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
In [1]:
import pyagrum as gum
import pyagrum.lib.notebook as gnb
In [2]:
bn = gum.fastBN("A->B->C<-D->E->F<-B")
gnb.flow.row(bn, gnb.getInference(bn))
Out[2]:
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.
In [3]:
cr = gum.CredalNet(bn, bn)
gnb.show(cr)
In [4]:
cr.bnToCredal(1e-10, False, False)
In [5]:
cr.computeBinaryCPTMinMax()
In [6]:
print(cr)
A:Range([0,1])
<> : [[0.34704 , 0.65296] , [0.0358161 , 0.964184]]
B:Range([0,1])
<A:0> : [[0.400207 , 0.599793] , [0.399775 , 0.600225]]
<A:1> : [[0.205351 , 0.794649] , [0.0845036 , 0.915496]]
C:Range([0,1])
<B:0|D:0> : [[0.188767 , 0.811233] , [0.157735 , 0.842265]]
<B:1|D:0> : [[0.406522 , 0.593478] , [0.406133 , 0.593867]]
<B:0|D:1> : [[0.929882 , 0.0701182] , [0.00022317 , 0.999777]]
<B:1|D:1> : [[0.279502 , 0.720498] , [0.275908 , 0.724092]]
D:Range([0,1])
<> : [[0.767496 , 0.232504] , [0.767494 , 0.232506]]
E:Range([0,1])
<D:0> : [[0.859877 , 0.140123]]
<D:1> : [[0.195555 , 0.804445] , [0.0936299 , 0.90637]]
F:Range([0,1])
<E:0|B:0> : [[0.764658 , 0.235342] , [0.764656 , 0.235344]]
<E:1|B:0> : [[0.451128 , 0.548872] , [0.450938 , 0.549062]]
<E:0|B:1> : [[0.529168 , 0.470832] , [0.529112 , 0.470888]]
<E:1|B:1> : [[0.836577 , 0.163422]]
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.
In [7]:
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)
In [8]:
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()
In [ ]: