pyAgrum inference of the bias of a coin from observed coin flips using a re-parameterization of the Beta distribution

beta_reparameterization_coin.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "4f1a5a8b-16c0-42f9-8bd0-ee50932e2a8b",
   "metadata": {},
   "source": [
    "# Purpose\n",
    "- build a fully bayesian beta distributed coin inference"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "d91da0ef-2ab3-4026-903b-15b37364ec75",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: watermark in /srv/conda/envs/notebook/lib/python3.9/site-packages (2.3.1)\n",
      "Requirement already satisfied: ipython in /srv/conda/envs/notebook/lib/python3.9/site-packages (from watermark) (8.2.0)\n",
      "Requirement already satisfied: setuptools>=18.5 in /srv/conda/envs/notebook/lib/python3.9/site-packages (from ipython->watermark) (62.0.0)\n",
      "Requirement already satisfied: pygments>=2.4.0 in /srv/conda/envs/notebook/lib/python3.9/site-packages (from ipython->watermark) (2.11.2)\n",
      "Requirement already satisfied: jedi>=0.16 in /srv/conda/envs/notebook/lib/python3.9/site-packages (from ipython->watermark) (0.18.1)\n",
      "Requirement already satisfied: stack-data in /srv/conda/envs/notebook/lib/python3.9/site-packages (from ipython->watermark) (0.2.0)\n",
      "Requirement already satisfied: traitlets>=5 in /srv/conda/envs/notebook/lib/python3.9/site-packages (from ipython->watermark) (5.1.1)\n",
      "Requirement already satisfied: pexpect>4.3 in /srv/conda/envs/notebook/lib/python3.9/site-packages (from ipython->watermark) (4.8.0)\n",
      "Requirement already satisfied: backcall in /srv/conda/envs/notebook/lib/python3.9/site-packages (from ipython->watermark) (0.2.0)\n",
      "Requirement already satisfied: prompt-toolkit!=3.0.0,!=3.0.1,<3.1.0,>=2.0.0 in /srv/conda/envs/notebook/lib/python3.9/site-packages (from ipython->watermark) (3.0.29)\n",
      "Requirement already satisfied: decorator in /srv/conda/envs/notebook/lib/python3.9/site-packages (from ipython->watermark) (5.1.1)\n",
      "Requirement already satisfied: pickleshare in /srv/conda/envs/notebook/lib/python3.9/site-packages (from ipython->watermark) (0.7.5)\n",
      "Requirement already satisfied: matplotlib-inline in /srv/conda/envs/notebook/lib/python3.9/site-packages (from ipython->watermark) (0.1.3)\n",
      "Requirement already satisfied: parso<0.9.0,>=0.8.0 in /srv/conda/envs/notebook/lib/python3.9/site-packages (from jedi>=0.16->ipython->watermark) (0.8.3)\n",
      "Requirement already satisfied: ptyprocess>=0.5 in /srv/conda/envs/notebook/lib/python3.9/site-packages (from pexpect>4.3->ipython->watermark) (0.7.0)\n",
      "Requirement already satisfied: wcwidth in /srv/conda/envs/notebook/lib/python3.9/site-packages (from prompt-toolkit!=3.0.0,!=3.0.1,<3.1.0,>=2.0.0->ipython->watermark) (0.2.5)\n",
      "Requirement already satisfied: executing in /srv/conda/envs/notebook/lib/python3.9/site-packages (from stack-data->ipython->watermark) (0.8.3)\n",
      "Requirement already satisfied: asttokens in /srv/conda/envs/notebook/lib/python3.9/site-packages (from stack-data->ipython->watermark) (2.0.5)\n",
      "Requirement already satisfied: pure-eval in /srv/conda/envs/notebook/lib/python3.9/site-packages (from stack-data->ipython->watermark) (0.2.2)\n",
      "Requirement already satisfied: six in /srv/conda/envs/notebook/lib/python3.9/site-packages (from asttokens->stack-data->ipython->watermark) (1.16.0)\n"
     ]
    }
   ],
   "source": [
    "!pip install watermark"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "78065ea1-6529-4676-b212-2d5c6a3113a9",
   "metadata": {},
   "outputs": [],
   "source": [
    "from pylab import *\n",
    "import matplotlib.pyplot as plt\n",
    "import pyAgrum as gum\n",
    "import pyAgrum.lib.notebook as gnb\n",
    "import numpy as np\n",
    "import scipy.stats\n",
    "from tqdm import tqdm\n",
    "import itertools\n",
    "import time\n",
    "from collections import defaultdict\n",
    "from scipy.ndimage import center_of_mass"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b7939029-a3b0-45d2-b775-43a3f648eac8",
   "metadata": {},
   "source": [
    "- this notebook was run in the Binder image provide by pyAgrum https://agrum.gitlab.io/extra/agrum_at_binder.html, click the Binder icon found on the bottom left corner of the agrum project home page\n",
    "    - the link for the binder image used for this notebook is https://agrum.gitlab.io/extra/agrum_at_binder.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6e64bc78-618e-49c6-9b6b-17e430fd3fca",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mon Jul 18 01:33:33 UTC 2022\n"
     ]
    }
   ],
   "source": [
    "!date"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c1a20bc5-d092-4ef1-8049-b8c4c6bc2918",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "%reload_ext autoreload\n",
    "%autoreload 2\n",
    "%load_ext watermark"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5ab10be8-8c40-439d-8d27-887885936a88",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Python implementation: CPython\n",
      "Python version       : 3.9.12\n",
      "IPython version      : 8.2.0\n",
      "\n",
      "numpy     : 1.23.1\n",
      "pandas    : 1.4.3\n",
      "matplotlib: 3.5.2\n",
      "pyAgrum   : 1.2.0\n",
      "scipy     : 1.8.1\n",
      "\n",
      "Compiler    : GCC 10.3.0\n",
      "OS          : Linux\n",
      "Release     : 4.15.0-180-generic\n",
      "Machine     : x86_64\n",
      "Processor   : x86_64\n",
      "CPU cores   : 4\n",
      "Architecture: 64bit\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%watermark -v -m -p numpy,pandas,matplotlib,pyAgrum,scipy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ab001ddd-a699-422a-9a9c-9522e3bbbbe7",
   "metadata": {},
   "outputs": [],
   "source": [
    "gum.config[\"notebook\",\"default_graph_size\"]=\"12!\"\n",
    "gum.config[\"notebook\",\"default_graph_inference_size\"]=\"12!\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "82cf3e55-2db4-4653-8959-9f777429aa31",
   "metadata": {},
   "source": [
    "# Fill Beta parameters with a re-parameterization\n",
    "* https://en.wikipedia.org/wiki/Beta_distribution"
   ]
  },
  {
   "attachments": {
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    }
   },
   "cell_type": "markdown",
   "id": "3802217c-5675-4409-97e0-0ad44e015c92",
   "metadata": {},
   "source": [
    "![image.png](attachment:2798e7e2-59dc-467f-93d0-d6624a77d6fa.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a13cd133-a2e2-4258-8830-f91cc9edc594",
   "metadata": {},
   "source": [
    "* below are some useful definitions\n",
    "$$ \\alpha = \\mu \\nu$$\n",
    "$$ \\beta = (1 - \\mu) \\nu $$\n",
    "\n",
    "$$ \\mu = \\frac{\\alpha}{\\alpha + \\beta} $$\n",
    "\n",
    "* like in Wikipedia article, we will have a uniform prior on μ and an expoential prior on ν"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "9eacc3cc-4365-4da8-b06d-994e039f59ef",
   "metadata": {},
   "outputs": [],
   "source": [
    "def fillvect_(rv,vmin,vmax,size, **pdf_kwargs):\n",
    "    x = linspace(vmin,vmax,size)\n",
    "    pdf=rv.pdf(x, **pdf_kwargs)\n",
    "    return x,pdf\n",
    "\n",
    "def normalize_(rv,vmin,vmax,size, **pdf_kwargs):\n",
    "    x = linspace(vmin,vmax,size)\n",
    "    pdf=rv.pdf(x, **pdf_kwargs)\n",
    "    return x,(pdf/sum(pdf))\n",
    "    \n",
    "def idx_to_proba(idxs: list, *, domain):\n",
    "    \"\"\"Hepler function to realize or map an index values to the given domain\"\"\"\n",
    "    for idx in idxs:\n",
    "        print(f\"What is the probability of theta if the index is {idx}? {domain[idx]}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "a94e4446-c7e1-4756-9c3d-bf8c4c43a94d",
   "metadata": {},
   "outputs": [],
   "source": [
    "NB_ = 100\n",
    "vmin, vmax = 0.001, 0.999\n",
    "pmin_mu, pmax_mu = 0.001, 0.999\n",
    "pmin_nu, pmax_nu = 1,50\n",
    "size_ = 16"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "bd4465f5-6447-421e-a6ff-ea22e2fa639a",
   "metadata": {},
   "outputs": [
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   "source": [
    "loc_, scale_ = 2, 5\n",
    "x_nu, y_nu = normalize_(scipy.stats.expon,pmin_nu,pmax_nu,NB_,loc=loc_, scale=scale_)\n",
    "plot(x_nu,y_nu)\n",
    "title(r\"Prior: $\\frac{1}{%s}exp(\\frac{x - %s}{%s}$)\" % (scale_, loc_, scale_))\n",
    "legend([r\"P($\\nu$)\"],loc='best');"
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  {
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   "id": "6996da12-7ada-4346-afe9-a6366b01248a",
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
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     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_mu, y_mu = normalize_(scipy.stats.uniform,pmin_mu,pmax_mu,NB_,)\n",
    "plot(x_mu,y_mu)\n",
    "title(r\"Prior: $\\mu$\")\n",
    "legend([r\"P($\\nu$)\"],loc='best');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "e47d97ee-4945-4fe5-a13a-d52dce9e78e3",
   "metadata": {},
   "outputs": [
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     "output_type": "stream",
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      ],
      "text/plain": [
       "(pyAgrum.BayesNet<double>@0x561008a155b0) BN{nodes: 19, arcs: 18, domainSize: 10^10.8165, dim: 1003400}"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bn=gum.BayesNet(\"SEQUENCE OF COINS MODEL\")\n",
    "mu = bn.add(gum.RangeVariable(\"mu\",\"mean of the Beta distribution\",0,NB_-1))\n",
    "nu = bn.add(gum.RangeVariable(\"nu\",\"'sample size' of the Beta where nu = a + b > 0\",0,NB_-1))\n",
    "bias=bn.add(gum.RangeVariable(\"bias\",\"The bias of the coin\",0,NB_-1))\n",
    "hs=[bn.add(gum.LabelizedVariable(f\"H{i}\",\"The hallucinations of coin flips\",2)) for i in range(size_)]\n",
    "\n",
    "bn.addArc(mu,bias)\n",
    "bn.addArc(nu,bias)\n",
    "for h in hs:\n",
    "    bn.addArc(bias,h)\n",
    "print(bn)\n",
    "bn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "b62758e2-1fca-40c5-a1c9-a5211917882c",
   "metadata": {},
   "outputs": [],
   "source": [
    "bn.cpt(mu)[:] = y_mu # uniform prior for hyperparameter\n",
    "bn.cpt(nu)[:] = y_nu # expoential prior for hyperparameter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "fe4a7fdc-9407-43f6-8c6e-0292f2c4367b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((100, 100), (100, 100))"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# https://scicomp.stackexchange.com/a/10800\n",
    "al_ = (x_mu[:,newaxis] * x_nu[newaxis,:])\n",
    "be_ = (1 - x_mu)[:,newaxis] * x_nu[newaxis,:]\n",
    "al_.shape, be_.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "e3fdacb9-3115-442b-8aff-30aa7e6b12de",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 100, 100)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bn.cpt(\"bias\").shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "01050362-e0a8-477e-9d50-c89f12a45368",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "end_time=0.3800621032714844 (s)\n"
     ]
    }
   ],
   "source": [
    "t_start = time.time()\n",
    "pdf = scipy.stats.beta(al_,be_).pdf(linspace(vmin, vmax,NB_)[:,newaxis, newaxis])\n",
    "bn.cpt(\"bias\").fillWith(np.swapaxes(pdf, 0, -1).flatten())\n",
    "bn.cpt(\"bias\").normalizeAsCPT()\n",
    "end_time = time.time() - t_start\n",
    "print(f\"{end_time=} (s)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "2f777143-4ea0-4c4a-99c6-26b6a92a220b",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_bias = linspace(vmin, vmax, NB_)\n",
    "x_hs = np.array([1 - x_bias, x_bias]).T\n",
    "for h in hs:\n",
    "    bn.cpt(h).fillWith(x_hs.flatten()).normalizeAsCPT()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "c393ae62-5464-44db-86a3-f78e9cce2aef",
   "metadata": {},
   "outputs": [
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   "id": "02327727-a05a-46ba-a62a-977f2d91579e",
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   "source": [
    "# the sequence of COINS\n",
    "serie=[1,0,0,0,1,0,1,1,0,1,0,0,1,0,0,1]"
   ]
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   "source": [
    "coin_evidence={f\"H{i}\":serie[i] for i in range(len(serie))}\n",
    "\n",
    "gnb.showInference(bn,evs=coin_evidence)"
   ]
  },
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   "cell_type": "code",
   "execution_count": 20,
   "id": "c9485d93-b291-4a93-b38f-a9db8538568c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MAP for mu : 0.44455555555555554\n",
      "center of mass for nu : 13.581934398669219\n",
      "MAP for bias : 0.43447474747474746\n"
     ]
    }
   ],
   "source": [
    "ie=gum.LazyPropagation(bn)\n",
    "ie.setEvidence(coin_evidence)\n",
    "ie.makeInference()\n",
    "idx, _ = ie.posterior('bias').argmax()\n",
    "map_bias = x_bias[idx[0][\"bias\"]]\n",
    "idx, _ = ie.posterior('mu').argmax()\n",
    "map_mu = x_mu[idx[0][\"mu\"]]\n",
    "com = center_of_mass(ie.posterior('nu').toarray())[0]\n",
    "\n",
    "print(f\"MAP for mu : {map_mu}\")\n",
    "print(f\"center of mass for nu : {com}\")\n",
    "print(f\"MAP for bias : {map_bias}\")"
   ]
  },
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