Probablistic Inference with pyAgrum

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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
In [3]:
print(bn)
BN{nodes: 37, arcs: 46, domainSize: 10^16.2389, dim: 509, mem: 5Ko 896o}

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

In [4]:
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 [5]:
gnb.showPosterior(bn,evs={},target='CATECHOL')
../_images/notebooks_41-Inference_graphicalInference_10_0.svg

You may also want to see the graph with some posteriors

In [6]:
# due to matplotlib, format is forced to png.
gnb.showInference(bn,evs={},targets={"VENTALV","CATECHOL","HR","MINVOLSET"},size="11")
../_images/notebooks_41-Inference_graphicalInference_12_0.svg
In [7]:
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_14_0.svg

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

In [8]:
gnb.showInference(bn,evs={"CO":1,"VENTLUNG":1},size="14")
../_images/notebooks_41-Inference_graphicalInference_16_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 [9]:
import pyAgrum.lib.explain as explain
explain.showInformation(bn,{},size="14")
G VENTLUNG VENTLUNG VENTALV VENTALV VENTLUNG->VENTALV EXPCO2 EXPCO2 VENTLUNG->EXPCO2 MINVOL MINVOL VENTLUNG->MINVOL KINKEDTUBE KINKEDTUBE KINKEDTUBE->VENTLUNG PRESS PRESS KINKEDTUBE->PRESS HR HR HRBP HRBP HR->HRBP CO CO HR->CO HRSAT HRSAT HR->HRSAT HREKG HREKG HR->HREKG LVEDVOLUME LVEDVOLUME PCWP PCWP LVEDVOLUME->PCWP CVP CVP LVEDVOLUME->CVP ERRLOWOUTPUT ERRLOWOUTPUT ERRLOWOUTPUT->HRBP HYPOVOLEMIA HYPOVOLEMIA HYPOVOLEMIA->LVEDVOLUME STROKEVOLUME STROKEVOLUME HYPOVOLEMIA->STROKEVOLUME ARTCO2 ARTCO2 VENTALV->ARTCO2 PVSAT PVSAT VENTALV->PVSAT CATECHOL CATECHOL ARTCO2->CATECHOL ARTCO2->EXPCO2 INSUFFANESTH INSUFFANESTH INSUFFANESTH->CATECHOL DISCONNECT DISCONNECT VENTTUBE VENTTUBE DISCONNECT->VENTTUBE BP BP ERRCAUTER ERRCAUTER ERRCAUTER->HRSAT ERRCAUTER->HREKG INTUBATION INTUBATION INTUBATION->VENTLUNG INTUBATION->VENTALV INTUBATION->PRESS INTUBATION->MINVOL SHUNT SHUNT INTUBATION->SHUNT VENTMACH VENTMACH VENTMACH->VENTTUBE ANAPHYLAXIS ANAPHYLAXIS TPR TPR ANAPHYLAXIS->TPR PULMEMBOLUS PULMEMBOLUS PULMEMBOLUS->SHUNT PAP PAP PULMEMBOLUS->PAP TPR->BP TPR->CATECHOL SAO2 SAO2 PVSAT->SAO2 SAO2->CATECHOL HISTORY HISTORY CO->BP FIO2 FIO2 FIO2->PVSAT CATECHOL->HR VENTTUBE->VENTLUNG VENTTUBE->PRESS MINVOLSET MINVOLSET MINVOLSET->VENTMACH SHUNT->SAO2 LVFAILURE LVFAILURE LVFAILURE->LVEDVOLUME LVFAILURE->HISTORY LVFAILURE->STROKEVOLUME STROKEVOLUME->CO

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

In [10]:
explain.showInformation(bn,{"CO":0},size="9")
G VENTLUNG VENTLUNG VENTALV VENTALV VENTLUNG->VENTALV EXPCO2 EXPCO2 VENTLUNG->EXPCO2 MINVOL MINVOL VENTLUNG->MINVOL KINKEDTUBE KINKEDTUBE KINKEDTUBE->VENTLUNG PRESS PRESS KINKEDTUBE->PRESS HR HR HRBP HRBP HR->HRBP CO CO HR->CO HRSAT HRSAT HR->HRSAT HREKG HREKG HR->HREKG LVEDVOLUME LVEDVOLUME PCWP PCWP LVEDVOLUME->PCWP CVP CVP LVEDVOLUME->CVP ERRLOWOUTPUT ERRLOWOUTPUT ERRLOWOUTPUT->HRBP HYPOVOLEMIA HYPOVOLEMIA HYPOVOLEMIA->LVEDVOLUME STROKEVOLUME STROKEVOLUME HYPOVOLEMIA->STROKEVOLUME ARTCO2 ARTCO2 VENTALV->ARTCO2 PVSAT PVSAT VENTALV->PVSAT CATECHOL CATECHOL ARTCO2->CATECHOL ARTCO2->EXPCO2 INSUFFANESTH INSUFFANESTH INSUFFANESTH->CATECHOL DISCONNECT DISCONNECT VENTTUBE VENTTUBE DISCONNECT->VENTTUBE BP BP ERRCAUTER ERRCAUTER ERRCAUTER->HRSAT ERRCAUTER->HREKG INTUBATION INTUBATION INTUBATION->VENTLUNG INTUBATION->VENTALV INTUBATION->PRESS INTUBATION->MINVOL SHUNT SHUNT INTUBATION->SHUNT VENTMACH VENTMACH VENTMACH->VENTTUBE ANAPHYLAXIS ANAPHYLAXIS TPR TPR ANAPHYLAXIS->TPR PULMEMBOLUS PULMEMBOLUS PULMEMBOLUS->SHUNT PAP PAP PULMEMBOLUS->PAP TPR->BP TPR->CATECHOL SAO2 SAO2 PVSAT->SAO2 SAO2->CATECHOL HISTORY HISTORY CO->BP FIO2 FIO2 FIO2->PVSAT CATECHOL->HR VENTTUBE->VENTLUNG VENTTUBE->PRESS MINVOLSET MINVOLSET MINVOLSET->VENTMACH SHUNT->SAO2 LVFAILURE LVFAILURE LVFAILURE->LVEDVOLUME LVFAILURE->HISTORY LVFAILURE->STROKEVOLUME STROKEVOLUME->CO

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 [11]:
jt=ie.junctionTree()
gnb.showJunctionTree(bn,size="12")
../_images/notebooks_41-Inference_graphicalInference_22_0.svg
In [12]:
# 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[12]:
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 [13]:
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 [14]:
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 [15]:
jt.hasRunningIntersection()
Out[15]:
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 [16]:
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 7 7 6 6 0 0 1 1 0->1 2 2 1->2 4 4 5 5 4->5 3 3 3->4 3->2 5->6 2->7 2->6
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 [17]:
#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 [18]:
#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 [19]:
#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 7 7 6 6 0 0 1 1 0->1 2 2 1->2 4 4 5 5 4->5 3 3 3->4 3->2 5->6 2->7 2->6
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 [20]:
#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)