Sensitivity analysis for Bayesian networks using credal networks

There are several sensitivity analysis frameworks for Bayesian networks. A fairly efficient method is certainly to use credal networks to do this analysis.

Creating a Bayesian network

import pyagrum as gum
import pyagrum.lib.notebook as gnb

bn = gum.fastBN("A->B->C<-D->E->F<-B")
gnb.flow.row(bn, gnb.getInference(bn))

Building a credal network from a BN

It is easy to build a credal network from a Bayesian network by indicating the ‘noise’ on each parameter.

cr = gum.CredalNet(bn, bn)
gnb.show(cr)

cr.bnToCredal(1e-10, False, False)

cr.computeBinaryCPTMinMax()

print(cr)

A:Range([0,1])
<> : [[0.55286 , 0.44714] , [0.552821 , 0.447179]]

B:Range([0,1])

<A:0> : [[0.403363 , 0.596637] , [0.402953 , 0.597047]] <A:1> : [[0.55775 , 0.44225] , [0.557714 , 0.442286]]

C:Range([0,1])

<B:0|D:0> : [[0.189192 , 0.810808] , [0.102062 , 0.897938]] <B:1|D:0> : [[0.481363 , 0.518637] , [0.0182525 , 0.981748]] <B:0|D:1> : [[0.526098 , 0.473902] , [0.526039 , 0.473961]] <B:1|D:1> : [[0.37199 , 0.62801] , [0.371297 , 0.628703]]

D:Range([0,1])
<> : [[0.185717 , 0.814283] , [0.149711 , 0.850289]]

E:Range([0,1])

<D:0> : [[0.699161 , 0.300839] , [0.699156 , 0.300844]] <D:1> : [[0.710072 , 0.289928] , [0.00449306 , 0.995507]]

F:Range([0,1])

<E:0|B:0> : [[0.659403 , 0.340597] , [0.659394 , 0.340606]] <E:1|B:0> : [[0.490903 , 0.509097] , [0.490801 , 0.509199]] <E:0|B:1> : [[0.237246 , 0.762754] , [0.228863 , 0.771137]] <E:1|B:1> : [[0.36149 , 0.63851] , [0.360662 , 0.639338]]

Testing difference hypothesis about the global precision on the parameters

We can therefore easily conduct a sensitivity analysis based on an assumption of error on all the parameters of the network.

def showNoisy(bn, beta):
  cr = gum.CredalNet(bn, bn)
  cr.bnToCredal(beta, False, False)
  cr.computeBinaryCPTMinMax()
  ielbp = gum.CNLoopyPropagation(cr)
  return gnb.getInference(cr, engine=ielbp)

for eps in [1, 1e-1, 1e-2, 1e-3, 1e-10]:
  gnb.flow.add(showNoisy(bn, eps), caption=f"noise={eps}")
gnb.flow.display()

noise=1

noise=0.1

noise=0.01

noise=0.001

noise=1e-10