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 | nt [win32] |
| Python | 3.11.0 (main, Oct 24 2022, 18:26:48) [MSC v.1933 64 bit (AMD64)] |
| IPython | 8.6.0 |
| Matplotlib | 3.6.2 |
| Numpy | 1.23.4 |
| pyDot | 1.4.2 |
| pyAgrum | 1.4.1.9 |
Fri Nov 11 20:07:53 2022 Paris, Madrid
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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| 0.6467 | 0.1475 | 0.2057 | |
| 0.3166 | 0.1090 | 0.5744 | |
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| 0.6031 | 0.1040 | 0.1621 | |
| 0.2730 | 0.0654 | 0.5308 | |
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| 0.6903 | 0.1911 | 0.2493 | |
| 0.3602 | 0.1526 | 0.6180 | |
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:math:i : the \(i\)-th bit of B - instrumental \(B\)-v:math: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])
<> : [[0.0837589 , 0.916241] , [0.195435 , 0.804565]]
B:Range([0,2])
<A:0> : [[0.60315 , 0.147547 , 0.249304] , [0.60315 , 0.19114 , 0.20571] , [0.646745 , 0.19114 , 0.162115] , [0.690339 , 0.147547 , 0.162115] , [0.646744 , 0.103952 , 0.249304] , [0.690339 , 0.103952 , 0.20571]]
<A:1> : [[0.272995 , 0.108987 , 0.618018] , [0.272995 , 0.152582 , 0.574423] , [0.316589 , 0.152582 , 0.530829] , [0.360184 , 0.108987 , 0.530829] , [0.31659 , 0.0653924 , 0.618018] , [0.360184 , 0.0653924 , 0.574424]]
C:Range([0,1])
<B:0|D:0> : [[0.500982 , 0.499018] , [0.513663 , 0.486337]]
<B:1|D:0> : [[0.418886 , 0.581114] , [0.431566 , 0.568434]]
<B:2|D:0> : [[0.114657 , 0.885343] , [0.127336 , 0.872664]]
<B:0|D:1> : [[0.977811 , 0.0221893] , [0.990491 , 0.00950872]]
<B:1|D:1> : [[0.143169 , 0.856831] , [0.155849 , 0.844151]]
<B:2|D:1> : [[0.62924 , 0.37076] , [0.641919 , 0.358081]]
D:Range([0,1])
<A:0> : [[0.593434 , 0.406566] , [0.783228 , 0.216772]]
<A:1> : [[0.142344 , 0.857656] , [0.332139 , 0.667861]]
E:Range([0,1])
<A:0> : [[0.209976 , 0.790024] , [0.489943 , 0.510057]]
<A:1> : [[0.389381 , 0.610619] , [0.669348 , 0.330652]]
F:Range([0,1])
<E:0> : [[0.251754 , 0.748246] , [0.479112 , 0.520888]]
<E:1> : [[0.602119 , 0.397881] , [0.82948 , 0.17052]]
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, 11.769513762315974, 12.190483075680442, 12.017742181033096, 12.004198572496797, 12.008328195599265, 12.007694250617146, 12.007688078235907, 12.00772208700393)
In [20]:
fig=figure()
ax=fig.add_subplot(111)
ax.fill_between(range(9),ie.dynamicExpMax("temp"),ie.dynamicExpMin("temp"))
Out[20]:
<matplotlib.collections.PolyCollection at 0x215d5715110>
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"))
Out[22]:
<matplotlib.collections.PolyCollection at 0x215d54bfbd0>
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"));
In [ ]: