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"])
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0.2357 | 0.3102 | 0.4541 | |
0.3343 | 0.2743 | 0.3914 |
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0.1414 | 0.2160 | 0.3598 | |
0.2400 | 0.1800 | 0.2971 |
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0.3300 | 0.4045 | 0.5483 | |
0.4286 | 0.3686 | 0.4857 |
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])
<> : [[0.939668 , 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")
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
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"))
(14.203404648293022, 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()
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 [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()
In [24]:
fig=figure()
ax=fig.add_subplot(111)
ax.fill_between(range(9),ie.dynamicExpMax("temp"),ie.dynamicExpMin("temp"));
plt.show()