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bdatko/pyagrum_domain_fix_16-Examples_quasiContinuous.ipynb

Last active July 11, 2022 01:49
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Trying to fix the domain for the [example shown in the pyAgrum library](http://www-desir.lip6.fr/~phw/aGrUM/docs/last/notebooks/quasiContinuous.ipynb.html)
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pyagrum_domain_fix_16-Examples_quasiContinuous.ipynb
{
"cells": [
{
"cell_type": "markdown",
"id": "6cfc7f26-a8f3-4499-8253-8faaa622bfa0",
"metadata": {},
"source": [
"# Purpose\n",
"* fix the domain miss-match in the [Quasi-continuous BN](http://www-desir.lip6.fr/~phw/aGrUM/docs/last/notebooks/quasiContinuous.ipynb.html)"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "88c78fd9-6cdd-47a9-a0aa-fad7a24ac3ad",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Collecting watermark\n",
" Downloading watermark-2.3.1-py2.py3-none-any.whl (7.2 kB)\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: decorator in /srv/conda/envs/notebook/lib/python3.9/site-packages (from ipython->watermark) (5.1.1)\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: pexpect>4.3 in /srv/conda/envs/notebook/lib/python3.9/site-packages (from ipython->watermark) (4.8.0)\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: setuptools>=18.5 in /srv/conda/envs/notebook/lib/python3.9/site-packages (from ipython->watermark) (62.0.0)\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: jedi>=0.16 in /srv/conda/envs/notebook/lib/python3.9/site-packages (from ipython->watermark) (0.18.1)\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: pure-eval in /srv/conda/envs/notebook/lib/python3.9/site-packages (from stack-data->ipython->watermark) (0.2.2)\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: six in /srv/conda/envs/notebook/lib/python3.9/site-packages (from asttokens->stack-data->ipython->watermark) (1.16.0)\n",
"Installing collected packages: watermark\n",
"Successfully installed watermark-2.3.1\n"
]
}
],
"source": [
"!pip install watermark"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "6c97b9e2-ad02-44fc-a94e-2d7f4c595a58",
"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",
"from scipy.stats import norm,maxwell"
]
},
{
"cell_type": "markdown",
"id": "b403689e-6ee5-4e5a-b433-9d3fe08af08a",
"metadata": {},
"source": [
"* this notebook was run in the Binder image provide by [pyAgrum](https://agrum.gitlab.io/), 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": "1a8b6e93-cbbd-4b36-9f62-35cccb2f64fa",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Mon Jul 11 01:40:34 UTC 2022\n"
]
}
],
"source": [
"!date"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "29b3bddb-b08d-4d77-9dfa-6cd67ab9b69c",
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"%reload_ext autoreload\n",
"%autoreload 2\n",
"%load_ext watermark"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "3dce5073-f930-47a1-957c-161a63deaf50",
"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": "45f007d6-a3e4-44e1-82d0-74aa6accfdf3",
"metadata": {},
"source": [
"aGrUM cannot (currently) deal with with continuous variables. However, a discrete variable with a large enough domain size is an approximation of such variables."
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "78d58dbc-b04d-43c3-a1fb-ac31505103c3",
"metadata": {},
"outputs": [],
"source": [
"#nbr of states for quasi continuous variables. You can change the value \n",
"#but be careful of the quadratic behavior of both memory and time complexity\n",
"#in this example.\n",
"NB=300"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "dffa53be-de84-4c1a-9600-be03fe4d4270",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"BN{nodes: 2, arcs: 1, domainSize: 600, dim: 602}\n"
]
},
{
"data": {
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"<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",
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"text/plain": [
"<IPython.core.display.SVG object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"bn=gum.BayesNet(\"Quasi-Continuous\")\n",
"a=bn.add(gum.LabelizedVariable(\"A\",\"A binary variable\",2))\n",
"b=bn.add(gum.RangeVariable(\"B\",\"A range variable\",0,NB-1))\n",
"bn.addArc(a,b)\n",
"print(bn)\n",
"gnb.showBN(bn)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "c73630e9-69fb-4be7-993d-3282aa0e0475",
"metadata": {},
"outputs": [
{
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"source": [
"bn.cpt(a)[:]=[0.4, 0.6]\n",
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]
},
{
"cell_type": "markdown",
"id": "c5f65d76-9c08-4981-9ce1-e76a04f7c52d",
"metadata": {},
"source": [
"## CPT for quasi-continuous variables (with parents)\n",
"Using python (and scipy), it is easy to find pdf for continuous variable"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "42dcfd63-9b16-4f72-b952-63c1bc7a3ff6",
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"source": [
"# we truncate a pdf, so we need to normalize \n",
"def normalize(rv,vmin,vmax,size):\n",
" pdf=rv.pdf(linspace(vmin,vmax,size))\n",
" return (pdf/sum(pdf))\n",
"\n",
"from scipy.stats import norm,maxwell\n",
"\n",
"plot(normalize(norm(),-4,1,NB)) # P(B|A=0) is a Gaussian distribution\n",
"plot(normalize(maxwell(),0.5,6,NB)) # P(B|A=1) is a Maxwell-Boltzmann distribution\n",
"title(\"P(B | A)\")\n",
"legend([\"P(B|A=0)\",\"P(B|A=1)\"],loc='best')\n",
"\n",
"bn.cpt(b)[{'A':0}]=normalize(norm(),-4,1,NB)\n",
"bn.cpt(b)[{'A':1}]=normalize(maxwell(),0.5,6,NB)"
]
},
{
"cell_type": "markdown",
"id": "0f02d8fa-a72c-4135-adaa-a72d88a8aae8",
"metadata": {},
"source": [
"## Quasi =-continuous inference"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "0a0af58f-f1ed-45aa-847d-6d9e2b575372",
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"source": [
"ie=gum.LazyPropagation(bn)\n",
"ie.makeInference()\n",
"plot(ie.posterior(b)[:]) # the posterior for B\n",
"t=title(\"P(B)\")"
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"# The Problem\n",
"* The above code showing the normal and maxwell distribution do not have the same domains\n",
"* the `linspace` from `normalize` is meaningless so I was really confused"
]
},
{
"cell_type": "markdown",
"id": "4d3a1e52-7d83-4c41-bdfd-22b7ecae1ee6",
"metadata": {},
"source": [
"## Fixing the domain"
]
},
{
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"execution_count": 11,
"id": "9b8bb1e7-19b7-4d66-aa0a-430dfe9c88af",
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"source": [
"def normalize_(rv,vmin,vmax,size):\n",
" x = linspace(vmin,vmax,size)\n",
" pdf=rv.pdf(x)\n",
" return x,(pdf/sum(pdf))\n",
"\n",
"x, y = normalize_(norm(),-4,1,NB)\n",
"plot(x,y)\n",
"x,y = normalize_(maxwell(),-4,1,NB)\n",
"plot(x,y)\n",
"title(\"P(B | A)\")\n",
"legend([\"P(B|A=0)\",\"P(B|A=1)\"],loc='best')"
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},
{
"cell_type": "code",
"execution_count": 12,
"id": "3588fb35-0902-4dcf-9401-3bee079785c2",
"metadata": {},
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{
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" <defs>\n",
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" </defs>\n",
"</svg>\n"
],
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
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"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"NB_ = 600\n",
"vmin, vmax = -4, 6\n",
"\n",
"x, y = normalize_(norm(),vmin,vmax,NB_)\n",
"plot(x,y)\n",
"x,y = normalize_(maxwell(),vmin,vmax,NB_)\n",
"plot(x,y)\n",
"title(\"P(B | A)\")\n",
"legend([\"P(B|A=0)\",\"P(B|A=1)\"],loc='best')"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "6cedd4c4-0df0-445f-bc32-1df1b7e08081",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"BN{nodes: 2, arcs: 1, domainSize: 1200, dim: 1202}\n"
]
},
{
"data": {
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"<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",
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"</a>\n",
"</g>\n",
"</g>\n",
"<!-- A -->\n",
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"<title>A</title>\n",
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"</a>\n",
"</g>\n",
"</g>\n",
"<!-- A&#45;&gt;B -->\n",
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"<title>A-&gt;B</title>\n",
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"</g>\n",
"</g>\n",
"</g>\n",
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],
"text/plain": [
"<IPython.core.display.SVG object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"bn=gum.BayesNet(\"Quasi-Continuous\")\n",
"a=bn.add(gum.LabelizedVariable(\"A\",\"A binary variable\",2))\n",
"b=bn.add(gum.RangeVariable(\"B\",\"A range variable\",0,NB_-1))\n",
"bn.addArc(a,b)\n",
"print(bn)\n",
"gnb.showBN(bn)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "bea07805-8898-46c6-ae5e-c235e633831c",
"metadata": {},
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"source": [
"bn.cpt(a)[:]=[0.4, 0.6]\n",
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},
{
"cell_type": "code",
"execution_count": 15,
"id": "c516dabe-2966-4254-abee-86946730a664",
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"source": [
"_,y_A0 = normalize_(norm(),vmin,vmax,NB_)\n",
"x,y_A1 = normalize_(maxwell(),vmin,vmax,NB_)\n",
"\n",
"bn.cpt(b)[{'A':0}]=y_A0\n",
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{
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"text/plain": [
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},
"metadata": {
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"output_type": "display_data"
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],
"source": [
"ie=gum.LazyPropagation(bn)\n",
"ie.makeInference()\n",
"plot(x,ie.posterior(b)[:]) # the posterior for B\n",
"t=title(\"P(B)\")"
]
},
{
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"id": "92c00734-93d5-4669-a8f9-a5f0e7f02ff3",
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