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 [darwin] |
| Python | 3.12.1 (main, Dec 7 2023, 20:45:44) [Clang 15.0.0 (clang-1500.1.0.2.5)] |
| IPython | 8.21.0 |
| Matplotlib | 3.8.2 |
| Numpy | 1.26.4 |
| pyDot | 2.0.0 |
| pyAgrum | 1.12.0 |
Wed Feb 14 15:37:38 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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| 0.3650 | 0.2330 | 0.4020 | |
| 0.2864 | 0.0581 | 0.6555 | |
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| 0.3418 | 0.2097 | 0.3788 | |
| 0.2632 | 0.0348 | 0.6323 | |
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| 0.3883 | 0.2562 | 0.4253 | |
| 0.3097 | 0.0813 | 0.6787 | |
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])
<> : [[0.24898 , 0.75102] , [0.580952 , 0.419048]]
B:Range([0,2])
<A:0> : [[0.341791 , 0.232951 , 0.425258] , [0.341791 , 0.256184 , 0.402025] , [0.365022 , 0.256184 , 0.378794] , [0.388254 , 0.232952 , 0.378794] , [0.365021 , 0.209721 , 0.425258] , [0.388254 , 0.209721 , 0.402025]]
<A:1> : [[0.263198 , 0.058079 , 0.678723] , [0.263198 , 0.0813124 , 0.65549] , [0.28643 , 0.0813124 , 0.632258] , [0.309661 , 0.0580805 , 0.632258] , [0.286428 , 0.0348485 , 0.678723] , [0.309661 , 0.0348485 , 0.65549]]
C:Range([0,1])
<B:0|D:0> : [[0.634417 , 0.365583] , [0.843322 , 0.156678]]
<B:1|D:0> : [[0.189608 , 0.810392] , [0.398513 , 0.601487]]
<B:2|D:0> : [[0.275986 , 0.724014] , [0.48489 , 0.51511]]
<B:0|D:1> : [[0.410443 , 0.589557] , [0.619348 , 0.380652]]
<B:1|D:1> : [[0.621969 , 0.378031] , [0.830872 , 0.169128]]
<B:2|D:1> : [[0.293712 , 0.706288] , [0.502618 , 0.497382]]
D:Range([0,1])
<A:0> : [[0.42238 , 0.57762] , [0.659359 , 0.340641]]
<A:1> : [[0.585288 , 0.414712] , [0.822266 , 0.177734]]
E:Range([0,1])
<A:0> : [[0.197551 , 0.802449] , [0.460952 , 0.539048]]
<A:1> : [[0.255723 , 0.744277] , [0.519126 , 0.480874]]
F:Range([0,1])
<E:0> : [[0.851237 , 0.148763] , [0.86346 , 0.13654]]
<E:1> : [[0.0091659 , 0.990834] , [0.0213876 , 0.978612]]
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"))
(14.203404648293022, 11.864395265918773, 12.173214728164902, 12.023367090540296, 11.942163246338595, 11.940030233983371, 11.946760975764684, 11.943947159943452, 11.943827275579622)
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()
