{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The Dawid-Skene model with priors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Dawid-Skene model (1979) is perhaps one of the first models to discover true item states/effects from multiple noisy measurements. Since then, there have been multiple models that improve over the basic model. This notebook covers the Dawid-Skene model which has been enhanced with priors.\n",
    "\n",
    "The model follows implementation in Rebecca J. Passonneau, Bob Carpenter, \"The Benefits of a Model of Annotation\", TACL, 2014.\n",
    "\n",
    "## Introduction\n",
    "In healthcare, a number of patients can receive potentially noisy judgments from several professionals. In computer science, work items of different difficulty get labeled by multiple annotators of different skill. In this notebook we will attempt to recover true work item labels from noisy annotator input.\n",
    "\n",
    "The primary goal is to recover the true item states. The secondary goal is to estimate various additional factors of potential interest. We will use probabilistic programming approach in attempt to solve the problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import pymc3 as pm\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from sklearn.metrics import confusion_matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data\n",
    "Load also the data matrix with following dimensions: work items, annotators, categories. The data for this notebook has been taken from https://github.com/abhishekmalali/questioning-strategy-classification/tree/master/data\n",
    "\n",
    "Note: The data in this notebook is organized in matrix where each work item gets exactly one response for each work item. This is often not possible in practice. The discussed model accepts triplets of data: (work item, annotator, response) which relaxes the constraint to have all observations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data = np.load(pm.get_data('extrahard_MC_500_5_4.npz.npy'))\n",
    "z_true = np.load(pm.get_data('extrahard_MC_500_5_4_reference_classes.npy'))\n",
    "\n",
    "I = data.shape[0]               # number of items\n",
    "J = data.shape[1]               # number of annotators\n",
    "K = data.shape[2]               # number of classes\n",
    "N = I * J"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's create the necessary data structures. In particular, we will convert the data cube into triplet format. One data point with index n allows to access the following information: jj[n] as annotator ID, providing his/her vote y[n] for item ii[n].\n",
    "\n",
    "At the same time, we compute the majority vote estimate. This will serve both as a baseline and as initialization for our model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# create data triplets\n",
    "jj = list()  # annotator IDs\n",
    "ii = list()  # item IDs\n",
    "y = list()   # response\n",
    "\n",
    "# initialize true category with majority votes\n",
    "z_init = np.zeros( I, dtype=np.int64 )\n",
    "\n",
    "# create data triplets\n",
    "for i in range( I ):\n",
    "    ks = list()\n",
    "    for j in range( J ):\n",
    "        dat = data[ i, j, : ]\n",
    "        k = np.where( dat == 1 )[0][0]\n",
    "        ks.append( k )\n",
    "        ii.append( i )\n",
    "        jj.append( j )\n",
    "        y.append( k )\n",
    "\n",
    "    # getting maj vote for work item i (dealing with numpy casts)\n",
    "    z_init[ i ] = np.bincount( np.array( ks ) ).argmax()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comparing true item labels and majority vote estimated labels one by one is tedious. Computing accuracy gives a single performance metric but does not reveal where the mistakes are made (e.g. which categories tend to be confused) and by how much. A confusion matrix with majority vote estimates will serve as our baseline:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Majority vote estimate of true category:\n",
      " [[120   2   1   2]\n",
      " [  5 116   4   0]\n",
      " [  4   6 113   2]\n",
      " [  4   3   3 115]]\n"
     ]
    }
   ],
   "source": [
    "confMat = confusion_matrix( z_true, z_init )\n",
    "print( \"Majority vote estimate of true category:\\n\" , confMat )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model\n",
    "With the data loaded and baseline set, we can now start building the Dawid-Skene model. We will start by setting the top level priors: class prevalence and annotator-specific confusion matrices. The two priors are of secondary interest.\n",
    "\n",
    "The class prevalence prior tells the proportion of categories in the data. Since we are completely ignorant about category proportions, it is meaningful to set a flat distribution.\n",
    "\n",
    "The annotator-specific confusion matrices will \"describe\" every annotator. Notably, a confusion matrix for an annotator j tells us which categories the annotator is expert (very high value on diagonal) and where his expertise is limited (relatively small value on diagonal and relatively big values off-diagonal). We will initialize confusion matrices with uniform values with slightly dominant diagonal -- our annotators are expected to provide meaningful labels."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# class prevalence (flat prior)\n",
    "alpha = np.ones( K )\n",
    "\n",
    "# individual annotator confusion matrices - dominant diagonal\n",
    "beta = np.ones( (K,K) ) + np.diag( np.ones(K) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, the interesting part -- the definition of the model.\n",
    "\n",
    "First, we will need two random variables to encode class prevalence (pi) and annotator confusion matrices (theta). The two random variables can be naturally modeled with Dirichlet.\n",
    "\n",
    "Second, we will define a variable for the true/hidden category for each work item. The Categorical distribution fits well our purpose to model a work item with K possible states.\n",
    "\n",
    "Finally, a special variable for observed data brings together all random variables. This is the variable (Categorical) where the data is injected. The parametrization of the variable needs to be explained: the observation y[n] is generated according to Categorical distribution by worker y[n] for item ii[n], where the true label is z[ ii[n] ].\n",
    "\n",
    "The following block will build the model only but won't do any inference."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model = pm.Model()\n",
    "\n",
    "with model:\n",
    "    pi = pm.Dirichlet( 'pi', a=alpha, shape=K )\n",
    "    theta = pm.Dirichlet( 'theta', a=beta, shape=(J,K,K) )\n",
    "    z = pm.Categorical( 'z', p=pi, shape=I, testval=z_init )\n",
    "    y_obs = pm.Categorical( 'y_obs', p=theta[ jj, z[ ii ] ], observed=y )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With model defined, we also need to set up the inference machinery. The variables of interest (pi, theta and z) will be divided in two groups: continuous (pi,theta) and discrete (z). The step methods are different: Metropolis or NUTS for former and CategoricalGibbsMetropolis for latter.\n",
    "\n",
    "Note: Running the following block will perform inference for our variables of interest and store results in the trace variable. The trace variable will contain a wealth of information that will be useful to perfom diagnostics and get posteriors for our three hidden variables -- class prevalence, annotator confusion matrices and true categories for all work items."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 5000/5000 [28:06<00:00,  4.73it/s]     \n"
     ]
    }
   ],
   "source": [
    "with model:\n",
    "    step1 = pm.Metropolis( vars=[pi,theta] )\n",
    "    step2 = pm.CategoricalGibbsMetropolis( vars=[z] )\n",
    "    trace = pm.sample( 5000, step=[step1, step2], progressbar=True )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Results\n",
    "\n",
    "Let's get a global overview of the trace. On the left side of the figure, posterior distributions; on the right - individual samples. The samples subplots should show \"uniform band of noise\" as the sampler locks around the true variable state. It is important to not see any jumps, switches or steady increase/decrease.\n",
    "\n",
    "Besides the class prevalence variable (\"pi\"), the categories and theta posteriors, the plots are of little utility. We will explore other variables in other form."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[<matplotlib.axes._subplots.AxesSubplot object at 0x7f245d5c2048>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x7f2456cb76a0>]], dtype=object)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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PQbAbph0HX/4rHH2xXX49xgftH/B4+eNs7tpMnsjjpOkn8fWjvs7c8XMpzS/F6XAipcSr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\nfK6x4t6yzHjWfcB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F7Pe2J9RNTyipNMVzpQK6h/ZQUqFOy+lC0hHsoMXXTM1bL5Hfaofb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\nJa6ecDWv7XqN5RuX8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4GVxv8Tsj2Aj4DsDssG/TkZjhqsacAmKeUWKWU78Aiw1LyBlPIj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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f24769ebcf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.traceplot( trace, varnames=['pi'] )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will take 1000 last samples from posterior for random variable (\"z\"). The majority vote from 1000 samples will give us our estimate of true item labels."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "z = trace['z'][-1000:,:]\n",
    "\n",
    "z_hat = np.zeros( I )\n",
    "for i in range( I ):\n",
    "    z_hat[ i ] = np.bincount( z[:,i] ).argmax()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The confusion matrix tells us how good our estimate is with respect to the ground truth. Compare it to the baseline: a better estimate has less off diagonal values (and more on main diagonal)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dawid-Skene estimate of true category:\n",
      " [[122   1   1   1]\n",
      " [  0 121   1   3]\n",
      " [  4   1 115   5]\n",
      " [  2   1   1 121]]\n"
     ]
    }
   ],
   "source": [
    "confMat = confusion_matrix( z_true, z_hat )\n",
    "print( \"Dawid-Skene estimate of true category:\\n\", confMat )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Finally, let's plot the confusion matrices of annotators. Notice the dominant diagonal nature of matrices -- measure of annotator performance. Compare the first annotator (j=0) and the last one (j=4)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Annotator j=0\n",
      "[[ 0.89  0.    0.07  0.03]\n",
      " [ 0.    0.97  0.03  0.  ]\n",
      " [ 0.02  0.01  0.95  0.02]\n",
      " [ 0.06  0.02  0.    0.92]]\n",
      "Annotator j=1\n",
      "[[ 0.62  0.13  0.09  0.16]\n",
      " [ 0.15  0.61  0.09  0.16]\n",
      " [ 0.11  0.18  0.66  0.04]\n",
      " [ 0.06  0.15  0.1   0.68]]\n",
      "Annotator j=2\n",
      "[[ 0.57  0.17  0.15  0.11]\n",
      " [ 0.13  0.5   0.25  0.12]\n",
      " [ 0.11  0.02  0.68  0.19]\n",
      " [ 0.13  0.14  0.12  0.62]]\n",
      "Annotator j=3\n",
      "[[ 0.68  0.14  0.1   0.07]\n",
      " [ 0.09  0.73  0.08  0.11]\n",
      " [ 0.12  0.05  0.74  0.1 ]\n",
      " [ 0.07  0.07  0.12  0.73]]\n",
      "Annotator j=4\n",
      "[[ 0.56  0.17  0.15  0.12]\n",
      " [ 0.14  0.53  0.22  0.11]\n",
      " [ 0.12  0.19  0.51  0.18]\n",
      " [ 0.22  0.12  0.13  0.53]]\n"
     ]
    }
   ],
   "source": [
    "np.set_printoptions(precision=2)\n",
    "for j in range( J ):\n",
    "    print( \"Annotator j=\" + str(j) )\n",
    "    Cj = trace['theta'][-1,j]\n",
    "    print( Cj )"
   ]
  }
 ],
 "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",
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 },
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