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 [darwin]
Python	3.12.2 (main, Feb 6 2024, 20:19:44) [Clang 15.0.0 (clang-1500.1.0.2.5)]
IPython	8.22.2
Matplotlib	3.8.3
Numpy	1.26.4
pyDot	2.0.0
pyAgrum	1.12.1.9

Thu Mar 21 11:31:29 2024 CET

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	0.2357	0.3102	0.4541
1	0.3343	0.2743	0.3914

CPT

Credal Net

	B
A	0	1	2
0	0.1414	0.2160	0.3598
1	0.2400	0.1800	0.2971

CPTmin

	B
A	0	1	2
0	0.3300	0.4045	0.5483
1	0.4286	0.3686	0.4857

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
0.5880	0.2181

F
0	1
0.7819	0.4120

F
0	1
0.5880	0.2181

F
0	1
0.7819	0.4120


A:Range([0,1])
<> : [[0.939668 , 0.0603318] , [0.974144 , 0.025856]]

B:Range([0,2])
<A:0> : [[0.141425 , 0.310241 , 0.548333] , [0.141425 , 0.404525 , 0.45405] , [0.235707 , 0.404525 , 0.359768] , [0.329992 , 0.31024 , 0.359768] , [0.235709 , 0.215957 , 0.548333] , [0.329992 , 0.215957 , 0.454051]]
<A:1> : [[0.23999 , 0.274298 , 0.485712] , [0.23999 , 0.36858 , 0.39143] , [0.334273 , 0.36858 , 0.297147] , [0.428557 , 0.274296 , 0.297147] , [0.334275 , 0.180013 , 0.485712] , [0.428557 , 0.180013 , 0.39143]]

C:Range([0,1])
<B:0|D:0> : [[0.175729 , 0.824271] , [0.402498 , 0.597502]]
<B:1|D:0> : [[0.259334 , 0.740666] , [0.486101 , 0.513899]]
<B:2|D:0> : [[0.250533 , 0.749467] , [0.477301 , 0.522699]]
<B:0|D:1> : [[0.495322 , 0.504678] , [0.72209 , 0.27791]]
<B:1|D:1> : [[0.170075 , 0.829925] , [0.396843 , 0.603157]]
<B:2|D:1> : [[0.566174 , 0.433826] , [0.792943 , 0.207057]]

D:Range([0,1])
<A:0> : [[0.202312 , 0.797688] , [0.472062 , 0.527938]]
<A:1> : [[0.468855 , 0.531145] , [0.738604 , 0.261396]]

E:Range([0,1])
<A:0> : [[0.505796 , 0.494204] , [0.776852 , 0.223148]]
<A:1> : [[0.203291 , 0.796709] , [0.474348 , 0.525652]]

F:Range([0,1])
<E:0> : [[0.527326 , 0.472674] , [0.647423 , 0.352577]]
<E:1> : [[0.789832 , 0.210168] , [0.909928 , 0.0900716]]

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")

../_images/notebooks_24-Models_credalNetworks_14_0.svg

In [10]:

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

In [11]:

ie.setRepetitiveInd(False)
ie.setMaxTime(1)
ie.setMaxIter(1000)

ie.makeInference()

In [12]:

cn

Out[12]:

In [13]:

gnb.showInference(cn,targets={"A","H","L","D"},engine=ie,evs={"L":[0,1],"G":[1,0]})

../_images/notebooks_24-Models_credalNetworks_18_0.svg

Comparing inference in credal networks

In [14]:

import pyAgrum as gum

def showDiffInference(model,mc,lbp):
    for i in model.current_bn().nodes():
        a,b=mc.marginalMin(i)[:]
        c,d=mc.marginalMax(i)[:]

        e,f=lbp.marginalMin(i)[:]
        g,h=lbp.marginalMax(i)[:]

        plt.scatter([a,b,c,d],[e,f,g,h])


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

The two inference give quite the same result

In [15]:

ie_mc=gum.CNMonteCarloSampling(cn)
ie_mc.makeInference()

cn.computeBinaryCPTMinMax()
ie_lbp=gum.CNLoopyPropagation(cn)
ie_lbp.makeInference()

showDiffInference(cn,ie_mc,ie_lbp)

../_images/notebooks_24-Models_credalNetworks_22_0.svg

but not when evidence are inserted

In [16]:

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

ie_lbp=gum.CNLoopyPropagation(cn)
ie_lbp.insertEvidenceFile("res/cn/L2U.evi")
ie_lbp.makeInference()

showDiffInference(cn,ie_mc,ie_lbp)

../_images/notebooks_24-Models_credalNetworks_24_0.svg

Dynamical Credal Net

In [17]:

cn=gum.CredalNet("res/cn/bn_c_8.bif","res/cn/den_c_8.bif")
cn.bnToCredal(0.8,False)

In [18]:

ie=gum.CNMonteCarloSampling(cn)
ie.insertModalsFile("res/cn/modalities.modal")

ie.setRepetitiveInd(True)
ie.setMaxTime(5)
ie.setMaxIter(1000)

ie.makeInference()

In [19]:

print(ie.dynamicExpMax("temp"))

(14.203404648293022, 11.911090684366485, 12.048452518236164, 12.031555584857191, 12.003107180947513, 12.007979271958872, 12.007860641421736, 12.007652604938034, 12.007725006693335)

In [20]:

fig=figure()
ax=fig.add_subplot(111)
ax.fill_between(range(9),ie.dynamicExpMax("temp"),ie.dynamicExpMin("temp"))
plt.show()

../_images/notebooks_24-Models_credalNetworks_29_0.svg

In [21]:

ie=gum.CNMonteCarloSampling(cn)
ie.insertModalsFile("res/cn/modalities.modal")

ie.setRepetitiveInd(False)
ie.setMaxTime(5)
ie.setMaxIter(1000)

ie.makeInference()
print(ie.messageApproximationScheme())

stopped with epsilon=0

In [22]:

fig=figure()
ax=fig.add_subplot(111)
ax.fill_between(range(9),ie.dynamicExpMax("temp"),ie.dynamicExpMin("temp"))
plt.show()

../_images/notebooks_24-Models_credalNetworks_31_0.svg

In [25]:

ie=gum.CNMonteCarloSampling(cn)
ie.insertModalsFile("res/cn/modalities.modal")

ie.setRepetitiveInd(False)
ie.setMaxTime(5)
ie.setMaxIter(5000)

gnb.animApproximationScheme(ie)
ie.makeInference()

../_images/notebooks_24-Models_credalNetworks_32_0.svg

In [24]:

fig=figure()
ax=fig.add_subplot(111)
ax.fill_between(range(9),ie.dynamicExpMax("temp"),ie.dynamicExpMin("temp"));
plt.show()

../_images/notebooks_24-Models_credalNetworks_33_0.svg