Credal Networks¶

In [1]:

import os

%matplotlib inline
from pylab import *
import matplotlib.pyplot as plt

In [2]:

import pyAgrum as gum
import pyAgrum.lib.notebook as gnb
gnb.configuration()

Library	Version
OS	posix [linux]
Python	3.10.10 (main, Mar 5 2023, 22:26:53) [GCC 12.2.1 20230201]
IPython	8.13.2
Matplotlib	3.7.1
Numpy	1.24.3
pyDot	1.4.2
pyAgrum	1.8.1

Wed May 24 14:52:21 2023 CEST

Credal Net from BN¶

In [3]:

bn=gum.fastBN("A->B[3]->C<-D<-A->E->F")
bn_min=gum.BayesNet(bn)
bn_max=gum.BayesNet(bn)
for n in bn.nodes():
  x=0.4*min(bn.cpt(n).min(),1-bn.cpt(n).max())
  bn_min.cpt(n).translate(-x)
  bn_max.cpt(n).translate(x)
    
cn=gum.CredalNet(bn_min,bn_max)
cn.intervalToCredal()

gnb.flow.row(bn,bn.cpt("B"),cn,bn_min.cpt("B"),bn_max.cpt("B"),captions=["Bayes Net","CPT","Credal Net","CPTmin","CPTmax"])

Bayes Net

	B
A	0	1	2
0	0.6212	0.0518	0.3270
1	0.4700	0.2808	0.2492

CPT

Credal Net

	B
A	0	1	2
0	0.6004	0.0311	0.3062
1	0.4493	0.2600	0.2284

CPTmin

	B
A	0	1	2
0	0.6419	0.0726	0.3477
1	0.4908	0.3015	0.2699

CPTmax

We can use LBP on CN (L2U) only for binary credal networks (here B is not binary). We then propose the classical binarization (but warn the user that this leads to approximation in the inference)¶

In [4]:

cn2=gum.CredalNet(bn_min,bn_max)
cn2.intervalToCredal()
cn2.approximatedBinarization()
cn2.computeBinaryCPTMinMax()

gnb.flow.row(cn,cn2,captions=["Credal net","Binarized credal net"])

Credal net

Binarized credal net

Here, $B$ becomes

$B$-b$i$ : the $i$-th bit of B
instrumental $B$-v$k$ : the indicator variable for each modality $k$ of $B$

In [5]:

ie_mc=gum.CNMonteCarloSampling(cn)
ie2_lbp=gum.CNLoopyPropagation(cn2)
ie2_mc=gum.CNMonteCarloSampling(cn2)

In [6]:

gnb.sideBySide(gnb.getInference(cn,engine=ie_mc),
               gnb.getInference(cn2,engine=ie2_mc),
               gnb.getInference(cn2,engine=ie2_lbp))

In [7]:

gnb.sideBySide(ie_mc.CN(),ie_mc.marginalMin("F"),ie_mc.marginalMax("F"),
               ie_mc.CN(),ie2_lbp.marginalMin("F"),ie2_lbp.marginalMax("F"),
              ncols=3)
print(cn)

F
0	1
0.1514	0.6467

F
0	1
0.3533	0.8486

F
0	1
0.1514	0.6467

F
0	1
0.3533	0.8486

A:Range([0,1])
<> : [[0.510773 , 0.489227] , [0.790333 , 0.209667]]

B:Range([0,2])
<A:0> : [[0.600444 , 0.0518454 , 0.347711] , [0.600444 , 0.0725846 , 0.326971] , [0.621182 , 0.0725846 , 0.306233] , [0.641921 , 0.0518455 , 0.306233] , [0.621182 , 0.031107 , 0.347711] , [0.641921 , 0.031107 , 0.326972]]
<A:1> : [[0.449309 , 0.280784 , 0.269907] , [0.449309 , 0.301523 , 0.249168] , [0.470046 , 0.301523 , 0.228431] , [0.490786 , 0.280783 , 0.228431] , [0.470046 , 0.260047 , 0.269907] , [0.490786 , 0.260047 , 0.249167]]

C:Range([0,1])
<B:0|D:0> : [[0.43335 , 0.56665] , [0.579348 , 0.420652]]
<B:1|D:0> : [[0.744503 , 0.255497] , [0.890501 , 0.109499]]
<B:2|D:0> : [[0.687504 , 0.312496] , [0.833503 , 0.166497]]
<B:0|D:1> : [[0.453807 , 0.546193] , [0.599804 , 0.400196]]
<B:1|D:1> : [[0.603533 , 0.396467] , [0.749531 , 0.250469]]
<B:2|D:1> : [[0.202389 , 0.797611] , [0.348387 , 0.651613]]

D:Range([0,1])
<A:0> : [[0.720952 , 0.279048] , [0.792616 , 0.207384]]
<A:1> : [[0.0537482 , 0.946252] , [0.125413 , 0.874587]]

E:Range([0,1])
<A:0> : [[0.0782698 , 0.92173] , [0.18263 , 0.81737]]
<A:1> : [[0.648741 , 0.351259] , [0.7531 , 0.2469]]

F:Range([0,1])
<E:0> : [[0.647705 , 0.352295] , [0.686324 , 0.313676]]
<E:1> : [[0.0289655 , 0.971034] , [0.0675862 , 0.932414]]

Credal Net from bif files¶

In [8]:

cn=gum.CredalNet("res/cn/2Umin.bif","res/cn/2Umax.bif")
cn.intervalToCredal()

In [9]:

gnb.showCN(cn,"2")

In [10]:

ie=gum.CNMonteCarloSampling(cn)
ie.insertEvidenceFile("res/cn/L2U.evi")

In [11]:

ie.setRepetitiveInd(False)
ie.setMaxTime(1)
ie.setMaxIter