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phwuil/revised_coin_inference.ipynb

Created July 12, 2022 07:53
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Proposition of modification following bdatko's Bayesian inference of a bias coin using discrete Bayesian Networks in pyAgrum
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revised_coin_inference.ipynb
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"%matplotlib inline\n",
"%reload_ext autoreload\n",
"%autoreload 2"
]
},
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"source": [
"from pylab import *\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"import scipy.stats \n",
"\n",
"import pyAgrum as gum\n",
"import pyAgrum.lib.notebook as gnb"
]
},
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"execution_count": 3,
"id": "78172cfd-6af6-4365-b634-3bfe3ca3c49a",
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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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"cell_type": "code",
"execution_count": 4,
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"metadata": {},
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"source": [
"def fillvect_(rv,vmin,vmax,size):\n",
" x = linspace(vmin,vmax,size)\n",
" pdf=rv.pdf(x)\n",
" return pdf\n",
"\n",
"NB_ =300\n",
"vmin, vmax = 0.001, 0.999\n",
"pmin, pmax = 1,50\n",
"\n",
"SIZE_= len(serie)\n",
"\n",
"\n",
"gum.config[\"notebook\",\"default_graph_size\"]=\"12!\"\n",
"gum.config[\"notebook\",\"default_graph_inference_size\"]=\"12!\""
]
},
{
"cell_type": "markdown",
"id": "accf452a-316b-4ca6-98a8-d8e72a29c19a",
"metadata": {},
"source": [
"## The model, including hyper parameters alpha and beta (with uniform prior)"
]
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"id": "8d9fb220-8abc-49e8-b71c-1b06a5287c25",
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"text/plain": [
"(pyAgrum.BayesNet<double>@0x563783474390) BN{nodes: 19, arcs: 18, domainSize: 10^10.6915, dim: 759700}"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"bn=gum.BayesNet(\"SEQUENCE OF COINS MODEL\")\n",
"alpha=bn.add(gum.RangeVariable(\"alpha\",\"alpha hypterparamter\",pmin,pmax))\n",
"beta=bn.add(gum.RangeVariable(\"beta\",\"beta hyperparameter\",pmin,pmax))\n",
"a=bn.add(gum.RangeVariable(\"A\",\"A range variable\",0,NB_-1))\n",
"bs=[bn.add(gum.LabelizedVariable(f\"B{i}\",\"A binary variable\",2)) for i in range(SIZE_)]\n",
"\n",
"bn.addArc(alpha,a)\n",
"bn.addArc(beta,a)\n",
"for b in bs:\n",
" bn.addArc(a,b)\n",
"\n",
"print(bn)\n",
"bn"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "063d8098-ea5d-449f-826a-952804951777",
"metadata": {},
"outputs": [
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"source": [
"bn.cpt(alpha).fillWith(1).normalize() \n",
"bn.cpt(beta).fillWith(1).normalize() # uniform prior for hyperparameter\n",
"\n",
"for al in range(pmin,pmax+1):\n",
" for be in range(pmin,pmax+1):\n",
" bn.cpt(\"A\")[{\"alpha\":str(al),\"beta\":str(be)}]=fillvect_(scipy.stats.beta(al,be),\n",
" vmin,vmax,NB_)\n",
"bn.cpt(\"A\").normalizeAsCPT()\n",
"\n",
"l=[]\n",
"r=(vmax-vmin)/NB_\n",
"for i in range(NB_):\n",
" l.append(vmax-i*r)\n",
" l.append(i*r+vmin)\n",
"for b in bs:\n",
" bn.cpt(b).fillWith(l).normalizeAsCPT()\n",
"\n",
"gnb.showInference(bn)"
]
},
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"id": "6d509ced-945a-4add-82ed-4bb9371e967b",
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"source": [
"## The original version with alpha=1 and beta=10"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "c2c6b54c-33ed-4199-add6-9bb97bf60c9b",
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"## Observing the sequence of coins in "
]
},
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"id": "97feefb1-03a4-4b65-9c96-45bce1f80051",
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