872\u001b[0;31m             \u001b[0;32mfor\u001b[0m \u001b[0mobj\u001b[0m \u001b[0;32min\u001b[0m \u001b[0miterable\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    873\u001b[0m                 \u001b[0;32myield\u001b[0m \u001b[0mobj\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    874\u001b[0m                 \u001b[0;31m# Update and print the progressbar.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/vmullachery/anaconda/envs/dl2.7/lib/python2.7/site-packages/pymc3/sampling.pyc\u001b[0m in \u001b[0;36m_iter_sample\u001b[0;34m(draws, step, start, trace, chain, tune, model, random_seed)\u001b[0m\n\u001b[1;32m    429\u001b[0m                 \u001b[0mstep\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mstop_tuning\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstep\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    430\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mstep\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgenerates_stats\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 431\u001b[0;31m                 \u001b[0mpoint\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstates\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mstep\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstep\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpoint\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    432\u001b[0m                 \u001b[0;32mif\u001b[0m \u001b[0mstrace\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msupports_sampler_stats\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    433\u001b[0m                     \u001b[0mstrace\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrecord\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpoint\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstates\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/vmullachery/anaconda/envs/dl2.7/lib/python2.7/site-packages/pymc3/step_methods/arraystep.pyc\u001b[0m in \u001b[0;36mstep\u001b[0;34m(self, point)\u001b[0m\n\u001b[1;32m    173\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    174\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgenerates_stats\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 175\u001b[0;31m             \u001b[0mapoint\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstats\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mastep\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    176\u001b[0m             \u001b[0mpoint\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_logp_dlogp_func\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray_to_full_dict\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mapoint\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    177\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0mpoint\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstats\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/vmullachery/anaconda/envs/dl2.7/lib/python2.7/site-packages/pymc3/step_methods/hmc/nuts.pyc\u001b[0m in \u001b[0;36mastep\u001b[0;34m(self, q0)\u001b[0m\n\u001b[1;32m    180\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0misfinite\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstart\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0menergy\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    181\u001b[0m             raise ValueError('Bad initial energy: %s. The model '\n\u001b[0;32m--> 182\u001b[0;31m                              'might be misspecified.' % start.energy)\n\u001b[0m\u001b[1;32m    183\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    184\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madapt_step_size\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mValueError\u001b[0m: Bad initial energy: inf. The model might be misspecified."
     ]
    }
   ],
   "source": [
    "nn_in = theano.shared(X_train)\n",
    "nn_out = theano.shared(y_train)\n",
    "bnn = construct_nn(nn_in, nn_out)\n",
    "with bnn:\n",
    "    # inference = pm.ADVI()\n",
    "    approx = pm.sample(1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "with bnn:\n",
    "    pm.plot_posterior(approx)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Miscellaneous\n",
    "## A Zero Truncated Poisson\n",
    "__Custom Probability Distribution in PyMC3__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import theano.tensor as tt\n",
    "from theano import function\n",
    "from theano import printing\n",
    "import pymc3 as pm\n",
    "\n",
    "class ZeroTruncatedPoisson(pm.Discrete):\n",
    "    '''\n",
    "    Similar to a Poisson distribution, but the support is over positive integes \n",
    "    and so, excludes zero. An example, number of items in your grocery shopping cart\n",
    "    at checkout\n",
    "    '''\n",
    "    def __init__(self, mu, *args, **kwargs):\n",
    "        super(ZeroTruncatedPoisson, self).__init__(*args, **kwargs)\n",
    "        self.mu = tt.as_tensor_variable(mu)\n",
    "    \n",
    "    def logp(self, value):\n",
    "        '''\n",
    "        compute total_log_probability\n",
    "        '''\n",
    "        return tt.sum(value * tt.log(self.mu) - tt.log(tt.exp(self.mu) -1) - tt.gammaln(value))\n",
    "    \n",
    "    def random(self, point=None, size=None):\n",
    "        '''\n",
    "        Generates a random sample from Zero Truncated Poisson\n",
    "        '''\n",
    "        k = 1\n",
    "        mu = self.mu.tag.test_value\n",
    "        t = tt.exp(-self.mu)/(1 - tt.exp(-self.mu))/(1. * self.mu)\n",
    "        tn = t.tag.test_value\n",
    "        s = tn\n",
    "        u = np.random.uniform()\n",
    "        while s < u:\n",
    "            k = k + 1\n",
    "            tn = tn * mu / k\n",
    "            s = s + tn\n",
    "            u = np.random.uniform()\n",
    "        return k"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# If using a ZeroTruncatedPoisson\n",
    "# obs = df_train['x1']\n",
    "# with pm.Model() as zmodel:\n",
    "#     mu = pm.HalfNormal('mu', sd=10.)\n",
    "#     zp_poisson = ZeroTruncatedPoisson('zp', mu=mu, observed=obs)\n",
    "#     ztrace = pm.sample(1000)\n",
    "#     pm.plot_posterior(ztrace)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import theano.tensor as tt\n",
    "from theano import function\n",
    "#tt.config.compute_test_value = \n",
    "x = tt.dscalar('x')\n",
    "y = tt.dscalar('y')\n",
    "z = x + y\n",
    "tt.pprint(z)\n",
    "add = function([x, y], z)\n",
    "n1 = add(402., 1)\n",
    "type(n1)\n",
    "#n1\n",
    "with pm.Model() as mmodel:\n",
    "    a1 = \n",
    "    w1 = pm.Normal('w1', mu=0., sd=1., shape=(1, 2))\n",
    "    a2 = pm.math.dot(a1, w1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "k = np.array([1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,48,1])\n",
    "import theano.tensor as tt\n",
    "def ztp_logp(k):\n",
    "    return tt.sum(k * tt.log(lam) - tt.log(tt.exp(lam) - 1) - tt.gammaln(k))\n",
    "\n",
    "ztp_logp(k)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Shape.0"
      ]
     },
     "execution_count": 185,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vm1 = np.random.randn(1, 5).astype(theano.config.floatX)\n",
    "type(vm1)\n",
    "#vm1.shape\n",
    "vm2= halfnorm.rvs(size=(1,5)).astype(theano.config.floatX)\n",
    "type(vm2)\n",
    "vm2.shape\n",
    "X_train[0].shape\n",
    "nn_in.shape\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define the neural network"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot the posterior parameter distribution from 5000 samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "with bnn:\n",
    "    trace = approx.sample(draws=5000)\n",
    "    pm.traceplot(trace)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot the learnt boundary against training data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "with bnn:\n",
    "    rpc = pm.sample_ppc(trace, 500)\n",
    "    rpred = rpc['Category'].mean(axis=0)\n",
    "    #rproba = rpc['Category'].std(axis=0)\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.scatter(X_train[rpred > 0.5], rpred[rpred > 0.5], color='b', alpha=0.01)\n",
    "    ax.scatter(X_train[rpred <= 0.5], rpred[rpred <= 0.5], color='r', alpha=0.01)\n",
    "    ax.scatter(X_train[y_train], y_train[y_train], color='g', alpha=0.01)\n",
    "    ax.scatter(X_train[~y_train], y_train[~y_train], color='k', alpha=0.01)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plot the Evidence Lower Bound (ELBO) maximization history"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "with bnn:\n",
    "    plt.plot(-inference.hist, label='ADVI', color='b', alpha=0.4)\n",
    "    plt.xlabel('Iteration')\n",
    "    plt.ylabel('ELBO')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**__What is the functional form of the neural net?__**\n",
    "<p>\n",
    "The neural net computes the probability parameter of a Bernoulli distribution based on a series of non-linearities and affine transformations of the input"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "bnn.Category.distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Now time to predict (Posterior Predictive Check) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "nn_in.set_value(X_test)\n",
    "nn_out.set_value(y_test)\n",
    "with bnn:\n",
    "    ppc = pm.sample_ppc(trace, 500)\n",
    "    pred = ppc['Category'].mean(axis=0)\n",
    "    proba = ppc['Category'].std(axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot the predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.scatter(X_test[pred > 0.5], pred[pred > 0.5])\n",
    "ax.scatter(X_test[pred <= 0.5], pred[pred <= 0.5], color='r', alpha=0.2)\n",
    "ax.scatter(X_test[y_test], y_test[y_test], color='c', alpha=0.1)\n",
    "ax.scatter(X_test[~y_test], y_test[~y_test], color='c', alpha=0.1)\n",
    "\n",
    "print('Accuracy: {}'.format( ( y_test == (pred > 0.5) ).mean() * 100 ))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Confusion Matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.metrics import confusion_matrix\n",
    "cm = [ 1 if x > 0.5 else 0 for x in pred ]\n",
    "cnf = confusion_matrix(cm, y_test)\n",
    "sns.heatmap(cnf, annot=True, fmt='d', cmap='PiYG')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "cnf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Now the uncertainty in prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "fig, ax = plt.subplots(figsize=(10, 5))\n",
    "ax.errorbar(X_test[pred > 0.5], pred[pred > 0.5], yerr = proba[pred > 0.5], fmt='o', ecolor='g', capthick=2, alpha=0.1)\n",
    "ax.errorbar(X_test[pred <= 0.5], pred[pred <= 0.5], yerr = proba[pred <= 0.5], \n",
    "            fmt='o', ecolor='r', color='y', capthick=2, alpha=0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comparison to a Gaussian Process classifier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%%time\n",
    "from sklearn.gaussian_process import GaussianProcessClassifier\n",
    "from sklearn.gaussian_process.kernels import RBF\n",
    "\n",
    "gp_clf = GaussianProcessClassifier(1.0 * RBF(1.0))\n",
    "nsize=1000\n",
    "gp_clf.fit(X_train[:nsize,:], y_train[:nsize,:])\n",
    "#clf.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**__Phew.... that took for ever. Especially in comparison to BNN__**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%%time\n",
    "print gp_clf.score(X_test, y_test)\n",
    "xx = np.arange(1,70)\n",
    "pp = gp_clf.predict_proba(xx.reshape(-1,1))\n",
    "fig, ax = plt.subplots()\n",
    "ax.scatter(xx, pp[:,1], color='r')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compare to a random forest classifier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%%time\n",
    "from sklearn.ensemble import RandomForestClassifier\n",
    "\n",
    "rf_clf = RandomForestClassifier(max_depth=5, n_estimators=10, max_features=1)\n",
    "rf_clf.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%%time\n",
    "print (rf_clf.score(X_test, y_test))\n",
    "xx = np.arange(1,70)\n",
    "pp = rf_clf.predict_proba(xx.reshape(-1,1))\n",
    "fig, ax = plt.subplots()\n",
    "ax.scatter(xx, pp[:,1], color='r')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compare to AdaBoosted Decision Trees"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%%time\n",
    "from sklearn.ensemble import AdaBoostClassifier\n",
    "ad_clf = AdaBoostClassifier()\n",
    "ad_clf.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%%time\n",
    "print (ad_clf.score(X_test, y_test))\n",
    "xx = np.arange(1, 70)\n",
    "pp = ad_clf.predict_proba(xx.reshape(-1,1))\n",
    "fig, ax = plt.subplots()\n",
    "ax.scatter(xx, pp[:,1], color='r')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Miscellaneous"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "with pm.Model():\n",
    "    bs = pm.BetaBinomial('betasample', alpha=3., beta=4., n=50)\n",
    "    bstrace = pm.sample(10000)\n",
    "    pm.plot_posterior(bstrace)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "sns.distplot(df_train['x6'])"
   ]
  }
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