Kullback-Leibler for Bayesian networks

In [1]:

import os

%matplotlib inline

from pylab import *
import matplotlib.pyplot as plt

Initialisation

importing pyAgrum
importing pyAgrum.lib tools
loading a BN

In [2]:

import pyAgrum as gum
import pyAgrum.lib.notebook as gnb

Create a first BN : bn

In [3]:

bn=gum.loadBN("res/asia.bif")
# randomly re-generate parameters for every Conditional Probability Table
bn.generateCPTs()
bn

Out[3]:

Create a second BN : bn2

In [4]:

bn2=gum.loadBN("res/asia.bif")
bn2.generateCPTs()
bn2

Out[4]:

bn vs bn2 : different parameters

In [5]:

gnb.flow.row(bn.cpt(3),bn2.cpt(3),
              captions=["a CPT in bn","same CPT in bn2 (with different parameters)"])

	positive_XraY
tuberculos_or_cancer	0	1
0	0.6516	0.3484
1	0.4449	0.5551

a CPT in bn

	positive_XraY
tuberculos_or_cancer	0	1
0	0.6965	0.3035
1	0.1083	0.8917

same CPT in bn2 (with different parameters)

Exact and (Gibbs) approximated KL-divergence

In order to compute KL-divergence, we just need to be sure that the 2 distributions are defined on the same domain (same variables, etc.)

Exact KL

In [6]:

g1=gum.ExactBNdistance(bn,bn2)
print(g1.compute())

{'klPQ': 1.9191657665041133, 'errorPQ': 0, 'klQP': 1.942616105384583, 'errorQP': 0, 'hellinger': 0.7605316099375611, 'bhattacharya': 0.3413700421126023, 'jensen-shannon': 0.37371212141901083}

If the models are not on the same domain :

In [7]:

bn_different_domain=gum.loadBN("res/alarm.dsl")

# g=gum.BruteForceKL(bn,bn_different_domain) # a KL-divergence between asia and alarm ... :(
#
# would cause
#---------------------------------------------------------------------------
#OperationNotAllowed                       Traceback (most recent call last)
#
#OperationNotAllowed: this operation is not allowed : KL : the 2 BNs are not compatible (not the same vars : visit_to_Asia?)

Gibbs-approximated KL

In [8]:

g=gum.GibbsBNdistance(bn,bn2)
g.setVerbosity(True)
g.setMaxTime(120)
g.setBurnIn(5000)
g.setEpsilon(1e-7)
g.setPeriodSize(500)

In [9]:

print(g.compute())
print("Computed in {0} s".format(g.currentTime()))

{'klPQ': 1.888582675328128, 'errorPQ': 0, 'klQP': 2.409520503291685, 'errorQP': 0, 'hellinger': 0.79919830491918, 'bhattacharya': 0.3147642841353423, 'jensen-shannon': 0.4108069121688592}
Computed in 0.31129116599999995 s

In [10]:

print("--")

print(g.messageApproximationScheme())
print("--")

print("Temps de calcul : {0}".format(g.currentTime()))
print("Nombre d'itérations : {0}".format(g.nbrIterations()))

--
stopped with epsilon=1e-07
--
Temps de calcul : 0.31129116599999995
Nombre d'itérations : 52500

In [11]:

p=plot(g.history(), 'g')

../_images/notebooks_96-Tools_klForBns_21_0.svg

Animation of Gibbs KL

Since it may be difficult to know what happens during approximation algorithm, pyAgrum allows to follow the iteration using animated matplotlib figure

In [12]:

g=gum.GibbsBNdistance(bn,bn2)
g.setMaxTime(60)
g.setBurnIn(500)
g.setEpsilon(1e-7)
g.setPeriodSize(5000)

In [13]:

gnb.animApproximationScheme(g) # logarithmique scale for Y
g.compute()

Out[13]:

{'klPQ': 1.9088695207054012,
 'errorPQ': 0,
 'klQP': 1.8891423220301469,
 'errorQP': 0,
 'hellinger': 0.7553029868459951,
 'bhattacharya': 0.3409495029750985,
 'jensen-shannon': 0.3691557649394705}

../_images/notebooks_96-Tools_klForBns_25_1.svg