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bdatko/coin_inference.ipynb

Last active July 10, 2022 23:00
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Bayesian inference of a bias coin using discrete Bayesian Networks in pyAgrum
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coin_inference.ipynb
{
"cells": [
{
"cell_type": "markdown",
"id": "01b849cc-ce7f-44cc-bd64-bb0c9e004412",
"metadata": {
"tags": []
},
"source": [
"# Purpose\n",
"* trying to see if I can use a discrete Bayesian network to due inference of a latent variable\n",
"* practice skill and learning the syntacx towards discrtizing continous random variables to fille conditional probability tables\n",
"* Try to solve the inference problem having observed flips of a coin, what is the posterior of the bias of the coin using a Beta distribution\n",
" * seems to be a simple problem\n",
" \n",
"## Resources\n",
"* Bayesian network library of choice is [pyAgrum](https://agrum.gitlab.io/)\n",
"* Refered to the following pyAgrum tutorial notebooks\n",
" * [Tools>Potentials](http://www-desir.lip6.fr/~phw/aGrUM/docs/last/notebooks/potentials.ipynb.html)\n",
" - used to review potential syntax\n",
" * [Learnnig>Structural Learning](http://www-desir.lip6.fr/~phw/aGrUM/docs/last/notebooks/structuralLearning.ipynb.html)\n",
" - reviewed `gum.generateSample`\n",
" - reviewed `learnParameters` for learning parameters of the network without altering a dag\n",
" * [Learning>Parametric Em](http://www-desir.lip6.fr/~phw/aGrUM/docs/last/notebooks/ParametricEM.ipynb.html)\n",
" - reviewed learning with missing values\n",
" * [Examples>Causality And Learning](http://www-desir.lip6.fr/~phw/aGrUM/docs/last/notebooks/CausalityAndLearning.ipynb.html)\n",
" - reviewed learning with latent variables\n",
" - see `useMIIC`\n",
" * [Causality>Counterfactual](http://www-desir.lip6.fr/~phw/aGrUM/docs/last/notebooks/Counterfactual.ipynb.html)\n",
" - reviewed a `potential` with three paraents"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "dec4ac71-3328-463f-b6bb-a6a22d4db4ed",
"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: 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: backcall in /srv/conda/envs/notebook/lib/python3.9/site-packages (from ipython->watermark) (0.2.0)\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: 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: jedi>=0.16 in /srv/conda/envs/notebook/lib/python3.9/site-packages (from ipython->watermark) (0.18.1)\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: 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: stack-data in /srv/conda/envs/notebook/lib/python3.9/site-packages (from ipython->watermark) (0.2.0)\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: asttokens in /srv/conda/envs/notebook/lib/python3.9/site-packages (from stack-data->ipython->watermark) (2.0.5)\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: 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": "74e19d4c-5cec-4dbe-8a65-c55ef7c4c1fe",
"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",
"from scipy.stats import beta, bernoulli"
]
},
{
"cell_type": "markdown",
"id": "742d1304-ff87-493c-92f9-fb16e1efa232",
"metadata": {},
"source": [
"* this notebook was run in the Binder image provide by `pyAgrum`, click the Binder icon found on the bottom left corner of the [agrum project home page](https://agrum.gitlab.io/)\n",
" - the link for the binder image used for this notebook is [https://agrum.gitlab.io/extra/agrum_at_binder.html](https://agrum.gitlab.io/extra/agrum_at_binder.html)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "e93279ce-1c5e-4501-9dd7-4560a72540a1",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Sun Jul 10 22:55:07 UTC 2022\n"
]
}
],
"source": [
"!date"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "e6a343c2-aba1-4aa1-9f92-c9b4c711a743",
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"%reload_ext autoreload\n",
"%autoreload 2\n",
"%load_ext watermark"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "343a0503-7d53-4d34-82cf-bca26c9fa101",
"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": "markdown",
"id": "5b121245-ed4c-4111-8168-f7bd1f60dbbb",
"metadata": {},
"source": [
"## A simple example - from Pyro\n",
"\n",
"* Inspired by https://pyro.ai/examples/svi_part_i.html#A-simple-example"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "b26f2b31-cc4f-4a75-86dc-baaaa9cb063e",
"metadata": {},
"outputs": [],
"source": [
"def normalize_(rv,vmin,vmax,size):\n",
" x = linspace(vmin,vmax,size)\n",
" pdf=rv.pdf(x)\n",
" return x,(pdf/sum(pdf))"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "3c32b27a-c7f5-420b-9d7e-c10507a4d40b",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7f13a56a55b0>"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"NB_ = 300\n",
"vmin, vmax = 0., 1.\n",
"\n",
"x, y = normalize_(beta(1,10),vmin,vmax,NB_)\n",
"plot(x,y)\n",
"title(\"Beta(1,10)\")\n",
"legend([\"P(A)\"],loc='best')"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "c5e4ab6c-aee0-4b04-a2fe-921a9c50decd",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"BN{nodes: 2, arcs: 1, domainSize: 600, dim: 900}\n"
]
},
{
"data": {
"image/svg+xml": [
"<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"62pt\" height=\"116pt\" viewBox=\"0.00 0.00 62.00 116.00\">\n",
"<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 112)\">\n",
"<title>G</title>\n",
"<!-- B -->\n",
"<g id=\"node1\" class=\"node\">\n",
"<title>B</title>\n",
"<g id=\"a_node1\"><a xlink:title=\"(1) B\">\n",
"<ellipse fill=\"#404040\" stroke=\"#000000\" cx=\"27\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
"<text text-anchor=\"middle\" x=\"27\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#ffffff\">B</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- A -->\n",
"<g id=\"node2\" class=\"node\">\n",
"<title>A</title>\n",
"<g id=\"a_node2\"><a xlink:title=\"(0) A\">\n",
"<ellipse fill=\"#404040\" stroke=\"#000000\" cx=\"27\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
"<text text-anchor=\"middle\" x=\"27\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#ffffff\">A</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- A&#45;&gt;B -->\n",
"<g id=\"edge1\" class=\"edge\">\n",
"<title>A-&gt;B</title>\n",
"<g id=\"a_edge1\"><a xlink:title=\"(0, 1) : \">\n",
"<path fill=\"none\" stroke=\"#4a4a4a\" d=\"M27,-71.8314C27,-64.131 27,-54.9743 27,-46.4166\"/>\n",
"<polygon fill=\"#4a4a4a\" stroke=\"#4a4a4a\" points=\"30.5001,-46.4132 27,-36.4133 23.5001,-46.4133 30.5001,-46.4132\"/>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"</g>\n",
"</svg>"
],
"text/plain": [
"<IPython.core.display.SVG object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"bn=gum.BayesNet(\"Quasi-Continuous\")\n",
"a=bn.add(gum.RangeVariable(\"A\",\"A range variable\",0,NB_-1))\n",
"b=bn.add(gum.LabelizedVariable(\"B\",\"A binary variable\",2))\n",
"\n",
"bn.cpt(a)[:] = y\n",
"\n",
"# cpt(c) is NB x NB matrix !\n",
"l=[]\n",
"for i in range(NB_):\n",
" l.append(np.array([1 - x[i], x[i]]))\n",
"\n",
"bn.addArc(a,b)\n",
"bn.cpt(b)[:]=l\n",
"print(bn)\n",
"gnb.showBN(bn)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "2da43098-6221-4e2a-8469-95a6f1517672",
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"288pt\" height=\"238pt\" viewBox=\"0.00 0.00 288.00 238.00\">\n",
"<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 234)\">\n",
"<title>structs</title>\n",
"<text text-anchor=\"middle\" x=\"140\" y=\"-7.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#4a4a4a\">Inference in 0.24ms</text>\n",
"<!-- A -->\n",
"<g id=\"node1\" class=\"node\">\n",
"<title>A</title>\n",
"<polygon fill=\"#e0e0e0\" stroke=\"#000000\" points=\"280,-230 0,-230 0,-100 280,-100 280,-230\"/>\n",
"<svg viewBox=\"0 0 371.265625 170.563\" width=\"280px\" height=\"130px\" preserveAspectRatio=\"xMinYMin meet\" x=\"0\" y=\"-230\"> <metadata>\n",
" <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n",
" <cc:Work>\n",
" <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
" <dc:date>2022-07-10T22:55:08.956014</dc:date>\n",
" <dc:format>image/svg+xml</dc:format>\n",
" <dc:creator>\n",
" <cc:Agent>\n",
" <dc:title>Matplotlib v3.5.2, https://matplotlib.org/</dc:title>\n",
" </cc:Agent>\n",
" </dc:creator>\n",
" </cc:Work>\n",
" </rdf:RDF>\n",
" </metadata>\n",
" <defs>\n",
" <style type=\"text/css\">*{stroke-linejoin: round; stroke-linecap: butt}</style>\n",
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"source": [
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]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "82c8f835-d1e5-4f61-a2cf-a0e62cecfbbc",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"number of parameters in the bn : 599\n",
"domain of the bn : 10^2.778151250383644\n"
]
}
],
"source": [
"print(\"number of parameters in the bn : {0}\".format(bn.dim()))\n",
"print(\"domain of the bn : 10^{0}\".format(bn.log10DomainSize()))"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "b112b75c-e31d-4dba-b565-1445f87fe3bd",
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{
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import time\n",
"\n",
"ts = time.time()\n",
"ie=gum.LazyPropagation(bn)\n",
"ie.setEvidence({'B':1})\n",
"ie.makeInference()\n",
"te=time.time()\n",
"\n",
"plot(x,ie.posterior(a)[:])\n",
"plot(x,y)\n",
"t=title(\"P(A) computed in {0:2.5f} sec\".format(te-ts))\n",
"legend([\"P(A | B = 1)\", \"P(A)\"],loc='best')"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "4f66fff1-9b9d-4618-9a7a-966a6e5b812a",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7f13a3312100>"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import time\n",
"\n",
"ts = time.time()\n",
"ie=gum.LazyPropagation(bn)\n",
"ie.setEvidence({'B':0})\n",
"ie.makeInference()\n",
"te=time.time()\n",
"\n",
"plot(x,ie.posterior(a)[:])\n",
"plot(x,y)\n",
"t=title(\"P(A) computed in {0:2.5f} sec\".format(te-ts))\n",
"legend([\"P(A | B = 0)\", \"P(A)\"],loc='best')"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "8cc43ad9-b08d-4bf8-978c-38c4e998ca9b",
"metadata": {},
"outputs": [
{
"data": {
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"<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 234)\">\n",
"<title>structs</title>\n",
"<text text-anchor=\"middle\" x=\"142.5\" y=\"-7.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#4a4a4a\">Inference in 0.27ms</text>\n",
"<!-- A -->\n",
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"<title>A</title>\n",
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" <cc:Work>\n",
" <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
" <dc:date>2022-07-10T22:55:09.965200</dc:date>\n",
" <dc:format>image/svg+xml</dc:format>\n",
" <dc:creator>\n",
" <cc:Agent>\n",
" <dc:title>Matplotlib v3.5.2, https://matplotlib.org/</dc:title>\n",
" </cc:Agent>\n",
" </dc:creator>\n",
" </cc:Work>\n",
" </rdf:RDF>\n",
" </metadata>\n",
" <defs>\n",
" <style type=\"text/css\">*{stroke-linejoin: round; stroke-linecap: butt}</style>\n",
" </defs>\n",
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" <g id=\"patch_1\">\n",
" <path d=\"M 0 170.563 L 377.628125 170.563 L 377.628125 0 L 0 0 z \" style=\"fill: #e0e0e0\"/>\n",
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" <g id=\"axes_1\">\n",
" <g id=\"patch_2\">\n",
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" <g id=\"PolyCollection_1\">\n",
" <defs>\n",
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"### Trying to fit a sample example to data\n",
"* only get to see the coin flip, variable `B`\n",
"* `A` is a latent variable\n",
"* Therefore I have to use EM algorithm\n",
"\n",
"<font color='red'>**Question:**</font> Should I specify the latent variables as latent?\n",
"\n",
"<font color='red'>**Question:**</font> Does a Bayesian Netowrk have to be a casual model to have latent variables?"
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"NB_ = 300\n",
"vmin, vmax = 0., 1.\n",
"\n",
"x, y = normalize_(beta(1,10),vmin,vmax,NB_)\n",
"plot(x,y)\n",
"title(\"Beta(1,10)\")\n",
"legend([\"P(A)\"],loc='best')"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "e1fb305f-17a6-4325-9452-81312137c5f3",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"BN{nodes: 2, arcs: 1, domainSize: 600, dim: 900}\n"
]
},
{
"data": {
"image/svg+xml": [
"<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"62pt\" height=\"116pt\" viewBox=\"0.00 0.00 62.00 116.00\">\n",
"<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 112)\">\n",
"<title>G</title>\n",
"<!-- B -->\n",
"<g id=\"node1\" class=\"node\">\n",
"<title>B</title>\n",
"<g id=\"a_node1\"><a xlink:title=\"(1) B\">\n",
"<ellipse fill=\"#404040\" stroke=\"#000000\" cx=\"27\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
"<text text-anchor=\"middle\" x=\"27\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#ffffff\">B</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- A -->\n",
"<g id=\"node2\" class=\"node\">\n",
"<title>A</title>\n",
"<g id=\"a_node2\"><a xlink:title=\"(0) A\">\n",
"<ellipse fill=\"#404040\" stroke=\"#000000\" cx=\"27\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
"<text text-anchor=\"middle\" x=\"27\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#ffffff\">A</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- A&#45;&gt;B -->\n",
"<g id=\"edge1\" class=\"edge\">\n",
"<title>A-&gt;B</title>\n",
"<g id=\"a_edge1\"><a xlink:title=\"(0, 1) : \">\n",
"<path fill=\"none\" stroke=\"#4a4a4a\" d=\"M27,-71.8314C27,-64.131 27,-54.9743 27,-46.4166\"/>\n",
"<polygon fill=\"#4a4a4a\" stroke=\"#4a4a4a\" points=\"30.5001,-46.4132 27,-36.4133 23.5001,-46.4133 30.5001,-46.4132\"/>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"</g>\n",
"</svg>"
],
"text/plain": [
"<IPython.core.display.SVG object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"bn=gum.BayesNet(\"Quasi-Continuous\")\n",
"a=bn.add(gum.RangeVariable(\"A\",\"A range variable\",0,NB_-1))\n",
"b=bn.add(gum.LabelizedVariable(\"B\",\"A binary variable\",2))\n",
"\n",
"bn.cpt(a)[:] = y\n",
"\n",
"l=[]\n",
"for i in range(NB_):\n",
" l.append(np.array([1 - x[i], x[i]]))\n",
"\n",
"bn.addArc(a,b)\n",
"bn.cpt(b)[:]=l\n",
"print(bn)\n",
"gnb.showBN(bn)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "5be9742d-6205-4e58-9a88-a8e6f326b512",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|██████████████████████████████████████████████████████|"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Log2-Likelihood : -32852.90468740906\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"\n"
]
}
],
"source": [
"(samples,log2_likelihood) = gum.generateSample(bn,n=5000,name_out=None,show_progress=True, with_labels=True, random_order=False);"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "595fc100-d04d-41d8-a7ad-9430af0b4b6f",
"metadata": {},
"outputs": [],
"source": [
"samples[\"A\"] = [\"?\"] * samples.shape[0]\n",
"samples.to_csv(\"out/coin_latent.csv\", index=False)"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "2d57bd8f-7918-459f-8d75-b50c87922eb4",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0 0\n",
"1 0\n",
"2 0\n",
"3 0\n",
"4 0\n",
" ..\n",
"4995 0\n",
"4996 0\n",
"4997 0\n",
"4998 1\n",
"4999 0\n",
"Name: B, Length: 5000, dtype: object"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"samples[\"B\"]"
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "7f43b041-b861-419f-a406-158bb298d1d1",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Missing values in out/coin_latent.csv : True\n"
]
}
],
"source": [
"learner = gum.BNLearner(\"out/coin_latent.csv\",bn,[\"?\"])\n",
"print(f\"Missing values in out/coin_latent.csv : {learner.hasMissingValues()}\")"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "b55062e2-1dcc-488b-b6f4-ac4c53d9e1f5",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Filename : out/coin_latent.csv\n",
"Size : (5000,2)\n",
"Variables : A[300], B[2]\n",
"Induced types : False\n",
"Missing values : True\n",
"Algorithm : Greedy Hill Climbing\n",
"Score : BDeu\n",
"Prior : Smoothing (The BDeu score already contains a different 'implicit' prior. Therefore, the learning will probably be biased.)\n",
"Prior weight : 1.000000\n",
"EM : True\n",
"EM epsilon : 0.001000\n",
"\n",
"# iterations : 2\n"
]
},
{
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"source": [
"learner.useEM(1e-3)\n",
"learner.useSmoothingPrior()\n",
"print(learner)\n",
"bn_em00=learner.learnParameters(bn.dag())\n",
"print(f\"# iterations : {learner.nbrIterations()}\")\n",
"gnb.flow.row(gnb.getInference(bn),gnb.getInference(bn_em00))"
]
},
{
"cell_type": "code",
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"id": "6ec8ffe8-c782-4805-8732-0e5ef8751909",
"metadata": {},
"outputs": [
{
"name": "stdout",
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"text": [
"Filename : out/coin_latent.csv\n",
"Size : (5000,2)\n",
"Variables : A[300], B[2]\n",
"Induced types : False\n",
"Missing values : True\n",
"Algorithm : Greedy Hill Climbing\n",
"Score : BDeu\n",
"Prior : Smoothing (The BDeu score already contains a different 'implicit' prior. Therefore, the learning will probably be biased.)\n",
"Prior weight : 1.000000\n",
"EM : True\n",
"EM epsilon : 0.000000\n",
"\n"
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"text/plain": [
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],
"source": [
"learner = gum.BNLearner(\"out/coin_latent.csv\",bn,[\"?\"])\n",
"learner.useSmoothingPrior()\n",
"learner.setVerbosity(True)\n",
"learner.useEM(1e-15)\n",
"print(learner)\n",
"bn_em01=learner.learnParameters(bn.dag())\n",
"gnb.flow.row(gnb.getInference(bn),gnb.getInference(bn_em01),captions=[\"Source\",f\"Estimation EM en {learner.nbrIterations()} iteration(s)\"])"
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "477fbd7b-9633-40c6-a27f-5a8571f3c6c5",
"metadata": {},
"outputs": [
{
"data": {
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"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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plot(np.arange(1,1+learner.nbrIterations()),learner.history())\n",
"xticks(np.arange(1, 1+learner.nbrIterations(), step=2))\n",
"title(\"Error during EM iterations\");"
]
},
{
"cell_type": "markdown",
"id": "fe24de5d-f90a-4003-b31f-e36aee74bcf8",
"metadata": {},
"source": [
"## Causal learning and causal impact\n",
"\n",
"* this seems like it's unreasonable for the `useMIIC` to discover the latent variable `A`, but I am trying for completion sake"
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "e8c9911a-04cf-4b42-95e4-57955937062d",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|██████████████████████████████████████████████████████|"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Log2-Likelihood : -32812.61732637457\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"\n"
]
}
],
"source": [
"(samples,log2_likelihood) = gum.generateSample(bn,n=5000,name_out=None,show_progress=True, with_labels=True, random_order=False);\n",
"samples[[\"B\"]].to_csv(\"out/classifier_latent.csv\", index=False)"
]
},
{
"cell_type": "code",
"execution_count": 25,
"id": "ec21bc83-0701-441e-ac13-9c25010240d0",
"metadata": {},
"outputs": [],
"source": [
"learner=gum.BNLearner(\"out/classifier_latent.csv\")\n",
"learner.useMIIC()\n",
"bn_latent=learner.learnBN()"
]
},
{
"cell_type": "code",
"execution_count": 26,
"id": "96c7e83c-6198-4285-8682-5ba3990bd5fe",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
" <style>\n",
" .floating-box {\n",
" display: inline-block;\n",
" margin: 7px;\n",
" padding : 3px;\n",
" border: 2px solid #FFFFFF; \n",
" valign:middle;\n",
" background-color: #FDFDFD;\n",
" }\n",
" </style>\n",
" <div class=\"floating-box\"><svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"62pt\" height=\"116pt\" viewBox=\"0.00 0.00 62.00 116.00\">\n",
"<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 112)\">\n",
"<title>G</title>\n",
"<!-- B -->\n",
"<g id=\"node1\" class=\"node\">\n",
"<title>B</title>\n",
"<g id=\"a_node1\"><a xlink:title=\"(1) B\">\n",
"<ellipse fill=\"#404040\" stroke=\"#000000\" cx=\"27\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
"<text text-anchor=\"middle\" x=\"27\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#ffffff\">B</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- A -->\n",
"<g id=\"node2\" class=\"node\">\n",
"<title>A</title>\n",
"<g id=\"a_node2\"><a xlink:title=\"(0) A\">\n",
"<ellipse fill=\"#404040\" stroke=\"#000000\" cx=\"27\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
"<text text-anchor=\"middle\" x=\"27\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#ffffff\">A</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"<!-- A&#45;&gt;B -->\n",
"<g id=\"edge1\" class=\"edge\">\n",
"<title>A-&gt;B</title>\n",
"<g id=\"a_edge1\"><a xlink:title=\"(0, 1) : \">\n",
"<path fill=\"none\" stroke=\"#4a4a4a\" d=\"M27,-71.8314C27,-64.131 27,-54.9743 27,-46.4166\"/>\n",
"<polygon fill=\"#4a4a4a\" stroke=\"#4a4a4a\" points=\"30.5001,-46.4132 27,-36.4133 23.5001,-46.4133 30.5001,-46.4132\"/>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"</g>\n",
"</svg><br><center><small><em>original model</em></small></center></div><div class=\"floating-box\"><svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"62pt\" height=\"44pt\" viewBox=\"0.00 0.00 62.00 44.00\">\n",
"<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 40)\">\n",
"<title>G</title>\n",
"<!-- B -->\n",
"<g id=\"node1\" class=\"node\">\n",
"<title>B</title>\n",
"<g id=\"a_node1\"><a xlink:title=\"(0) B\">\n",
"<ellipse fill=\"#404040\" stroke=\"#000000\" cx=\"27\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
"<text text-anchor=\"middle\" x=\"27\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#ffffff\">B</text>\n",
"</a>\n",
"</g>\n",
"</g>\n",
"</g>\n",
"</svg><br><center><small><em>learned model</em></small></center></div><div class=\"floating-box\">$$[]$$<br><center><small><em>Latent variables found</em></small></center></div>"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"gnb.flow.row(bn,bn_latent,f\"$${[(bn_latent.variable(i).name(),bn_latent.variable(j).name()) for (i,j) in learner.latentVariables()]}$$\",\n",
" captions=['original model','learned model','Latent variables found'])"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "4f50e93b-e44c-4bb4-8287-39d60f2af218",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
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},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.9.12"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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