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pyAgrum 0.17.3   
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generation: 2020-04-27 18:59  

Creative Commons License
This pyAgrum's notebook is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

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(os.path.join("res","asia.bif"))
# randomly re-generate parameters for every Conditional Probability Table
bn.generateCPTs() 
bn
Out[3]:
G visit_to_Asia visit_to_Asia tuberculosis tuberculosis visit_to_Asia->tuberculosis tuberculos_or_cancer tuberculos_or_cancer tuberculosis->tuberculos_or_cancer positive_XraY positive_XraY tuberculos_or_cancer->positive_XraY dyspnoea dyspnoea tuberculos_or_cancer->dyspnoea lung_cancer lung_cancer lung_cancer->tuberculos_or_cancer smoking smoking smoking->lung_cancer bronchitis bronchitis smoking->bronchitis bronchitis->dyspnoea

Create a second BN : bn2

In [4]:
bn2=gum.loadBN(os.path.join("res","asia.bif"))
bn2.generateCPTs()
bn2
Out[4]:
G visit_to_Asia visit_to_Asia tuberculosis tuberculosis visit_to_Asia->tuberculosis tuberculos_or_cancer tuberculos_or_cancer tuberculosis->tuberculos_or_cancer positive_XraY positive_XraY tuberculos_or_cancer->positive_XraY dyspnoea dyspnoea tuberculos_or_cancer->dyspnoea lung_cancer lung_cancer lung_cancer->tuberculos_or_cancer smoking smoking smoking->lung_cancer bronchitis bronchitis smoking->bronchitis bronchitis->dyspnoea

bn vs bn2 : different parameters

In [5]:
gnb.sideBySide(bn.cpt(3),bn2.cpt(3),
              captions=["a CPT in bn","same CPT in bn2"])
positive_XraY
tuberculos_or_cancer
0
1
0
0.12940.8706
1
0.64320.3568
positive_XraY
tuberculos_or_cancer
0
1
0
0.32680.6732
1
0.47500.5250
a CPT in bn
same CPT in bn2

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': 3.5334226057915172, 'errorPQ': 0, 'klQP': 3.804626688797998, 'errorQP': 0, 'hellinger': 0.9706597739128149, 'bhattacharya': 0.6369373689326281, 'jensen-shannon': 0.5670603224871804}

If the models are not on the same domain :

In [7]:
bn_different_domain=gum.loadBN(os.path.join("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': 3.5338682003973254, 'errorPQ': 0, 'klQP': 4.887064860138977, 'errorQP': 0, 'hellinger': 1.0127656459867924, 'bhattacharya': 0.6421770463909514, 'jensen-shannon': 0.6087254578230213}
Computed in 2.9957697910000003 s
In [10]:
print("--")

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

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

p=plot(g.history(), 'g')
--
stopped with epsilon=1e-07
--
Temps de calcul : 2.9957697910000003
Nombre d'itérations : 280500

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 [11]:
g=gum.GibbsBNdistance(bn,bn2)
g.setMaxTime(60)
g.setBurnIn(500)
g.setEpsilon(1e-7)
g.setPeriodSize(5000)
In [12]:
gnb.animApproximationScheme(g) # logarithmique scale for Y
g.compute()
Out[12]:
{'klPQ': 3.4374371861784785,
 'errorPQ': 0,
 'klQP': 5.785218169606545,
 'errorQP': 0,
 'hellinger': 1.0580719218321788,
 'bhattacharya': 0.5981594081753325,
 'jensen-shannon': 0.6623024068615122}
In [ ]: