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.credal_net 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])
<> : [[0.55409 , 0.44591] , [0.554051 , 0.445949]]

B:Range([0,1])

<A:0> : [[0.805177 , 0.194823] , [0.805175 , 0.194825]] <A:1> : [[0.228426 , 0.771574] , [0.218254 , 0.781746]]

C:Range([0,1])

<B:0|D:0> : [[0.515819 , 0.484181] , [0.515749 , 0.484251]] <B:1|D:0> : [[0.446477 , 0.553523] , [0.446273 , 0.553727]] <B:0|D:1> : [[0.764305 , 0.235695] , [0.764303 , 0.235697]] <B:1|D:1> : [[0.636461 , 0.363539] , [0.636449 , 0.363551]]

D:Range([0,1])
<> : [[0.792033 , 0.207967] , [0.792032 , 0.207968]]

E:Range([0,1])

<D:0> : [[0.448349 , 0.551651] , [0.448151 , 0.551849]] <D:1> : [[0.379635 , 0.620365] , [0.379027 , 0.620973]]

F:Range([0,1])

<E:0|B:0> : [[0.440777 , 0.559223] , [0.440554 , 0.559446]] <E:1|B:0> : [[0.577948 , 0.422052] , [0.577921 , 0.422079]] <E:0|B:1> : [[0.558909 , 0.441091] , [0.558873 , 0.441127]] <E:1|B:1> : [[0.675147 , 0.324853] , [0.67514 , 0.32486]]

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