Credal Networks
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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 | 3.11.6 (main, Nov 14 2023, 09:36:21) [GCC 13.2.1 20230801] |
| IPython | 8.19.0 |
| Matplotlib | 3.8.2 |
| Numpy | 1.26.3 |
| pyDot | 2.0.0 |
| pyAgrum | 1.11.0 |
Fri Jan 05 18:24:26 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"])
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| 0.4097 | 0.2794 | 0.3109 | |
| 0.2952 | 0.3943 | 0.3105 | |
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| 0.2979 | 0.1677 | 0.1991 | |
| 0.1835 | 0.2825 | 0.1988 | |
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| 0.5214 | 0.3912 | 0.4227 | |
| 0.4070 | 0.5060 | 0.4223 | |
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"])
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)
A:Range([0,1])
<> : [[0.325834 , 0.674166] , [0.711073 , 0.288927]]
B:Range([0,2])
<A:0> : [[0.297909 , 0.279419 , 0.422671] , [0.297909 , 0.391187 , 0.310904] , [0.409675 , 0.391187 , 0.199138] , [0.521445 , 0.279417 , 0.199138] , [0.409678 , 0.167651 , 0.422671] , [0.521445 , 0.167651 , 0.310905]]
<A:1> : [[0.183463 , 0.394252 , 0.422285] , [0.183463 , 0.506018 , 0.31052] , [0.295232 , 0.506018 , 0.19875] , [0.406998 , 0.394252 , 0.19875] , [0.295232 , 0.282483 , 0.422285] , [0.406998 , 0.282483 , 0.310519]]
C:Range([0,1])
<B:0|D:0> : [[0.540373 , 0.459627] , [0.579779 , 0.420221]]
<B:1|D:0> : [[0.34266 , 0.65734] , [0.382066 , 0.617934]]
<B:2|D:0> : [[0.486233 , 0.513767] , [0.525641 , 0.474359]]
<B:0|D:1> : [[0.571805 , 0.428195] , [0.611212 , 0.388788]]
<B:1|D:1> : [[0.347976 , 0.652024] , [0.387381 , 0.612619]]
<B:2|D:1> : [[0.029554 , 0.970446] , [0.0689604 , 0.93104]]
D:Range([0,1])
<A:0> : [[0.305195 , 0.694805] , [0.569164 , 0.430836]]
<A:1> : [[0.197977 , 0.802023] , [0.461947 , 0.538053]]
E:Range([0,1])
<A:0> : [[0.504018 , 0.495982] , [0.508674 , 0.491326]]
<A:1> : [[0.991855 , 0.0081448] , [0.99651 , 0.0034904]]
F:Range([0,1])
<E:0> : [[0.659123 , 0.340877] , [0.853909 , 0.146091]]
<E:1> : [[0.341393 , 0.658607] , [0.536179 , 0.463821]]
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(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]})
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)
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)
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"))
(14.20340464862347, 11.671441990090813, 12.173214728164902, 11.954176229168535, 11.966313382958862, 11.964867852223103, 11.965031829300205, 11.965013837826506, 11.965015808981818)
In [20]:
fig=figure()
ax=fig.add_subplot(111)
ax.fill_between(range(9),ie.dynamicExpMax("temp"),ie.dynamicExpMin("temp"))
plt.show()
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()
In [23]:
ie=gum.CNMonteCarloSampling(cn)
ie.insertModalsFile("res/cn/modalities.modal")
ie.setRepetitiveInd(False)
ie.setMaxTime(5)
ie.setMaxIter(5000)
gnb.animApproximationScheme(ie)
ie.makeInference()
In [24]:
fig=figure()
ax=fig.add_subplot(111)
ax.fill_between(range(9),ie.dynamicExpMax("temp"),ie.dynamicExpMin("temp"));
plt.show()
