Quasi-continuous BN¶

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aGrUM cannot (currently) deal with with continuous variables. However, a discrete variable with a large enough domain size is an approximation of such variables.

In [1]:

import pyAgrum as gum
import pyAgrum.lib.notebook as gnb

#nbr of states for quasi continuous variables. You can change the value 
#but be careful of the quadratic behavior of both memory and time complexity
#in this example.
minB,maxB=-3,3
minC,maxC=4,14
NB=200

In [2]:

# the line with fastBN replace the commented ones.
#bn=gum.BayesNet()
#bn.add(gum.LabelizedVariable("A","A binary variable",2))
#bn.add(gum.NumericalDiscreteVariable("B","A range variable",minB,maxB,NB))
#bn.addArc("A","B")
bn=gum.fastBN(f"A[3]->B[{minB}:{maxB}:{NB}]")

gnb.showBN(bn)

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In [3]:

bn.cpt("A")[:]=[0.4, 0.1,0.5]
gnb.showProba(bn.cpt("A"))

CPT for quasi-continuous variables (with parents)¶

Using python (and scipy), it is easy to find pdf for continuous variable

In [4]:

from scipy.stats import norm,genhyperbolic

bn.cpt("B").fillFromDistribution(norm,loc="-2+A*2",scale="(5+A*4)/20")

gnb.flow.clear()
gnb.flow.add(gnb.getProba(bn.cpt("B").extract({"A":0})),caption="P(B|A=0)")
gnb.flow.add(gnb.getProba(bn.cpt("B").extract({"A":1})),caption="P(B|A=1)")
gnb.flow.add(gnb.getProba(bn.cpt("B").extract({"A":2})),caption="P(B|A=1)")
gnb.flow.display()

P(B|A=0)

P(B|A=1)

Quasi-continuous inference (with no evidence)¶

In [5]:

gnb.showPosterior(bn,target="B",evs={})
gnb.showInference(bn)

Quasi-continuous inference with numerical evidence expressed as logical propositions `evEq` or `evIn`,`evLt`, `evGt`; and boolean operators¶

In [6]:

gnb.showInference(bn,evs=[bn.evIn("B",-1,2)]) # we observed B between -1 and 2

In [7]:

gnb.showInference(bn,evs=[~ bn.evIn("B",-1,0)]) # we observed B not being between -1 and 0

In [8]:

gnb.showInference(bn,evs=[bn.evLt("B",1)]) # we observed B being less than 1

In [9]:

gnb.showInference(bn,evs=[bn.evEq("B",0) | 
                          bn.evEq("B",-2)]) # we observed B being -1 or 2

Quasi-continuous variable with quasi-continuous parent¶

In [10]:

bn=gum.fastBN("A[3]->B->C",
       f"[{minB}:{maxB}:{NB}]") # default type of variables (for B and C)
gnb.showBN(bn) # B and C are quasi-continouous

Even if this BN is quite small (and linear), the size of nodes $B$ et $C$ are rather big and creates a complex model (NBxNB parameters in $P(C|B)$).

In [11]:

print("nombre de paramètres du bn : {0}".format(bn.dim()))
print("domaine du bn : 10^{0}".format(bn.log10DomainSize()))

nombre de paramètres du bn : 40399
domaine du bn : 10^5.079181246047625

In [12]:

from scipy.stats import gamma

bn.cpt("B").fillFromDistribution(norm,loc="-2+A*2",scale="(5+A*4)/20")
bn.cpt("C").fillFromDistribution(gamma,a="B+3.1",loc=-3,scale=5)

def showCgivenBequals(x:float):
    gnb.flow.add(gnb.getProba(bn.cpt("C").extract({"B":f"{x}"})),
                 caption=f"P(C|B={x})")
gnb.flow.clear()
showCgivenBequals(0)
showCgivenBequals(3)
showCgivenBequals(-3)
#showB(NB-1)
gnb.flow.display()

P(C|B=0)

P(C|B=3)

P(C|B=-3)

Inference in quasi-continuous BN¶

In [13]:

import time

ts = time.time()
ie=gum.LazyPropagation(bn)
ie.makeInference()
q=ie.posterior("C")
te=time.time()
gnb.flow.add(gnb.getPosterior(bn,target="C",evs={}),caption=f"P(C) computed in {te-ts:2.5f} sec for a model with {bn.dim()} parameters")
gnb.flow.display()

P(C) computed in 0.00059 sec for a model with 40399 parameters

Changing prior¶

In [14]:

gnb.showInference(bn,size="10")