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☰  ComparingBN 
pyAgrum 0.15.2   
Zipped notebooks   
generation: 2019-07-22 10:34  

Creative Commons License
This pyAgrum's notebook is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

In [1]:
def dict2html(di): 
    return "<br/>".join([f"<b>{k:15}</b>:{v}" for k,v in di.items()])
In [2]:
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 [3]:
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.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': 8, 'tn': 16, 'fp': 2, 'fn': 4}
recall :0.6666666666666666
precision :0.8
fscore :0.7272727272727272
dist2opt :0.38873012632302
B has different parents in the two bns whose names are in {'C'}
klPQ :2.1903126321313953
errorPQ :0
klQP :1.6807832970158665
errorQP :0
hellinger :0.751169430525294
bhattacharya :0.33146365985777043
jensen-shannon :0.3605123930126333
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 [4]:
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.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': 12, 'tn': 18, 'fp': 0, 'fn': 0}
recall :1.0
precision :1.0
fscore :1.0
dist2opt :0.0
Different CPTs for A
klPQ :2.207496158892435
errorPQ :0
klQP :2.853344351783943
errorQP :0
hellinger :0.8525268059240984
bhattacharya :0.4516152994943757
jensen-shannon :0.4599367533144224
bn1
bn2
graphical diff
Scores
equivalent ?
distances

identical BNs

In [5]:
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.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': 12, 'tn': 18, 'fp': 0, 'fn': 0}
recall :1.0
precision :1.0
fscore :1.0
dist2opt :0.0
OK
klPQ :0.0
errorPQ :0
klQP :0.0
errorQP :0
hellinger :0.0
bhattacharya :1.1102230246251565e-16
jensen-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.

In [ ]: