Sensitivity analysis for Bayesian networks using credal networks
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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
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import pyAgrum as gum
import pyAgrum.lib.notebook as gnb
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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.
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cr=gum.CredalNet(bn,bn)
gnb.show(cr)
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cr.bnToCredal(beta=1e-10,oneNet=False)
cr.computeBinaryCPTMinMax()
print(cr)
A:Range([0,1])
<> : [[0.477627 , 0.522373] , [0.477502 , 0.522498]]
B:Range([0,1])
<A:0> : [[0.740112 , 0.259888] , [0.740109 , 0.259891]]
<A:1> : [[0.181894 , 0.818106] , [0.130161 , 0.869839]]
C:Range([0,1])
<B:0|D:0> : [[0.798963 , 0.201037] , [0.798962 , 0.201038]]
<B:1|D:0> : [[0.244341 , 0.755659] , [0.237128 , 0.762872]]
<B:0|D:1> : [[0.460758 , 0.539242] , [0.460595 , 0.539405]]
<B:1|D:1> : [[0.236403 , 0.763597] , [0.227867 , 0.772133]]
D:Range([0,1])
<> : [[0.403444 , 0.596556] , [0.403034 , 0.596966]]
E:Range([0,1])
<D:0> : [[0.640627 , 0.359373] , [0.640616 , 0.359384]]
<D:1> : [[0.245979 , 0.754021] , [0.239006 , 0.760994]]
F:Range([0,1])
<E:0|B:0> : [[0.695332 , 0.304668] , [0.695327 , 0.304673]]
<E:1|B:0> : [[0.420242 , 0.579758] , [0.419931 , 0.580069]]
<E:0|B:1> : [[0.352903 , 0.647097] , [0.351943 , 0.648057]]
<E:1|B:1> : [[0.501186 , 0.498814] , [0.501099 , 0.498901]]
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.
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def showNoisy(bn,beta):
cr=gum.CredalNet(bn,bn)
cr.bnToCredal(beta=beta,oneNet=False)
cr.computeBinaryCPTMinMax()
ielbp=gum.CNLoopyPropagation(cr)
return gnb.getInference(cr,engine=ielbp)
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for eps in [1,1e-3,1e-5,1e-8,1e-10]:
gnb.flow.add(showNoisy(bn,eps),caption=f"noise={eps}")
gnb.flow.display()
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