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Bayesnet example using Pomegranate

07 Apr 2016

Example taken from Coursera's Probabilistic Graphical Models, taught by Prof. Daphne Koller (https://class.coursera.org/pgm/)

Pomegranate library: https://github.com/jmschrei/pomegranate

In [1]:
import pomegranate as pom
In [2]:
difficulty = pom.DiscreteDistribution({ 'hard':0.6, 'easy':0.4 })
intelligence = pom.DiscreteDistribution({ 'intelligent':0.7, 'not-intelligent':0.3 })
grade = pom.ConditionalProbabilityTable(
    [['hard', 'intelligent', 'A', 0.3 ],
     ['hard', 'intelligent', 'B', 0.4 ],
     ['hard', 'intelligent', 'C', 0.3 ],
     ['hard', 'not-intelligent', 'A', 0.05 ],
     ['hard', 'not-intelligent', 'B', 0.25 ],
     ['hard', 'not-intelligent', 'C', 0.7 ],
     ['easy', 'intelligent', 'A', 0.9 ],
     ['easy', 'intelligent', 'B', 0.08 ],
     ['easy', 'intelligent', 'C', 0.02 ],
     ['easy', 'not-intelligent', 'A', 0.5 ],
     ['easy', 'not-intelligent', 'B', 0.3 ],
     ['easy', 'not-intelligent', 'C', 0.2 ],
    ],
    [difficulty, intelligence]
)
sat = pom.ConditionalProbabilityTable(
    [['intelligent', 'high-mark', 0.95],
     ['intelligent', 'low-mark', 0.05],
     ['not-intelligent', 'high-mark', 0.2],
     ['not-intelligent', 'low-mark', 0.8]
    ],
    [intelligence]
)
letter = pom.ConditionalProbabilityTable(
    [['A', 'reference-letter', 0.9],
     ['B', 'reference-letter', 0.6],
     ['C', 'reference-letter', 0.01],
     ['A', 'no-reference-letter', 0.1],
     ['B', 'no-reference-letter', 0.4],
     ['C', 'no-reference-letter', 0.99]
    ],
    [grade]
)
In [3]:
d = pom.State(difficulty, name="difficulty")
i = pom.State(intelligence, name="intelligence")
g = pom.State(grade, name="grade")
s = pom.State(sat, name="sat")
l = pom.State(letter, name="letter")
In [4]:
network = pom.BayesianNetwork( "student" )
network.add_states( [ d, i, g, s, l ] )
In [5]:
network.add_transition( d, g )
network.add_transition( i, g )
network.add_transition( i, s )
network.add_transition( g, l )
In [6]:
network.bake()

Observe how the probabilites are effected by observing various outcomes:

In [7]:
observations = { 'difficulty': 'hard', 'sat':'high-mark' }
beliefs = map( str, network.predict_proba( observations ) )
print "\n".join( "{}\t{}".format( state.name, belief ) for state, belief in zip( network.states, beliefs ) )

difficulty	{
    "frozen" :false,
    "class" :"Distribution",
    "parameters" :[
        {
            "hard" :1.0,
            "easy" :0.0
        }
    ],
    "name" :"DiscreteDistribution"
}
intelligence	{
    "frozen" :false,
    "class" :"Distribution",
    "parameters" :[
        {
            "intelligent" :0.9172413793103448,
            "not-intelligent" :0.0827586206896552
        }
    ],
    "name" :"DiscreteDistribution"
}
grade	{
    "frozen" :false,
    "class" :"Distribution",
    "parameters" :[
        {
            "A" :0.2793103448275863,
            "C" :0.3331034482758622,
            "B" :0.38758620689655154
        }
    ],
    "name" :"DiscreteDistribution"
}
sat	{
    "frozen" :false,
    "class" :"Distribution",
    "parameters" :[
        {
            "low-mark" :0.0,
            "high-mark" :1.0
        }
    ],
    "name" :"DiscreteDistribution"
}
letter	{
    "frozen" :false,
    "class" :"Distribution",
    "parameters" :[
        {
            "reference-letter" :0.4872620689655171,
            "no-reference-letter" :0.512737931034483
        }
    ],
    "name" :"DiscreteDistribution"
}

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