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 [linux] |
| Python | 3.10.10 (main, Mar 5 2023, 22:26:53) [GCC 12.2.1 20230201] |
| IPython | 8.13.2 |
| Matplotlib | 3.7.1 |
| Numpy | 1.24.3 |
| pyDot | 1.4.2 |
| pyAgrum | 1.8.1 |
Wed May 24 14:52:21 2023 CEST
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"])
|
|
|
| |
|---|---|---|---|
| 0.6212 | 0.0518 | 0.3270 | |
| 0.4700 | 0.2808 | 0.2492 | |
|
|
|
| |
|---|---|---|---|
| 0.6004 | 0.0311 | 0.3062 | |
| 0.4493 | 0.2600 | 0.2284 | |
|
|
|
| |
|---|---|---|---|
| 0.6419 | 0.0726 | 0.3477 | |
| 0.4908 | 0.3015 | 0.2699 | |
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])
<> : [[0.510773 , 0.489227] , [0.790333 , 0.209667]]
B:Range([0,2])
<A:0> : [[0.600444 , 0.0518454 , 0.347711] , [0.600444 , 0.0725846 , 0.326971] , [0.621182 , 0.0725846 , 0.306233] , [0.641921 , 0.0518455 , 0.306233] , [0.621182 , 0.031107 , 0.347711] , [0.641921 , 0.031107 , 0.326972]]
<A:1> : [[0.449309 , 0.280784 , 0.269907] , [0.449309 , 0.301523 , 0.249168] , [0.470046 , 0.301523 , 0.228431] , [0.490786 , 0.280783 , 0.228431] , [0.470046 , 0.260047 , 0.269907] , [0.490786 , 0.260047 , 0.249167]]
C:Range([0,1])
<B:0|D:0> : [[0.43335 , 0.56665] , [0.579348 , 0.420652]]
<B:1|D:0> : [[0.744503 , 0.255497] , [0.890501 , 0.109499]]
<B:2|D:0> : [[0.687504 , 0.312496] , [0.833503 , 0.166497]]
<B:0|D:1> : [[0.453807 , 0.546193] , [0.599804 , 0.400196]]
<B:1|D:1> : [[0.603533 , 0.396467] , [0.749531 , 0.250469]]
<B:2|D:1> : [[0.202389 , 0.797611] , [0.348387 , 0.651613]]
D:Range([0,1])
<A:0> : [[0.720952 , 0.279048] , [0.792616 , 0.207384]]
<A:1> : [[0.0537482 , 0.946252] , [0.125413 , 0.874587]]
E:Range([0,1])
<A:0> : [[0.0782698 , 0.92173] , [0.18263 , 0.81737]]
<A:1> : [[0.648741 , 0.351259] , [0.7531 , 0.2469]]
F:Range([0,1])
<E:0> : [[0.647705 , 0.352295] , [0.686324 , 0.313676]]
<E:1> : [[0.0289655 , 0.971034] , [0.0675862 , 0.932414]]
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"))
(13.796595328550666, 11.864395265918771, 12.015629955123197, 12.007631081945778, 11.965797424106215, 11.964926735931694, 11.965025343870192, 11.965014533608835, 11.965015735850175)
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()
