DEMO - Latent class model for Bogus and Real Labelling .ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from scipy import stats\n",
    "from lcm import LCM\n",
    "%matplotlib inline\n",
    "\n",
    "plt.rc('text', usetex=True)\n",
    "plt.rc('font',**{'family':'serif','serif':['Times New Roman']})\n",
    "figSize  = (12, 6)\n",
    "fontSize = 20"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The aim of this tutorial is to provide a label 0 (bogus) or real (1) to each candidate ID or candidate file. In astronomy, the candidate file is simply an image that contains either a source (labelled as real) or bogus (contains noise).\n",
    "\n",
    "For supervised learning, we need to construct a large training set with label. We had 10 volunteers to label each candidate file. This means that for each candidate we will have 10 labels. Given that the volunteers independently labelled the files, 7 voulunteers might label a particular candidate file as 0 and 3 of them might labelled the same candidate file as 1. \n",
    "\n",
    "For example, the question one might ask: which label will we assign to a candidate if 5 volunteer label it as real and the other 5 volunteer labelled it as bogus? This is where latent class model can be helpful.\n",
    "\n",
    "The aim is to assign each candidate file a label and incorporate the uncertainties of the volunteer's labels in the final label. Let's first analyse the data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Load data\n",
    "Data should be in the format\n",
    "- rows: Number of images\n",
    "- columns: Volunteers vote as either real (1) or bogus (0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>transientid</th>\n",
       "      <th>volunteer_1</th>\n",
       "      <th>volunteer_2</th>\n",
       "      <th>volunteer_3</th>\n",
       "      <th>volunteer_4</th>\n",
       "      <th>volunteer_5</th>\n",
       "      <th>volunteer_6</th>\n",
       "      <th>volunteer_7</th>\n",
       "      <th>volunteer_8</th>\n",
       "      <th>volunteer_9</th>\n",
       "      <th>volunteer_10</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>510</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>607</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>707</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>725</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5233</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   transientid  volunteer_1  volunteer_2  volunteer_3  volunteer_4  \\\n",
       "0          510            0            0            0            0   \n",
       "1          607            0            0            0            0   \n",
       "2          707            0            0            0            0   \n",
       "3          725            0            0            0            0   \n",
       "4         5233            1            1            1            1   \n",
       "\n",
       "   volunteer_5  volunteer_6  volunteer_7  volunteer_8  volunteer_9  \\\n",
       "0            0            0            0            0            0   \n",
       "1            0            0            0            0            0   \n",
       "2            0            0            0            0            0   \n",
       "3            0            0            0            0            0   \n",
       "4            1            1            1            1            1   \n",
       "\n",
       "   volunteer_10  \n",
       "0             0  \n",
       "1             1  \n",
       "2             0  \n",
       "3             0  \n",
       "4             1  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_ori = pd.read_csv('10_volunteers_voting_5000.csv')\n",
    "data_ori.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 0, 0, ..., 0, 0, 0],\n",
       "       [0, 0, 0, ..., 0, 0, 1],\n",
       "       [0, 0, 0, ..., 0, 0, 0],\n",
       "       ...,\n",
       "       [0, 0, 0, ..., 0, 0, 0],\n",
       "       [1, 1, 1, ..., 1, 0, 0],\n",
       "       [1, 1, 1, ..., 1, 0, 0]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#remove transientId and turn dataframe into an array\n",
    "data = data_ori.iloc[:,1:]\n",
    "data = np.array(data)\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next step is to understand how latent class model works. In this tutorial we have use materials from this [link](https://static1.squarespace.com/static/5a970ef5372b96ff61c13d3b/t/5a9aee0b71c10b1a7d1400f3/1520102924040/math_4840_project_final.pdf).\n",
    "\n",
    "<img src=\"./figures/LCM_1.png\">\n",
    "\n",
    "<img src=\"./figures/LCM_2.png\">\n",
    "\n",
    "<img src=\"./figures/LCM_5.png\">\n",
    "\n",
    "<img src=\"./figures/LCM_6.png\">\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Apply LCM algorithm\n",
    "The LCM is implemented in lcm.py. Please refer to the equations above to understand the coding in lcm.py.\n",
    "We use <b>n_class=2</b> as we are dealing with binary classification. In this case, we use max_iteration = 20 as the EM algorithm converges quite quickly. That is, we achieve a maximum-log-likelihood at around 10 ietrations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "lcm_model = LCM(n_class=2, tol=10e-5, max_iter=20, verbose=1, random_state=1234)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fit the lcm model to the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Maximization step with EM algorithm starting\n",
      "\tEM step 0\n",
      "\tEM step 1\n",
      "\tEM step 2\n",
      "\tEM step 3\n",
      "\tEM step 4\n",
      "\tEM step 5\n",
      "\tEM step 6\n",
      "\tEM step 7\n"
     ]
    }
   ],
   "source": [
    "lcm_model.fit(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot the maximum log-likelihood with number of iterations using EM algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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rL9askc45h/ACAAAAwMwaNsBw97y79063HSSlq8y9yQrf0y1pvOTeaHK/kjlAyxsbk/7v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\nB9S3xx6TvvvdMDaT1q6NWw8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      "text/plain": [
       "<Figure size 1080x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15,7))\n",
    "plt.plot(lcm_model.log_likeld_[1:], linewidth=3, color='b')\n",
    "plt.title(\"Log-Likelihod\", fontsize=fontSize)\n",
    "plt.xlabel(\"Number of Iteration\", fontsize=fontSize)\n",
    "plt.ylabel(r\"$\\mathcal{P}(x\\mid\\theta$)\", fontsize=fontSize)\n",
    "plt.tick_params(axis='both', labelsize=fontSize)\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Model parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.47117838, 0.52882162])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# get the parameters beta (see Equation 5(i)) as follows\n",
    "lcm_model.beta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.01615971, 0.04715776, 0.04134277, 0.13474516, 0.1109761 ,\n",
       "        0.06899923, 0.02775151, 0.03089399, 0.00400664, 0.00517872],\n",
       "       [0.96665089, 0.98630665, 0.9835456 , 0.97747704, 0.97029024,\n",
       "        0.98008294, 0.96388662, 0.93990752, 0.76833499, 0.8062452 ]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# get the parameters beta (see Equation 5(ii)) as follows\n",
    "lcm_model.theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "26182.423069075125"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#compute the bic of the model\n",
    "lcm_model.calculate_bic(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Prediction \n",
    "Predict the final label of the candidate files based on the volunteers labelling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, ..., 0, 1, 1])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Predict the class as either 0(bogus) or 1 (real)\n",
    "predict_class = lcm_model.predict(data)\n",
    "predict_class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.00000000e+00, 1.82215056e-14],\n",
       "       [1.00000000e+00, 1.45653591e-11],\n",
       "       [1.00000000e+00, 1.82215056e-14],\n",
       "       ...,\n",
       "       [1.00000000e+00, 1.82215056e-14],\n",
       "       [4.60875326e-07, 9.99999539e-01],\n",
       "       [6.94129014e-10, 9.99999999e-01]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The probability of it being bogus or real\n",
    "predict_class_proba = lcm_model.predict_proba(data)\n",
    "predict_class_proba"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Merge the final label from LCM to the original table. \n",
    "This table can be used for supervised learning approach - where each candidate file is assigned a label by LCM model instead of taking the maximum probability vote."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data_ori['label'] = predict_class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>transientid</th>\n",
       "      <th>volunteer_1</th>\n",
       "      <th>volunteer_2</th>\n",
       "      <th>volunteer_3</th>\n",
       "      <th>volunteer_4</th>\n",
       "      <th>volunteer_5</th>\n",
       "      <th>volunteer_6</th>\n",
       "      <th>volunteer_7</th>\n",
       "      <th>volunteer_8</th>\n",
       "      <th>volunteer_9</th>\n",
       "      <th>volunteer_10</th>\n",
       "      <th>label</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
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       "      <th>0</th>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>725</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5233</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5236</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>5402</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>5408</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>5490</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>5574</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>5647</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>5704</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>5727</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>5855</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>5874</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>5923</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>5924</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>6008</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>6046</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>6071</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    transientid  volunteer_1  volunteer_2  volunteer_3  volunteer_4  \\\n",
       "0           510            0            0            0            0   \n",
       "1           607            0            0            0            0   \n",
       "2           707            0            0            0            0   \n",
       "3           725            0            0            0            0   \n",
       "4          5233            1            1            1            1   \n",
       "5          5236            0            0            0            0   \n",
       "6          5402            1            1            1            1   \n",
       "7          5408            1            1            1            1   \n",
       "8          5490            0            1            1            0   \n",
       "9          5574            1            1            1            1   \n",
       "10         5647            1            1            1            0   \n",
       "11         5704            1            1            1            1   \n",
       "12         5727            1            1            1            1   \n",
       "13         5855            1            1            1            1   \n",
       "14         5874            0            0            0            0   \n",
       "15         5923            1            1            1            1   \n",
       "16         5924            1            1            1            1   \n",
       "17         6008            1            1            1            1   \n",
       "18         6046            1            1            1            1   \n",
       "19         6071            1            1            1            1   \n",
       "\n",
       "    volunteer_5  volunteer_6  volunteer_7  volunteer_8  volunteer_9  \\\n",
       "0             0            0            0            0            0   \n",
       "1             0            0            0            0            0   \n",
       "2             0            0            0            0            0   \n",
       "3             0            0            0            0            0   \n",
       "4             1            1            1            1            1   \n",
       "5             0            0            0            0            0   \n",
       "6             1            1            1            1            1   \n",
       "7             1            0            0            1            0   \n",
       "8             1            1            1            1            0   \n",
       "9             1            1            1            1            1   \n",
       "10            1            1            1            1            1   \n",
       "11            1            1            1            1            0   \n",
       "12            1            1            1            1            1   \n",
       "13            1            1            1            1            1   \n",
       "14            0            0            0            0            0   \n",
       "15            1            1            1            1            0   \n",
       "16            1            1            1            1            1   \n",
       "17            0            1            1            1            1   \n",
       "18            1            1            1            1            1   \n",
       "19            1            1            1            1            1   \n",
       "\n",
       "    volunteer_10  label  \n",
       "0              0      0  \n",
       "1              1      0  \n",
       "2              0      0  \n",
       "3              0      0  \n",
       "4              1      1  \n",
       "5              0      0  \n",
       "6              1      1  \n",
       "7              1      1  \n",
       "8              1      1  \n",
       "9              1      1  \n",
       "10             1      1  \n",
       "11             1      1  \n",
       "12             1      1  \n",
       "13             1      1  \n",
       "14             0      0  \n",
       "15             1      1  \n",
       "16             1      1  \n",
       "17             1      1  \n",
       "18             1      1  \n",
       "19             1      1  "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_ori.iloc[0:20,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_ori.to_csv('LCA_voting_5000.csv', index=None)\n",
    "data_ori.to_excel('LCA_voting_5000.xlsx', index=None)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Use BIC values to check how many class labels is/are appropriate to fit the data\n",
    "In our context, since we already know that we had only 2 classes, we there use n_class = 2. However, in case this is not known since the begining, we use BIC to select the best model. Preferred models are those that minimize values of the BIC."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Maximization step with EM algorithm starting\n",
      "\tEM step 0\n",
      "\tEM step 1\n",
      "\tEM step 2\n",
      "\tEM step 3\n",
      "\tEM step 4\n",
      "\tEM step 5\n",
      "\tEM step 6\n",
      "Maximization step with EM algorithm starting\n",
      "\tEM step 0\n",
      "\tEM step 1\n",
      "\tEM step 2\n",
      "\tEM step 3\n",
      "\tEM step 4\n",
      "\tEM step 5\n",
      "\tEM step 6\n",
      "\tEM step 7\n",
      "\tEM step 8\n",
      "\tEM step 9\n",
      "\tEM step 10\n",
      "\tEM step 11\n",
      "\tEM step 12\n",
      "\tEM step 13\n",
      "\tEM step 14\n",
      "\tEM step 15\n",
      "\tEM step 16\n",
      "\tEM step 17\n",
      "\tEM step 18\n",
      "\tEM step 19\n",
      "\tEM step 20\n",
      "\tEM step 21\n",
      "\tEM step 22\n",
      "\tEM step 23\n",
      "\tEM step 24\n",
      "\tEM step 25\n",
      "\tEM step 26\n",
      "\tEM step 27\n",
      "\tEM step 28\n",
      "\tEM step 29\n",
      "\tEM step 30\n",
      "\tEM step 31\n",
      "\tEM step 32\n",
      "\tEM step 33\n",
      "\tEM step 34\n",
      "\tEM step 35\n",
      "\tEM step 36\n",
      "\tEM step 37\n",
      "\tEM step 38\n",
      "\tEM step 39\n",
      "\tEM step 40\n",
      "\tEM step 41\n",
      "\tEM step 42\n",
      "\tEM step 43\n",
      "\tEM step 44\n",
      "\tEM step 45\n",
      "Maximization step with EM algorithm starting\n",
      "\tEM step 0\n",
      "\tEM step 1\n",
      "\tEM step 2\n",
      "\tEM step 3\n",
      "\tEM step 4\n",
      "\tEM step 5\n",
      "\tEM step 6\n",
      "\tEM step 7\n",
      "\tEM step 8\n",
      "\tEM step 9\n",
      "\tEM step 10\n",
      "\tEM step 11\n",
      "\tEM step 12\n",
      "\tEM step 13\n",
      "\tEM step 14\n",
      "\tEM step 15\n",
      "\tEM step 16\n",
      "\tEM step 17\n",
      "\tEM step 18\n",
      "\tEM step 19\n",
      "\tEM step 20\n",
      "\tEM step 21\n",
      "\tEM step 22\n",
      "\tEM step 23\n",
      "\tEM step 24\n",
      "\tEM step 25\n",
      "\tEM step 26\n",
      "\tEM step 27\n",
      "\tEM step 28\n",
      "\tEM step 29\n",
      "\tEM step 30\n",
      "\tEM step 31\n",
      "\tEM step 32\n",
      "\tEM step 33\n",
      "\tEM step 34\n",
      "\tEM step 35\n",
      "\tEM step 36\n",
      "\tEM step 37\n",
      "\tEM step 38\n",
      "\tEM step 39\n",
      "\tEM step 40\n",
      "\tEM step 41\n",
      "\tEM step 42\n",
      "\tEM step 43\n",
      "\tEM step 44\n",
      "\tEM step 45\n",
      "\tEM step 46\n",
      "\tEM step 47\n",
      "\tEM step 48\n",
      "\tEM step 49\n",
      "Maximization step with EM algorithm starting\n",
      "\tEM step 0\n",
      "\tEM step 1\n",
      "\tEM step 2\n",
      "\tEM step 3\n",
      "\tEM step 4\n",
      "\tEM step 5\n",
      "\tEM step 6\n",
      "\tEM step 7\n",
      "\tEM step 8\n",
      "\tEM step 9\n",
      "\tEM step 10\n",
      "\tEM step 11\n",
      "\tEM step 12\n",
      "\tEM step 13\n",
      "\tEM step 14\n",
      "\tEM step 15\n",
      "\tEM step 16\n",
      "\tEM step 17\n",
      "\tEM step 18\n",
      "\tEM step 19\n",
      "\tEM step 20\n",
      "\tEM step 21\n",
      "\tEM step 22\n",
      "\tEM step 23\n",
      "\tEM step 24\n",
      "\tEM step 25\n",
      "\tEM step 26\n",
      "\tEM step 27\n",
      "\tEM step 28\n",
      "\tEM step 29\n",
      "\tEM step 30\n",
      "\tEM step 31\n",
      "\tEM step 32\n",
      "\tEM step 33\n",
      "\tEM step 34\n",
      "\tEM step 35\n",
      "\tEM step 36\n",
      "\tEM step 37\n",
      "\tEM step 38\n",
      "\tEM step 39\n",
      "\tEM step 40\n",
      "\tEM step 41\n",
      "\tEM step 42\n",
      "\tEM step 43\n",
      "\tEM step 44\n",
      "\tEM step 45\n",
      "\tEM step 46\n",
      "\tEM step 47\n",
      "\tEM step 48\n",
      "\tEM step 49\n",
      "\tEM step 50\n",
      "\tEM step 51\n",
      "\tEM step 52\n",
      "\tEM step 53\n",
      "\tEM step 54\n",
      "\tEM step 55\n",
      "\tEM step 56\n",
      "\tEM step 57\n",
      "\tEM step 58\n",
      "\tEM step 59\n",
      "\tEM step 60\n",
      "\tEM step 61\n",
      "\tEM step 62\n",
      "\tEM step 63\n",
      "\tEM step 64\n",
      "\tEM step 65\n",
      "\tEM step 66\n",
      "\tEM step 67\n",
      "\tEM step 68\n",
      "\tEM step 69\n",
      "\tEM step 70\n",
      "\tEM step 71\n",
      "\tEM step 72\n",
      "\tEM step 73\n",
      "\tEM step 74\n",
      "\tEM step 75\n",
      "\tEM step 76\n",
      "\tEM step 77\n",
      "\tEM step 78\n",
      "\tEM step 79\n",
      "\tEM step 80\n",
      "\tEM step 81\n",
      "\tEM step 82\n",
      "\tEM step 83\n",
      "\tEM step 84\n",
      "\tEM step 85\n",
      "\tEM step 86\n",
      "\tEM step 87\n",
      "\tEM step 88\n",
      "\tEM step 89\n",
      "\tEM step 90\n",
      "\tEM step 91\n",
      "\tEM step 92\n",
      "\tEM step 93\n",
      "\tEM step 94\n",
      "\tEM step 95\n",
      "\tEM step 96\n",
      "\tEM step 97\n",
      "\tEM step 98\n",
      "\tEM step 99\n",
      "\tEM step 100\n",
      "\tEM step 101\n",
      "\tEM step 102\n",
      "\tEM step 103\n",
      "\tEM step 104\n",
      "\tEM step 105\n",
      "\tEM step 106\n",
      "\tEM step 107\n",
      "\tEM step 108\n",
      "\tEM step 109\n",
      "\tEM step 110\n",
      "\tEM step 111\n",
      "\tEM step 112\n",
      "\tEM step 113\n",
      "\tEM step 114\n",
      "\tEM step 115\n",
      "\tEM step 116\n",
      "\tEM step 117\n",
      "\tEM step 118\n",
      "\tEM step 119\n",
      "\tEM step 120\n",
      "\tEM step 121\n",
      "\tEM step 122\n",
      "\tEM step 123\n",
      "\tEM step 124\n",
      "\tEM step 125\n",
      "\tEM step 126\n",
      "\tEM step 127\n",
      "\tEM step 128\n",
      "\tEM step 129\n",
      "\tEM step 130\n",
      "\tEM step 131\n",
      "\tEM step 132\n",
      "\tEM step 133\n",
      "\tEM step 134\n",
      "\tEM step 135\n",
      "\tEM step 136\n",
      "\tEM step 137\n",
      "\tEM step 138\n",
      "\tEM step 139\n",
      "\tEM step 140\n",
      "\tEM step 141\n",
      "\tEM step 142\n",
      "\tEM step 143\n",
      "\tEM step 144\n",
      "\tEM step 145\n",
      "\tEM step 146\n",
      "\tEM step 147\n",
      "Maximization step with EM algorithm starting\n",
      "\tEM step 0\n",
      "\tEM step 1\n",
      "\tEM step 2\n",
      "\tEM step 3\n",
      "\tEM step 4\n",
      "\tEM step 5\n",
      "\tEM step 6\n",
      "\tEM step 7\n",
      "\tEM step 8\n",
      "\tEM step 9\n",
      "\tEM step 10\n",
      "\tEM step 11\n",
      "\tEM step 12\n",
      "\tEM step 13\n",
      "\tEM step 14\n",
      "\tEM step 15\n",
      "\tEM step 16\n",
      "\tEM step 17\n",
      "\tEM step 18\n",
      "\tEM step 19\n",
      "\tEM step 20\n",
      "\tEM step 21\n",
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    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\tEM step 390\n",
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      "Maximization step with EM algorithm starting\n",
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      "\tEM step 131\n",
      "\tEM step 132\n",
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      "\tEM step 135\n",
      "\tEM step 136\n",
      "\tEM step 137\n",
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      "\tEM step 144\n",
      "\tEM step 145\n",
      "\tEM step 146\n",
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      "\tEM step 161\n",
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      "\tEM step 169\n",
      "\tEM step 170\n",
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      "\tEM step 180\n",
      "\tEM step 181\n",
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      "\tEM step 183\n",
      "\tEM step 184\n",
      "\tEM step 185\n",
      "\tEM step 186\n",
      "\tEM step 187\n",
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      "\tEM step 190\n",
      "\tEM step 191\n",
      "\tEM step 192\n",
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      "\tEM step 206\n",
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      "\tEM step 210\n",
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      "\tEM step 212\n",
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      "\tEM step 214\n",
      "\tEM step 215\n",
      "\tEM step 216\n",
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      "\tEM step 238\n",
      "\tEM step 239\n",
      "\tEM step 240\n",
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      "\tEM step 243\n",
      "\tEM step 244\n",
      "\tEM step 245\n",
      "\tEM step 246\n",
      "\tEM step 247\n",
      "\tEM step 248\n",
      "\tEM step 249\n",
      "\tEM step 250\n",
      "\tEM step 251\n",
      "\tEM step 252\n",
      "\tEM step 253\n",
      "\tEM step 254\n",
      "\tEM step 255\n",
      "\tEM step 256\n",
      "\tEM step 257\n",
      "\tEM step 258\n",
      "\tEM step 259\n",
      "\tEM step 260\n",
      "\tEM step 261\n",
      "\tEM step 262\n",
      "\tEM step 263\n",
      "\tEM step 264\n",
      "\tEM step 265\n",
      "\tEM step 266\n",
      "\tEM step 267\n",
      "\tEM step 268\n",
      "\tEM step 269\n",
      "\tEM step 270\n",
      "\tEM step 271\n",
      "\tEM step 272\n",
      "\tEM step 273\n",
      "\tEM step 274\n",
      "\tEM step 275\n",
      "\tEM step 276\n",
      "\tEM step 277\n",
      "\tEM step 278\n",
      "\tEM step 279\n",
      "\tEM step 280\n",
      "\tEM step 281\n",
      "\tEM step 282\n",
      "\tEM step 283\n",
      "\tEM step 284\n",
      "\tEM step 285\n",
      "\tEM step 286\n",
      "\tEM step 287\n",
      "\tEM step 288\n",
      "\tEM step 289\n",
      "\tEM step 290\n",
      "\tEM step 291\n",
      "\tEM step 292\n",
      "\tEM step 293\n",
      "\tEM step 294\n",
      "\tEM step 295\n",
      "\tEM step 296\n",
      "\tEM step 297\n",
      "\tEM step 298\n",
      "\tEM step 299\n",
      "\tEM step 300\n",
      "\tEM step 301\n",
      "\tEM step 302\n",
      "\tEM step 303\n",
      "\tEM step 304\n",
      "\tEM step 305\n",
      "\tEM step 306\n",
      "\tEM step 307\n",
      "\tEM step 308\n",
      "\tEM step 309\n",
      "\tEM step 310\n",
      "\tEM step 311\n",
      "\tEM step 312\n",
      "\tEM step 313\n",
      "\tEM step 314\n",
      "\tEM step 315\n",
      "\tEM step 316\n",
      "\tEM step 317\n",
      "\tEM step 318\n",
      "\tEM step 319\n",
      "\tEM step 320\n",
      "\tEM step 321\n",
      "\tEM step 322\n",
      "\tEM step 323\n",
      "\tEM step 324\n",
      "\tEM step 325\n",
      "\tEM step 326\n",
      "\tEM step 327\n",
      "\tEM step 328\n",
      "\tEM step 329\n",
      "\tEM step 330\n",
      "\tEM step 331\n",
      "\tEM step 332\n",
      "\tEM step 333\n",
      "\tEM step 334\n"
     ]
    }
   ],
   "source": [
    "n_classes = [2, 3, 4, 5, 6, 7]\n",
    "bics = []\n",
    "for n in n_classes:\n",
    "    lcm_model = LCM(n_class=n, tol=10e-4, max_iter=1000, verbose=1, random_state=1234)\n",
    "    lcm_model.fit(data)\n",
    "    bics.append(lcm_model.calculate_bic(data))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
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AAAgwgD6ck2680d9eVZIeesjfWhUAAAAAEBUBBpDrqKOkWbOy/fnzpVdeiVcP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\nhFVMlpfD6Izvf7/1OSMj0sGDO4FGqZT9+1JJGhv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QWJJ0SaEWwmry3JR9FxQKYG7UtTuW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\neAQYAAAAAACg8P4fpPwp8H2ksLQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1080x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15,7))\n",
    "plt.plot(n_classes, bics, linewidth=3, color='r')\n",
    "plt.title(\"Bayesian Information Criterion\", fontsize=fontSize)\n",
    "plt.xlabel(\"Number of Latent Classes\", fontsize=fontSize)\n",
    "plt.ylabel(r\"BIC\", fontsize=fontSize)\n",
    "plt.tick_params(axis='both', labelsize=fontSize)\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}