☰  ComparingBN
In :
def dict2html(di1,di2=None):
res= "<br/>".join([f"<b>{k:15}</b>:{v}" for k,v in di1.items()])
if di2 is not None:
res+="<br/><br/>"
res+= "<br/>".join([f"<b>{k:15}</b>:{v}" for k,v in di2.items()])
return res

In :
import pyAgrum as gum
import pyAgrum.lib.notebook as gnb
import pyAgrum.lib.bn_vs_bn as gcm


# How to compare two BNs¶

PyAgrum allows you to compare BNs in several ways. This notebook show you some of them:

• a graphical diff between the 2 BNs
• some scores form recal and precision
• distance measures (for more, see notebook 26-klForBNs for more)

## Between two different structures¶

In :
bn1=gum.fastBN("A->B->C->D->E<-A->F")
bn2=gum.fastBN("A->B<-C->D->E<-A;F->E")
cmp=gcm.GraphicalBNComparator(bn1,bn2)
kl=gum.ExactBNdistance(bn1,bn2) # bruteForce is possible car the BNs are small
gnb.sideBySide(bn1,bn2,gnb.getBNDiff(bn1,bn2),dict2html(cmp.scores(),cmp.hamming()),cmp.equivalentBNs(),dict2html(kl.compute()),
captions=['bn1','bn2','graphical diff','Scores','equivalent ?','distances'])

 G A A B B A->B E E A->E F F A->F C C B->C D D C->D D->E G A A B B A->B E E A->E C C C->B D D C->D D->E F F F->E G A A B B A->B E E A->E F F A->F C C C->B D D C->D D->E F->E count :{'tp': 4, 'tn': 22, 'fp': 2, 'fn': 2}recall :0.6666666666666666precision :0.6666666666666666fscore :0.6666666666666666dist2opt :0.47140452079103173hamming :2structural hamming:4 B has different parents in the two bns whose names are in {'C'} klPQ :3.4256934591002244errorPQ :0klQP :4.280798777973704errorQP :0hellinger :0.9949138002593297bhattacharya :0.6830517809688268jensen-shannon :0.5969293476303733 bn1 bn2 graphical diff Scores equivalent ? distances

The logic for the arcs of the graphical diff is the following. When comparaing bn1 with bn2 (in that order) :

• full black line: the arc is common for both
• full red line: the arc is common but inverted in bn2
• dotted black line: the arc is added in bn2
• dotted red line: the arc is removed in bn2

For the scores :

• precision and recall are computed considering BN1 as the reference
• $Fscore=\frac{2\cdot recall\cdot precision}{recall+precision}$ is the weighted average of Precision and Recall.
• $dist2opt=\sqrt{(1-precision)^2+(1-recall)^2}$ represents the euclidian distance to the ideal(precision=1,recall=1)

EquivalentBN return "OK" if equivalent or a reason for non equivalence

Finally, BruteForceKL compute in the same time several distances : I-projection, M-projection, Hellinger and Bhattacharya. For more complex BNs, there exists a GibbsKL to approximate those distances. Of course, the computation are much slower.

## Same structure, different parameters¶

In :
bn1=gum.fastBN("A->B->C->D->E<-A->F")
bn2=gum.fastBN("A->B->C->D->E<-A->F")
cmp=gcm.GraphicalBNComparator(bn1,bn2)
kl=gum.ExactBNdistance(bn1,bn2) # bruteForce is possible car the BNs are small
gnb.sideBySide(bn1,bn2,gnb.getBNDiff(bn1,bn2),dict2html(cmp.scores(),cmp.hamming()),cmp.equivalentBNs(),dict2html(kl.compute()),
captions=['bn1','bn2','graphical diff','Scores','equivalent ?','distances'])

 G A A B B A->B E E A->E F F A->F C C B->C D D C->D D->E G A A B B A->B E E A->E F F A->F C C B->C D D C->D D->E G A A B B A->B E E A->E F F A->F C C B->C D D C->D D->E count :{'tp': 6, 'tn': 24, 'fp': 0, 'fn': 0}recall :1.0precision :1.0fscore :1.0dist2opt :0.0hamming :0structural hamming:0 Different CPTs for A klPQ :4.982470589220756errorPQ :0klQP :6.46318241487143errorQP :0hellinger :1.1664417350478242bhattacharya :1.1403508300600567jensen-shannon :0.781625082460194 bn1 bn2 graphical diff Scores equivalent ? distances

## identical BNs¶

In :
bn1=gum.fastBN("A->B->C->D->E<-A->F")
bn2=bn1
cmp=gcm.GraphicalBNComparator(bn1,bn2)
kl=gum.ExactBNdistance(bn1,bn2) # bruteForce is possible car the BNs are small
gnb.sideBySide(bn1,bn2,gnb.getBNDiff(bn1,bn2),dict2html(cmp.scores(),cmp.hamming()),cmp.equivalentBNs(),dict2html(kl.compute()),
captions=['bn1','bn2','graphical diff','Scores','equivalent ?','distances'])

 G A A B B A->B E E A->E F F A->F C C B->C D D C->D D->E G A A B B A->B E E A->E F F A->F C C B->C D D C->D D->E G A A B B A->B E E A->E F F A->F C C B->C D D C->D D->E count :{'tp': 6, 'tn': 24, 'fp': 0, 'fn': 0}recall :1.0precision :1.0fscore :1.0dist2opt :0.0hamming :0structural hamming:0 OK klPQ :0.0errorPQ :0klQP :0.0errorQP :0hellinger :0.0bhattacharya :-0.0jensen-shannon :0.0 bn1 bn2 graphical diff Scores equivalent ? distances

In the notebook 15-DirichletPrior, you can find an interresting discussion on how can change those scores and distance.

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