Probablistic Inference with pyAgrum

Creative Commons License

aGrUM

interactive online version

In this notebook, we will show different basic features for probabilistic inference on Bayesian networks using pyAgrum.

First we need some external modules:

In [1]:

import os

%matplotlib inline
from pylab import *
import matplotlib.pyplot as plt

Basic inference and display

Then we import pyAgrum and the pyAgrum’s notebook module, that offers very usefull methods when writting a notebook.

This first example shows how you can load a BayesNet and show it as graph. Note that pyAgrum handles serveral BayesNet file format such as DSL, BIF and UAI.

In [2]:

import pyAgrum as gum
import pyAgrum.lib.notebook as gnb
bn=gum.loadBN("res/alarm.dsl")
gnb.showBN(bn,size="9")
../_images/notebooks_41-Inference_graphicalInference_5_0.svg

From there, it is easy to get a posterior using an inference engine :

In [3]:

ie=gum.LazyPropagation(bn)
ie.makeInference()
print(ie.posterior(bn.idFromName("CATECHOL")))


  CATECHOL         |
NORMAL   |HIGH     |
---------|---------|
 0.0512  | 0.9488  |

But since we are in notebook, why not use pyAgrum notebook’s methods ?

In [4]:

gnb.showPosterior(bn,evs={},target='CATECHOL')
../_images/notebooks_41-Inference_graphicalInference_9_0.svg

You may also want to see the graph with some posteriors

In [5]:

# due to matplotlib, format is forced to png.
gnb.showInference(bn,evs={},targets={"VENTALV","CATECHOL","HR","MINVOLSET"},size="11")
../_images/notebooks_41-Inference_graphicalInference_11_0.svg
In [6]:

gnb.showInference(bn,
                  evs={"CO":1,"VENTLUNG":1},
                  targets={"VENTALV",
                           "CATECHOL",
                           "HR",
                           "MINVOLSET",
                           "ANAPHYLAXIS",
                           "STROKEVOLUME",
                           "ERRLOWOUTPUT",
                           "HBR",
                           "PULMEMBOLUS",
                           "HISTORY",
                           "BP",
                           "PRESS",
                           "CO"},
                  size="10")
../_images/notebooks_41-Inference_graphicalInference_13_0.svg

You can even compute all posteriors by leaving the targets parameter empty (which is its default value).

In [7]:

gnb.showInference(bn,evs={"CO":1,"VENTLUNG":1},size="14")
../_images/notebooks_41-Inference_graphicalInference_15_0.svg

Showing the information graph

To have a global view of the knowledge brought by the inference, you can also draw the entropy of all nodes

In [8]:

import pyAgrum.lib.explain as explain
explain.showInformation(bn,{},size="14")
G ARTCO2 ARTCO2 EXPCO2 EXPCO2 ARTCO2->EXPCO2 CATECHOL CATECHOL ARTCO2->CATECHOL HISTORY HISTORY HYPOVOLEMIA HYPOVOLEMIA STROKEVOLUME STROKEVOLUME HYPOVOLEMIA->STROKEVOLUME LVEDVOLUME LVEDVOLUME HYPOVOLEMIA->LVEDVOLUME VENTLUNG VENTLUNG VENTLUNG->EXPCO2 VENTALV VENTALV VENTLUNG->VENTALV MINVOL MINVOL VENTLUNG->MINVOL HRBP HRBP ERRLOWOUTPUT ERRLOWOUTPUT ERRLOWOUTPUT->HRBP KINKEDTUBE KINKEDTUBE KINKEDTUBE->VENTLUNG PRESS PRESS KINKEDTUBE->PRESS MINVOLSET MINVOLSET VENTMACH VENTMACH MINVOLSET->VENTMACH SHUNT SHUNT SAO2 SAO2 SHUNT->SAO2 HR HR HR->HRBP CO CO HR->CO HREKG HREKG HR->HREKG HRSAT HRSAT HR->HRSAT STROKEVOLUME->CO PULMEMBOLUS PULMEMBOLUS PULMEMBOLUS->SHUNT PAP PAP PULMEMBOLUS->PAP VENTTUBE VENTTUBE VENTTUBE->VENTLUNG VENTTUBE->PRESS ERRCAUTER ERRCAUTER ERRCAUTER->HREKG ERRCAUTER->HRSAT PVSAT PVSAT PVSAT->SAO2 VENTMACH->VENTTUBE BP BP CO->BP CATECHOL->HR VENTALV->ARTCO2 VENTALV->PVSAT SAO2->CATECHOL LVFAILURE LVFAILURE LVFAILURE->HISTORY LVFAILURE->STROKEVOLUME LVFAILURE->LVEDVOLUME DISCONNECT DISCONNECT DISCONNECT->VENTTUBE INTUBATION INTUBATION INTUBATION->VENTLUNG INTUBATION->SHUNT INTUBATION->VENTALV INTUBATION->MINVOL INTUBATION->PRESS INSUFFANESTH INSUFFANESTH INSUFFANESTH->CATECHOL TPR TPR TPR->BP TPR->CATECHOL ANAPHYLAXIS ANAPHYLAXIS ANAPHYLAXIS->TPR CVP CVP LVEDVOLUME->CVP PCWP PCWP LVEDVOLUME->PCWP FIO2 FIO2 FIO2->PVSAT

… and then observe the impact of an evidence on the whole bayes network :

In [9]:

explain.showInformation(bn,{"CO":0},size="9")
G ARTCO2 ARTCO2 EXPCO2 EXPCO2 ARTCO2->EXPCO2 CATECHOL CATECHOL ARTCO2->CATECHOL HISTORY HISTORY HYPOVOLEMIA HYPOVOLEMIA STROKEVOLUME STROKEVOLUME HYPOVOLEMIA->STROKEVOLUME LVEDVOLUME LVEDVOLUME HYPOVOLEMIA->LVEDVOLUME VENTLUNG VENTLUNG VENTLUNG->EXPCO2 VENTALV VENTALV VENTLUNG->VENTALV MINVOL MINVOL VENTLUNG->MINVOL HRBP HRBP ERRLOWOUTPUT ERRLOWOUTPUT ERRLOWOUTPUT->HRBP KINKEDTUBE KINKEDTUBE KINKEDTUBE->VENTLUNG PRESS PRESS KINKEDTUBE->PRESS MINVOLSET MINVOLSET VENTMACH VENTMACH MINVOLSET->VENTMACH SHUNT SHUNT SAO2 SAO2 SHUNT->SAO2 HR HR HR->HRBP CO CO HR->CO HREKG HREKG HR->HREKG HRSAT HRSAT HR->HRSAT STROKEVOLUME->CO PULMEMBOLUS PULMEMBOLUS PULMEMBOLUS->SHUNT PAP PAP PULMEMBOLUS->PAP VENTTUBE VENTTUBE VENTTUBE->VENTLUNG VENTTUBE->PRESS ERRCAUTER ERRCAUTER ERRCAUTER->HREKG ERRCAUTER->HRSAT PVSAT PVSAT PVSAT->SAO2 VENTMACH->VENTTUBE BP BP CO->BP CATECHOL->HR VENTALV->ARTCO2 VENTALV->PVSAT SAO2->CATECHOL LVFAILURE LVFAILURE LVFAILURE->HISTORY LVFAILURE->STROKEVOLUME LVFAILURE->LVEDVOLUME DISCONNECT DISCONNECT DISCONNECT->VENTTUBE INTUBATION INTUBATION INTUBATION->VENTLUNG INTUBATION->SHUNT INTUBATION->VENTALV INTUBATION->MINVOL INTUBATION->PRESS INSUFFANESTH INSUFFANESTH INSUFFANESTH->CATECHOL TPR TPR TPR->BP TPR->CATECHOL ANAPHYLAXIS ANAPHYLAXIS ANAPHYLAXIS->TPR CVP CVP LVEDVOLUME->CVP PCWP PCWP LVEDVOLUME->PCWP FIO2 FIO2 FIO2->PVSAT

Exploring the junction tree

Lazy Propagation, like several other inference algorithms, uses a junction tree to propagate information.

You can show the junction tree used by Lazy Propagation with pyAgrum:

In [10]:

jt=ie.junctionTree()
gnb.showJunctionTree(bn,size="12")
../_images/notebooks_41-Inference_graphicalInference_21_0.svg
In [11]:

# another representation of the junction, more convenient for investigating the flow of data in the jt
# the size/width of cliques and separators are proportionnal to the number of nodes in the factor.
jt.map()

Out[11]:
G 0 0~16 0--0~16 1 1~32 1--1~32 2 2~33 2--2~33 3 3~4 3--3~4 4 4~22 4--4~22 5 5~22 5--5~22 6 6~23 6--6~23 7 7~26 7--7~26 8 8~17 8--8~17 10 10~14 10--10~14 11 11~16 11--11~16 12 12~13 12--12~13 13 13~30 13--13~30 14 14~26 14--14~26 16 16~17 16--16~17 17 17~24 17--17~24 19 19~27 19--19~27 20 20~33 20--20~33 22 22~33 22--22~33 23 23~27 23--23~27 23~31 23--23~31 24 24~26 24--24~26 26 26~27 26--26~27 27 30 30~31 30--30~31 31 31~32 31--31~32 32 32~33 32--32~33 33 19~27--27 12~13--13 2~33--33 23~27--27 22~33--33 11~16--16 24~26--26 31~32--32 10~14--14 26~27--27 13~30--30 5~22--22 7~26--26 20~33--33 16~17--17 32~33--33 23~31--31 8~17--17 1~32--32 3~4--4 4~22--22 17~24--24 14~26--26 30~31--31 6~23--23 0~16--16

Introspection in junction trees

One can easily walk through the junction tree.

In [12]:

for n in jt.nodes():
    print([bn.variable(n).name() for n in jt.clique(n)])

['CVP', 'LVEDVOLUME']
['FIO2', 'VENTALV', 'PVSAT']
['ARTCO2', 'EXPCO2', 'VENTLUNG']
['VENTMACH', 'MINVOLSET']
['VENTMACH', 'DISCONNECT', 'VENTTUBE']
['PRESS', 'KINKEDTUBE', 'INTUBATION', 'VENTTUBE']
['ANAPHYLAXIS', 'TPR']
['HRBP', 'ERRLOWOUTPUT', 'HR']
['LVFAILURE', 'HISTORY']
['HREKG', 'HR', 'ERRCAUTER']
['PCWP', 'LVEDVOLUME']
['PAP', 'PULMEMBOLUS']
['SHUNT', 'INTUBATION', 'PULMEMBOLUS']
['HRSAT', 'HR', 'ERRCAUTER']
['LVFAILURE', 'HYPOVOLEMIA', 'LVEDVOLUME']
['HYPOVOLEMIA', 'STROKEVOLUME', 'LVFAILURE']
['CO', 'BP', 'TPR']
['INTUBATION', 'VENTLUNG', 'MINVOL']
['KINKEDTUBE', 'INTUBATION', 'VENTTUBE', 'VENTLUNG']
['INSUFFANESTH', 'TPR', 'ARTCO2', 'SAO2', 'CATECHOL']
['CO', 'STROKEVOLUME', 'HR']
['CO', 'CATECHOL', 'HR']
['CO', 'TPR', 'CATECHOL']
['INTUBATION', 'SHUNT', 'PVSAT', 'SAO2']
['INTUBATION', 'ARTCO2', 'PVSAT', 'SAO2']
['ARTCO2', 'VENTALV', 'INTUBATION', 'PVSAT']
['VENTALV', 'INTUBATION', 'ARTCO2', 'VENTLUNG']

In [13]:

for e in jt.edges():
    print(f"Separator for {e} : {jt.clique(e[0]).intersection(jt.clique(e[1]))}")

Separator for (13, 30) : {18, 2}
Separator for (2, 33) : {26, 22}
Separator for (3, 4) : {16}
Separator for (26, 27) : {34, 30}
Separator for (7, 26) : {31}
Separator for (12, 13) : {4}
Separator for (31, 32) : {27, 26, 2}
Separator for (23, 31) : {26, 28}
Separator for (5, 22) : {0, 2, 20}
Separator for (17, 24) : {13}
Separator for (19, 27) : {34, 14}
Separator for (24, 26) : {34, 31}
Separator for (32, 33) : {25, 2, 26}
Separator for (6, 23) : {14}
Separator for (23, 27) : {14, 30}
Separator for (11, 16) : {15}
Separator for (10, 14) : {7, 31}
Separator for (8, 17) : {9}
Separator for (0, 16) : {15}
Separator for (1, 32) : {25, 27}
Separator for (20, 33) : {2, 22}
Separator for (4, 22) : {20}
Separator for (14, 26) : {31}
Separator for (22, 33) : {2, 22}
Separator for (30, 31) : {2, 27, 28}
Separator for (16, 17) : {1, 9}

In [14]:

jt.hasRunningIntersection()

Out[14]:

True

Introspecting junction trees and friends

The junction tree created by a LazyPropagation is optimized for the query (see RelevanceReasonning notebook). But you can also introspect a junction tree directly from a BN or a graph using the JunctionTreeGenerator’s class.

In [15]:

bn=gum.fastBN("0->1->2<-3->4->5->6<-2->7")
jtg=gum.JunctionTreeGenerator()
gnb.sideBySide(bn,jtg.junctionTree(bn),jtg.eliminationOrder(bn),jtg.binaryJoinTree(bn),
              captions=["A Bayesien network",
                        "a junction tree for this BN",
                        "its elimination order",
                        "an (optimized) binary join tree"])
G 2 2 7 7 2->7 6 6 2->6 0 0 1 1 0->1 4 4 5 5 4->5 5->6 1->2 3 3 3->2 3->4
A Bayesien network
G (0) 2-5-6 2-5-6 (0) 2-5-6^(4) 2-3-5 2-5 (0) 2-5-6--(0) 2-5-6^(4) 2-3-5 (1) 2-7 2-7 (1) 2-7^(4) 2-3-5 2 (1) 2-7--(1) 2-7^(4) 2-3-5 (2) 0-1 0-1 (2) 0-1^(3) 1-2-3 1 (2) 0-1--(2) 0-1^(3) 1-2-3 (3) 1-2-3 1-2-3 (3) 1-2-3^(4) 2-3-5 2-3 (3) 1-2-3--(3) 1-2-3^(4) 2-3-5 (4) 2-3-5 2-3-5 (4) 2-3-5^(5) 3-4-5 3-5 (4) 2-3-5--(4) 2-3-5^(5) 3-4-5 (5) 3-4-5 3-4-5 (2) 0-1^(3) 1-2-3--(3) 1-2-3 (4) 2-3-5^(5) 3-4-5--(5) 3-4-5 (0) 2-5-6^(4) 2-3-5--(4) 2-3-5 (1) 2-7^(4) 2-3-5--(4) 2-3-5 (3) 1-2-3^(4) 2-3-5--(4) 2-3-5
a junction tree for this BN
[6, 7, 0, 1, 2, 3, 4, 5]
its elimination order
G (0) 2-5-6 2-5-6 (0) 2-5-6^(6) 2-5 2-5 (0) 2-5-6--(0) 2-5-6^(6) 2-5 (1) 2-7 2-7 (1) 2-7^(6) 2-5 2 (1) 2-7--(1) 2-7^(6) 2-5 (2) 0-1 0-1 (2) 0-1^(3) 1-2-3 1 (2) 0-1--(2) 0-1^(3) 1-2-3 (3) 1-2-3 1-2-3 (3) 1-2-3^(4) 2-3-5 2-3 (3) 1-2-3--(3) 1-2-3^(4) 2-3-5 (4) 2-3-5 2-3-5 (4) 2-3-5^(5) 3-4-5 3-5 (4) 2-3-5--(4) 2-3-5^(5) 3-4-5 (4) 2-3-5^(6) 2-5 2-5 (4) 2-3-5--(4) 2-3-5^(6) 2-5 (5) 3-4-5 3-4-5 (6) 2-5 2-5 (2) 0-1^(3) 1-2-3--(3) 1-2-3 (4) 2-3-5^(5) 3-4-5--(5) 3-4-5 (3) 1-2-3^(4) 2-3-5--(4) 2-3-5 (1) 2-7^(6) 2-5--(6) 2-5 (0) 2-5-6^(6) 2-5--(6) 2-5 (4) 2-3-5^(6) 2-5--(6) 2-5
an (optimized) binary join tree

junction tree from graphs (using uniform domainSize)

In [16]:

#creating a dag slightly different
dag=bn.dag()
dag.addArc(0,3)
dag.addArc(0,7)
gnb.sideBySide(dag,dag.moralGraph(),jtg.junctionTree(dag),jtg.eliminationOrder(dag),jtg.binaryJoinTree(dag),
              captions=["A DAG","its moral graph",
                        "a junction tree for this dag (with partial order)",
                        "its elimination order (with partial order)",
                        "an (optipmized) binary jointree (with partial order)"])
G 0 0 1 1 0->1 3 3 0->3 7 7 0->7 2 2 1->2 6 6 2->6 2->7 3->2 4 4 3->4 5 5 4->5 5->6
A DAG
no_name 0 0 1 1 0->1 2 2 0->2 3 3 0->3 7 7 0->7 1->2 1->3 2->3 5 5 2->5 6 6 2->6 2->7 4 4 3->4 4->5 5->6
its moral graph
G (0) 2-5-6 2-5-6 (0) 2-5-6^(4) 2-3-5 2-5 (0) 2-5-6--(0) 2-5-6^(4) 2-3-5 (1) 0-1-2-3 0-1-2-3 (1) 0-1-2-3^(4) 2-3-5 2-3 (1) 0-1-2-3--(1) 0-1-2-3^(4) 2-3-5 (1) 0-1-2-3^(2) 0-2-7 0-2 (1) 0-1-2-3--(1) 0-1-2-3^(2) 0-2-7 (2) 0-2-7 0-2-7 (4) 2-3-5 2-3-5 (4) 2-3-5^(5) 3-4-5 3-5 (4) 2-3-5--(4) 2-3-5^(5) 3-4-5 (5) 3-4-5 3-4-5 (4) 2-3-5^(5) 3-4-5--(5) 3-4-5 (0) 2-5-6^(4) 2-3-5--(4) 2-3-5 (1) 0-1-2-3^(4) 2-3-5--(4) 2-3-5 (1) 0-1-2-3^(2) 0-2-7--(2) 0-2-7
a junction tree for this dag (with partial order)
[6, 1, 7, 0, 2, 3, 4, 5]
its elimination order (with partial order)
G (0) 2-5-6 2-5-6 (0) 2-5-6^(4) 2-3-5 2-5 (0) 2-5-6--(0) 2-5-6^(4) 2-3-5 (1) 0-1-2-3 0-1-2-3 (1) 0-1-2-3^(4) 2-3-5 2-3 (1) 0-1-2-3--(1) 0-1-2-3^(4) 2-3-5 (1) 0-1-2-3^(2) 0-2-7 0-2 (1) 0-1-2-3--(1) 0-1-2-3^(2) 0-2-7 (2) 0-2-7 0-2-7 (4) 2-3-5 2-3-5 (4) 2-3-5^(5) 3-4-5 3-5 (4) 2-3-5--(4) 2-3-5^(5) 3-4-5 (5) 3-4-5 3-4-5 (4) 2-3-5^(5) 3-4-5--(5) 3-4-5 (0) 2-5-6^(4) 2-3-5--(4) 2-3-5 (1) 0-1-2-3^(4) 2-3-5--(4) 2-3-5 (1) 0-1-2-3^(2) 0-2-7--(2) 0-2-7
an (optipmized) binary jointree (with partial order)
In [17]:

#creating an undigraph slightly different
ug=bn.dag().moralGraph()
ug.addEdge(0,7)
gnb.sideBySide(ug,jtg.junctionTree(ug),jtg.eliminationOrder(ug),jtg.binaryJoinTree(ug),
              captions=["A undigraph",
                        "a junction tree for this undigraph",
                        "its elimination order",
                        "an (optipmized) binary jointree"])
no_name 0 0 1 1 0->1 7 7 0->7 2 2 1->2 3 3 1->3 2->3 5 5 2->5 6 6 2->6 2->7 4 4 3->4 4->5 5->6
A undigraph
G (0) 2-5-6 2-5-6 (0) 2-5-6^(2) 2-3-5 2-5 (0) 2-5-6--(0) 2-5-6^(2) 2-3-5 (1) 3-4-5 3-4-5 (1) 3-4-5^(2) 2-3-5 3-5 (1) 3-4-5--(1) 3-4-5^(2) 2-3-5 (2) 2-3-5 2-3-5 (2) 2-3-5^(3) 1-2-3 2-3 (2) 2-3-5--(2) 2-3-5^(3) 1-2-3 (3) 1-2-3 1-2-3 (3) 1-2-3^(4) 1-2-7 1-2 (3) 1-2-3--(3) 1-2-3^(4) 1-2-7 (4) 1-2-7 1-2-7 (4) 1-2-7^(5) 0-1-7 1-7 (4) 1-2-7--(4) 1-2-7^(5) 0-1-7 (5) 0-1-7 0-1-7 (2) 2-3-5^(3) 1-2-3--(3) 1-2-3 (4) 1-2-7^(5) 0-1-7--(5) 0-1-7 (0) 2-5-6^(2) 2-3-5--(2) 2-3-5 (1) 3-4-5^(2) 2-3-5--(2) 2-3-5 (3) 1-2-3^(4) 1-2-7--(4) 1-2-7
a junction tree for this undigraph
[6, 4, 5, 3, 2, 1, 7, 0]
its elimination order
G (0) 2-5-6 2-5-6 (0) 2-5-6^(2) 2-3-5 2-5 (0) 2-5-6--(0) 2-5-6^(2) 2-3-5 (1) 3-4-5 3-4-5 (1) 3-4-5^(2) 2-3-5 3-5 (1) 3-4-5--(1) 3-4-5^(2) 2-3-5 (2) 2-3-5 2-3-5 (2) 2-3-5^(3) 1-2-3 2-3 (2) 2-3-5--(2) 2-3-5^(3) 1-2-3 (3) 1-2-3 1-2-3 (3) 1-2-3^(4) 1-2-7 1-2 (3) 1-2-3--(3) 1-2-3^(4) 1-2-7 (4) 1-2-7 1-2-7 (4) 1-2-7^(5) 0-1-7 1-7 (4) 1-2-7--(4) 1-2-7^(5) 0-1-7 (5) 0-1-7 0-1-7 (2) 2-3-5^(3) 1-2-3--(3) 1-2-3 (4) 1-2-7^(5) 0-1-7--(5) 0-1-7 (0) 2-5-6^(2) 2-3-5--(2) 2-3-5 (1) 3-4-5^(2) 2-3-5--(2) 2-3-5 (3) 1-2-3^(4) 1-2-7--(4) 1-2-7
an (optipmized) binary jointree

Using partial order to specify the elimination order

In [18]:

#adding a partial order for the elimination order
po=[[1,2,3],[0,4,7],[5,6]]
gnb.sideBySide(bn,jtg.junctionTree(bn,po),jtg.eliminationOrder(bn,po),jtg.binaryJoinTree(bn),
              captions=["A Bayesien network",
                        "a junction tree for this BN using partial order",
                        "its elimination order following partial order",
                        "an (optimized) binary join tree"])
G 2 2 7 7 2->7 6 6 2->6 0 0 1 1 0->1 4 4 5 5 4->5 5->6 1->2 3 3 3->2 3->4
A Bayesien network
G (0) 1-2-3-4 1-2-3-4 (0) 1-2-3-4^(1) 0-1-2-4 1-2-4 (0) 1-2-3-4--(0) 1-2-3-4^(1) 0-1-2-4 (1) 0-1-2-4 0-1-2-4 (1) 0-1-2-4^(2) 0-2-4-5-6-7 0-2-4 (1) 0-1-2-4--(1) 0-1-2-4^(2) 0-2-4-5-6-7 (2) 0-2-4-5-6-7 0-2-4-5-6-7 (0) 1-2-3-4^(1) 0-1-2-4--(1) 0-1-2-4 (1) 0-1-2-4^(2) 0-2-4-5-6-7--(2) 0-2-4-5-6-7
a junction tree for this BN using partial order
[3, 1, 2, 7, 0, 4, 6, 5]
its elimination order following partial order
G (0) 2-5-6 2-5-6 (0) 2-5-6^(6) 2-5 2-5 (0) 2-5-6--(0) 2-5-6^(6) 2-5 (1) 2-7 2-7 (1) 2-7^(6) 2-5 2 (1) 2-7--(1) 2-7^(6) 2-5 (2) 0-1 0-1 (2) 0-1^(3) 1-2-3 1 (2) 0-1--(2) 0-1^(3) 1-2-3 (3) 1-2-3 1-2-3 (3) 1-2-3^(4) 2-3-5 2-3 (3) 1-2-3--(3) 1-2-3^(4) 2-3-5 (4) 2-3-5 2-3-5 (4) 2-3-5^(5) 3-4-5 3-5 (4) 2-3-5--(4) 2-3-5^(5) 3-4-5 (4) 2-3-5^(6) 2-5 2-5 (4) 2-3-5--(4) 2-3-5^(6) 2-5 (5) 3-4-5 3-4-5 (6) 2-5 2-5 (2) 0-1^(3) 1-2-3--(3) 1-2-3 (4) 2-3-5^(5) 3-4-5--(5) 3-4-5 (3) 1-2-3^(4) 2-3-5--(4) 2-3-5 (1) 2-7^(6) 2-5--(6) 2-5 (0) 2-5-6^(6) 2-5--(6) 2-5 (4) 2-3-5^(6) 2-5--(6) 2-5
an (optimized) binary join tree
In [19]:

#adding a partial order for the elimination order also for the graphs
po=[[0,4,7],[1,3],[5,6,2]]

#creating a dag slightly different
dag=bn.dag()
dag.addArc(0,3)
dag.addArc(0,7)

gnb.sideBySide(dag,dag.moralGraph(),jtg.junctionTree(dag,po),jtg.eliminationOrder(dag,po),jtg.binaryJoinTree(dag,po),
              captions=["A DAG","its moral graph",
                        "a junction tree for this dag (with partial order)",
                        "its elimination order (with partial order)",
                        "an (optipmized) binary jointree (with partial order)"])
G 0 0 1 1 0->1 3 3 0->3 7 7 0->7 2 2 1->2 6 6 2->6 2->7 3->2 4 4 3->4 5 5 4->5 5->6
A DAG
no_name 0 0 1 1 0->1 2 2 0->2 3 3 0->3 7 7 0->7 1->2 1->3 2->3 5 5 2->5 6 6 2->6 2->7 4 4 3->4 4->5 5->6
its moral graph
G (0) 0-2-7 0-2-7 (0) 0-2-7^(1) 0-1-2-3 0-2 (0) 0-2-7--(0) 0-2-7^(1) 0-1-2-3 (1) 0-1-2-3 0-1-2-3 (1) 0-1-2-3^(4) 2-3-5 2-3 (1) 0-1-2-3--(1) 0-1-2-3^(4) 2-3-5 (2) 3-4-5 3-4-5 (2) 3-4-5^(4) 2-3-5 3-5 (2) 3-4-5--(2) 3-4-5^(4) 2-3-5 (4) 2-3-5 2-3-5 (4) 2-3-5^(5) 2-5-6 2-5 (4) 2-3-5--(4) 2-3-5^(5) 2-5-6 (5) 2-5-6 2-5-6 (0) 0-2-7^(1) 0-1-2-3--(1) 0-1-2-3 (4) 2-3-5^(5) 2-5-6--(5) 2-5-6 (2) 3-4-5^(4) 2-3-5--(4) 2-3-5 (1) 0-1-2-3^(4) 2-3-5--(4) 2-3-5
a junction tree for this dag (with partial order)
[7, 0, 4, 1, 3, 2, 6, 5]
its elimination order (with partial order)
G (0) 0-2-7 0-2-7 (0) 0-2-7^(1) 0-1-2-3 0-2 (0) 0-2-7--(0) 0-2-7^(1) 0-1-2-3 (1) 0-1-2-3 0-1-2-3 (1) 0-1-2-3^(4) 2-3-5 2-3 (1) 0-1-2-3--(1) 0-1-2-3^(4) 2-3-5 (2) 3-4-5 3-4-5 (2) 3-4-5^(4) 2-3-5 3-5 (2) 3-4-5--(2) 3-4-5^(4) 2-3-5 (4) 2-3-5 2-3-5 (4) 2-3-5^(5) 2-5-6 2-5 (4) 2-3-5--(4) 2-3-5^(5) 2-5-6 (5) 2-5-6 2-5-6 (0) 0-2-7^(1) 0-1-2-3--(1) 0-1-2-3 (4) 2-3-5^(5) 2-5-6--(5) 2-5-6 (2) 3-4-5^(4) 2-3-5--(4) 2-3-5 (1) 0-1-2-3^(4) 2-3-5--(4) 2-3-5
an (optipmized) binary jointree (with partial order)