# Learning the structure of a Bayesian network

In [1]:

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

import os

In [2]:

import pyAgrum as gum
import pyAgrum.lib.notebook as gnb
import pyAgrum.lib.explain as explain
import pyAgrum.lib.bn_vs_bn as bnvsbn

gnb.configuration()

pyAgrum 1.12.1.9
(c) 2015-2023 Pierre-Henri Wuillemin, Christophe Gonzales

This is free software; see the source code for copying conditions.
There is ABSOLUTELY NO WARRANTY; not even for MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE.  For details, see 'pyAgrum.warranty'.


LibraryVersion
OSposix [darwin]
Python3.12.2 (main, Feb 6 2024, 20:19:44) [Clang 15.0.0 (clang-1500.1.0.2.5)]
IPython8.22.2
Matplotlib3.8.3
Numpy1.26.4
pyDot2.0.0
pyAgrum1.12.1.9
Thu Mar 21 11:56:05 2024 CET

## Generating the database from a BN

In [3]:

bn=gum.loadBN("res/asia.bif")
bn

Out[3]:

In [4]:

gum.generateSample(bn,50000,"out/sample_asia.csv",True);

out/sample_asia.csv: 100%|█████████████████████████████████|

Log2-Likelihood : -161315.9041721179



In [5]:

with open("out/sample_asia.csv","r") as src:
for _ in range(10):

dyspnoea,smoking,positive_XraY,bronchitis,tuberculosis,lung_cancer,visit_to_Asia,tuberculos_or_cancer
0,0,0,0,1,0,1,0
1,0,1,1,1,1,1,1
1,0,1,1,1,1,1,1
1,1,1,1,1,1,1,1
0,0,1,0,1,1,1,1
1,0,0,1,1,0,1,0
0,1,1,1,1,1,1,1
1,0,1,1,1,1,1,1
0,1,1,0,1,1,1,1

In [6]:

learner=gum.BNLearner("out/sample_asia.csv",bn) #using bn as template for variables
print(learner)

Filename       : out/sample_asia.csv
Size           : (50000,8)
Variables      : visit_to_Asia[2], tuberculosis[2], tuberculos_or_cancer[2], positive_XraY[2], lung_cancer[2], smoking[2], bronchitis[2], dyspnoea[2]
Induced types  : False
Missing values : False
Algorithm      : MIIC
Score          : BDeu  (Not used for constraint-based algorithms)
Correction     : MDL  (Not used for score-based algorithms)
Prior          : -


In [7]:

print(f"Row of visit_to_Asia : {learner.idFromName('visit_to_Asia')}") # first row is 0

Row of visit_to_Asia : 0

In [8]:

print(f"Variable in row 4 : {learner.nameFromId(4)}")

Variable in row 4 : lung_cancer


The BNLearner is capable of recognizing missing values in databases. For this purpose, just indicate as a last argument the list of the strings that represent missing values.

In [9]:

# it is possible to add as a last argument a list of the symbols that represent missing values:
# whenever a cell of the database is equal to one of these strings, it is considered as a
# missing value
learner=gum.BNLearner("res/asia_missing.csv",bn, ['?', 'N/A'] )
print(f"Are there missing values in the database ? {learner.state()['Missing values'][0]}")

Are there missing values in the database ? True


### type induction

When reading a csv file, BNLearner can try to find the correct type for discrete variable. Especially for numeric values.

In [10]:

%%writefile out/testTypeInduction.csv
A,B,C,D
1,2,0,hot
0,3,-2,cold
0,1,2,hot
1,2,2,warm

Overwriting out/testTypeInduction.csv

In [11]:

print("* by default, type induction is on (True) :")
learner=gum.BNLearner("out/testTypeInduction.csv")
bn3=learner.learnBN()
for v in sorted(bn3.names()):
print(f"  - {bn3.variable(v)}")

print("")
print("* but you can disable it :")
learner=gum.BNLearner("out/testTypeInduction.csv",["?"],False)
bn3=learner.learnBN()
for v in sorted(bn3.names()):
print(f"  - {bn3.variable(v)}")

print("")
print("Note that when a Labelized variable is found, the labesl are alphabetically sorted.")

* by default, type induction is on (True) :
- A:Range([0,1])
- B:Range([1,3])
- C:Integer({-2|0|2})
- D:Labelized({cold|hot|warm})

* but you can disable it :
- A:Labelized({0|1})
- B:Labelized({1|2|3})
- C:Labelized({-2|0|2})
- D:Labelized({cold|hot|warm})

Note that when a Labelized variable is found, the labesl are alphabetically sorted.


## Parameters learning from the database

We give the $$bn$$ as a parameter for the learner in order to have the variables and the order of the labels for each variables. Please try to remove the argument $$bn$$ in the first line below to see the difference …

In [12]:

learner=gum.BNLearner("out/sample_asia.csv",bn) #using bn as template for variables and labels
bn2=learner.learnParameters(bn.dag())
gnb.showBN(bn2)

In [13]:

from IPython.display import HTML

gnb.sideBySide("<H3>Original BN</H3>","<H3>Learned NB</H3>",
bn.cpt ('visit_to_Asia'),bn2.cpt ('visit_to_Asia'),
bn.cpt ('tuberculosis'),bn2.cpt ('tuberculosis'),
ncols=2)


visit_to_Asia
0
1
0.01000.9900
visit_to_Asia
0
1
0.01010.9899
tuberculosis
visit_to_Asia
0
1
0
0.05000.9500
1
0.01000.9900
tuberculosis
visit_to_Asia
0
1
0
0.05130.9487
1
0.01030.9897

## Structural learning a BN from the database

Note that, currently, the BNLearner is not yet able to learn in the presence of missing values. This is the reason why, when it discovers that there exist such values, it raises a gum.MissingValueInDatabase exception.

In [14]:

with open("res/asia_missing.csv","r") as asiafile:
for _ in range(10):
try:
learner=gum.BNLearner("res/asia_missing.csv",bn, ['?', 'N/A'] )
bn2=learner.learnBN()
except gum.MissingValueInDatabase:
print ( "exception raised: there are missing values in the database" )

smoking,lung_cancer,bronchitis,visit_to_Asia,tuberculosis,tuberculos_or_cancer,dyspnoea,positive_XraY
0,0,0,1,1,0,0,0
1,1,0,1,1,1,0,1
1,1,1,1,1,1,1,1
1,1,0,1,1,1,0,N/A
0,1,0,1,1,1,1,1
1,1,1,1,1,1,1,1
1,1,1,1,1,1,0,1
1,1,0,1,1,1,0,1
1,1,1,1,1,1,1,1
exception raised: there are missing values in the database


### Different learning algorithms

For now, there are three scored-based algorithms that are wrapped in pyAgrum : LocalSearchWithTabuList, GreedyHillClimbing and K2

In [15]:

learner=gum.BNLearner("out/sample_asia.csv",bn) #using bn as template for variables
learner.useLocalSearchWithTabuList()
print(learner)
bn2=learner.learnBN()
print("Learned in {0}ms".format(1000*learner.currentTime()))
gnb.flow.row(bn,bn2,explain.getInformation(bn2),captions=["Original BN","Learned BN","information"])

Filename       : out/sample_asia.csv
Size           : (50000,8)
Variables      : visit_to_Asia[2], tuberculosis[2], tuberculos_or_cancer[2], positive_XraY[2], lung_cancer[2], smoking[2], bronchitis[2], dyspnoea[2]
Induced types  : False
Missing values : False
Algorithm      : Local Search with Tabu List
Tabu list size : 2
Score          : BDeu  (Not used for constraint-based algorithms)
Correction     : MDL  (Not used for score-based algorithms)
Prior          : -

Learned in 35.04ms


Original BN

Learned BN

information

To apprehend the distance between the original and the learned BN, we have several tools : - Compute the KL divergence (and other distance) between original and learned joint distribution

In [16]:

kl=gum.ExactBNdistance(bn,bn2)
kl.compute()

Out[16]:

{'klPQ': 0.00026404314393736576,
'errorPQ': 0,
'klQP': 0.0002322472678712083,
'errorQP': 128,
'hellinger': 0.009797153536826357,
'bhattacharya': 4.798761823345152e-05,
'jensen-shannon': 6.70129303341394e-05}

• Compute some scores on the BNs (as binary classifiers) abd show the graphical diff between the two graphs

In [17]:

gnb.flow.row(bn,bn2,captions=["bn","bn2"])
gnb.flow.row(bnvsbn.graphDiff(bn,bn2),bnvsbn.graphDiff(bn2,bn),bnvsbn.graphDiffLegend(),captions=["bn versus bn2","bn2 versus bn",""])

gcmp=bnvsbn.GraphicalBNComparator(bn,bn2)
gnb.flow.add_html("<br/>".join([f"{k} : {v:.2f}" for k,v in gcmp.skeletonScores().items() if k!='count']),"Skeleton scores")
gnb.flow.add_html("<br/>".join([f"{k} : {v:.2f}" for k,v in gcmp.scores().items() if k!='count']),"Scores")

gnb.flow.display()


bn

bn2

bn versus bn2

bn2 versus bn
recall : 1.00
precision : 0.73
fscore : 0.84
dist2opt : 0.27
Skeleton scores
recall : 0.88
precision : 0.64
fscore : 0.74
dist2opt : 0.38
Scores

A greedy Hill Climbing algorithm (with insert, remove and change arc as atomic operations).

In [18]:

learner=gum.BNLearner("out/sample_asia.csv",bn) #using bn as template for variables
learner.useGreedyHillClimbing()
print(learner)
bn2=learner.learnBN()
print("Learned in {0}ms".format(1000*learner.currentTime()))
gnb.sideBySide(bn,bn2,gnb.getBNDiff(bn,bn2),explain.getInformation(bn2),captions=["Original BN","Learned BN","Graphical diff","information"])

Filename       : out/sample_asia.csv
Size           : (50000,8)
Variables      : visit_to_Asia[2], tuberculosis[2], tuberculos_or_cancer[2], positive_XraY[2], lung_cancer[2], smoking[2], bronchitis[2], dyspnoea[2]
Induced types  : False
Missing values : False
Algorithm      : Greedy Hill Climbing
Score          : BDeu  (Not used for constraint-based algorithms)
Correction     : MDL  (Not used for score-based algorithms)
Prior          : -

Learned in 19.933ms

 G positive_XraY positive_XraY tuberculosis tuberculosis tuberculos_or_cancer tuberculos_or_cancer tuberculosis->tuberculos_or_cancer tuberculos_or_cancer->positive_XraY dyspnoea dyspnoea tuberculos_or_cancer->dyspnoea bronchitis bronchitis bronchitis->dyspnoea smoking smoking smoking->bronchitis lung_cancer lung_cancer smoking->lung_cancer lung_cancer->tuberculos_or_cancer visit_to_Asia visit_to_Asia visit_to_Asia->tuberculosis Original BN G positive_XraY positive_XraY tuberculosis tuberculosis tuberculos_or_cancer tuberculos_or_cancer tuberculosis->tuberculos_or_cancer tuberculos_or_cancer->positive_XraY dyspnoea dyspnoea tuberculos_or_cancer->dyspnoea bronchitis bronchitis bronchitis->dyspnoea smoking smoking smoking->bronchitis lung_cancer lung_cancer lung_cancer->tuberculos_or_cancer lung_cancer->smoking visit_to_Asia visit_to_Asia visit_to_Asia->tuberculosis Learned BN G visit_to_Asia visit_to_Asia tuberculosis tuberculosis visit_to_Asia->tuberculosis tuberculos_or_cancer tuberculos_or_cancer tuberculosis->tuberculos_or_cancer positive_XraY positive_XraY tuberculos_or_cancer->positive_XraY dyspnoea dyspnoea tuberculos_or_cancer->dyspnoea lung_cancer lung_cancer lung_cancer->tuberculos_or_cancer smoking smoking lung_cancer->smoking bronchitis bronchitis smoking->bronchitis bronchitis->dyspnoea Graphical diff G positive_XraY positive_XraY tuberculosis tuberculosis tuberculos_or_cancer tuberculos_or_cancer tuberculosis->tuberculos_or_cancer tuberculos_or_cancer->positive_XraY dyspnoea dyspnoea tuberculos_or_cancer->dyspnoea bronchitis bronchitis bronchitis->dyspnoea smoking smoking smoking->bronchitis lung_cancer lung_cancer lung_cancer->tuberculos_or_cancer lung_cancer->smoking visit_to_Asia visit_to_Asia visit_to_Asia->tuberculosis information

And a K2 for those who likes it :)

In [19]:

learner=gum.BNLearner("out/sample_asia.csv",bn) #using bn as template for variables
learner.useK2([0,1,2,3,4,5,6,7])
print(learner)
bn2=learner.learnBN()
print("Learned in {0}ms".format(1000*learner.currentTime()))
gnb.sideBySide(bn,bn2,gnb.getBNDiff(bn,bn2),explain.getInformation(bn2),captions=["Original BN","Learned BN","Graphical diff","information"])

Filename       : out/sample_asia.csv
Size           : (50000,8)
Variables      : visit_to_Asia[2], tuberculosis[2], tuberculos_or_cancer[2], positive_XraY[2], lung_cancer[2], smoking[2], bronchitis[2], dyspnoea[2]
Induced types  : False
Missing values : False
Algorithm      : K2
K2 order       : visit_to_Asia, tuberculosis, tuberculos_or_cancer, positive_XraY, lung_cancer, smoking, bronchitis, dyspnoea
Score          : BDeu  (Not used for constraint-based algorithms)
Correction     : MDL  (Not used for score-based algorithms)
Prior          : -

Learned in 7.034ms

 G positive_XraY positive_XraY tuberculosis tuberculosis tuberculos_or_cancer tuberculos_or_cancer tuberculosis->tuberculos_or_cancer tuberculos_or_cancer->positive_XraY dyspnoea dyspnoea tuberculos_or_cancer->dyspnoea bronchitis bronchitis bronchitis->dyspnoea smoking smoking smoking->bronchitis lung_cancer lung_cancer smoking->lung_cancer lung_cancer->tuberculos_or_cancer visit_to_Asia visit_to_Asia visit_to_Asia->tuberculosis Original BN G positive_XraY positive_XraY tuberculosis tuberculosis tuberculos_or_cancer tuberculos_or_cancer tuberculosis->tuberculos_or_cancer lung_cancer lung_cancer tuberculosis->lung_cancer tuberculos_or_cancer->positive_XraY dyspnoea dyspnoea tuberculos_or_cancer->dyspnoea tuberculos_or_cancer->lung_cancer bronchitis bronchitis bronchitis->dyspnoea smoking smoking smoking->bronchitis lung_cancer->smoking visit_to_Asia visit_to_Asia visit_to_Asia->tuberculosis Learned BN G visit_to_Asia visit_to_Asia tuberculosis tuberculosis visit_to_Asia->tuberculosis tuberculos_or_cancer tuberculos_or_cancer tuberculosis->tuberculos_or_cancer lung_cancer lung_cancer tuberculosis->lung_cancer positive_XraY positive_XraY tuberculos_or_cancer->positive_XraY tuberculos_or_cancer->lung_cancer dyspnoea dyspnoea tuberculos_or_cancer->dyspnoea smoking smoking lung_cancer->smoking bronchitis bronchitis smoking->bronchitis bronchitis->dyspnoea Graphical diff G positive_XraY positive_XraY tuberculosis tuberculosis tuberculos_or_cancer tuberculos_or_cancer tuberculosis->tuberculos_or_cancer lung_cancer lung_cancer tuberculosis->lung_cancer tuberculos_or_cancer->positive_XraY dyspnoea dyspnoea tuberculos_or_cancer->dyspnoea tuberculos_or_cancer->lung_cancer bronchitis bronchitis bronchitis->dyspnoea smoking smoking smoking->bronchitis lung_cancer->smoking visit_to_Asia visit_to_Asia visit_to_Asia->tuberculosis information

K2 can be very good if the order is the good one (a topological order of nodes in the reference)

In [20]:

learner=gum.BNLearner("out/sample_asia.csv",bn) #using bn as template for variables
learner.useK2([7,6,5,4,3,2,1,0])
print(learner)
bn2=learner.learnBN()
print("Learned in {0}s".format(learner.currentTime()))
gnb.sideBySide(bn,bn2,gnb.getBNDiff(bn,bn2),explain.getInformation(bn2),captions=["Original BN","Learned BN","Graphical diff","information"])

Filename       : out/sample_asia.csv
Size           : (50000,8)
Variables      : visit_to_Asia[2], tuberculosis[2], tuberculos_or_cancer[2], positive_XraY[2], lung_cancer[2], smoking[2], bronchitis[2], dyspnoea[2]
Induced types  : False
Missing values : False
Algorithm      : K2
K2 order       : dyspnoea, bronchitis, smoking, lung_cancer, positive_XraY, tuberculos_or_cancer, tuberculosis, visit_to_Asia
Score          : BDeu  (Not used for constraint-based algorithms)
Correction     : MDL  (Not used for score-based algorithms)
Prior          : -

Learned in 0.008448s

 G positive_XraY positive_XraY tuberculosis tuberculosis tuberculos_or_cancer tuberculos_or_cancer tuberculosis->tuberculos_or_cancer tuberculos_or_cancer->positive_XraY dyspnoea dyspnoea tuberculos_or_cancer->dyspnoea bronchitis bronchitis bronchitis->dyspnoea smoking smoking smoking->bronchitis lung_cancer lung_cancer smoking->lung_cancer lung_cancer->tuberculos_or_cancer visit_to_Asia visit_to_Asia visit_to_Asia->tuberculosis Original BN G positive_XraY positive_XraY tuberculos_or_cancer tuberculos_or_cancer positive_XraY->tuberculos_or_cancer tuberculosis tuberculosis visit_to_Asia visit_to_Asia tuberculosis->visit_to_Asia tuberculos_or_cancer->tuberculosis dyspnoea dyspnoea dyspnoea->positive_XraY dyspnoea->tuberculos_or_cancer bronchitis bronchitis dyspnoea->bronchitis smoking smoking dyspnoea->smoking lung_cancer lung_cancer dyspnoea->lung_cancer bronchitis->positive_XraY bronchitis->tuberculos_or_cancer bronchitis->smoking bronchitis->lung_cancer smoking->lung_cancer lung_cancer->positive_XraY lung_cancer->tuberculosis lung_cancer->tuberculos_or_cancer Learned BN G visit_to_Asia visit_to_Asia tuberculosis tuberculosis tuberculosis->visit_to_Asia tuberculos_or_cancer tuberculos_or_cancer tuberculos_or_cancer->tuberculosis positive_XraY positive_XraY dyspnoea dyspnoea positive_XraY->tuberculos_or_cancer lung_cancer lung_cancer lung_cancer->tuberculosis lung_cancer->tuberculos_or_cancer lung_cancer->positive_XraY smoking smoking smoking->lung_cancer bronchitis bronchitis bronchitis->tuberculos_or_cancer bronchitis->positive_XraY bronchitis->lung_cancer bronchitis->smoking dyspnoea->tuberculos_or_cancer dyspnoea->positive_XraY dyspnoea->lung_cancer dyspnoea->smoking dyspnoea->bronchitis Graphical diff G positive_XraY positive_XraY tuberculos_or_cancer tuberculos_or_cancer positive_XraY->tuberculos_or_cancer tuberculosis tuberculosis visit_to_Asia visit_to_Asia tuberculosis->visit_to_Asia tuberculos_or_cancer->tuberculosis dyspnoea dyspnoea dyspnoea->positive_XraY dyspnoea->tuberculos_or_cancer bronchitis bronchitis dyspnoea->bronchitis smoking smoking dyspnoea->smoking lung_cancer lung_cancer dyspnoea->lung_cancer bronchitis->positive_XraY bronchitis->tuberculos_or_cancer bronchitis->smoking bronchitis->lung_cancer smoking->lung_cancer lung_cancer->positive_XraY lung_cancer->tuberculosis lung_cancer->tuberculos_or_cancer information

## Following the learning curve

In [21]:

import numpy as np
%matplotlib inline

learner=gum.BNLearner("out/sample_asia.csv",bn) #using bn as template for variables
learner.useLocalSearchWithTabuList()

# we could prefere a log2likelihood score
# learner.useScoreLog2Likelihood()
learner.setMaxTime(10)

# representation of the error as a pseudo log (negative values really represents negative epsilon
@np.vectorize
def pseudolog(x):
res=np.log(x)#np.log(y)

return res if x>0 else -res

# in order to control the complexity, we limit the number of parents
learner.setMaxIndegree(7) # no more than 3 parent by node
learner.setEpsilon(1e-10)
gnb.animApproximationScheme(learner,
scale=pseudolog) # scale by default is np.log10

bn2=learner.learnBN()


## Customizing the learning algorithms

### 1. Learn a tree ?

In [22]:

learner=gum.BNLearner("out/sample_asia.csv",bn) #using bn as template for variables
learner.useGreedyHillClimbing()

learner.setMaxIndegree(1) # no more than 1 parent by node
print(learner)
bntree=learner.learnBN()
gnb.sideBySide(bn,bntree,gnb.getBNDiff(bn,bntree),explain.getInformation(bntree),captions=["Original BN","Learned BN","Graphical diff","information"])

Filename                : out/sample_asia.csv
Size                    : (50000,8)
Variables               : visit_to_Asia[2], tuberculosis[2], tuberculos_or_cancer[2], positive_XraY[2], lung_cancer[2], smoking[2], bronchitis[2], dyspnoea[2]
Induced types           : False
Missing values          : False
Algorithm               : Greedy Hill Climbing
Score                   : BDeu  (Not used for constraint-based algorithms)
Correction              : MDL  (Not used for score-based algorithms)
Prior                   : -
Constraint Max InDegree : 1


 G positive_XraY positive_XraY tuberculosis tuberculosis tuberculos_or_cancer tuberculos_or_cancer tuberculosis->tuberculos_or_cancer tuberculos_or_cancer->positive_XraY dyspnoea dyspnoea tuberculos_or_cancer->dyspnoea bronchitis bronchitis bronchitis->dyspnoea smoking smoking smoking->bronchitis lung_cancer lung_cancer smoking->lung_cancer lung_cancer->tuberculos_or_cancer visit_to_Asia visit_to_Asia visit_to_Asia->tuberculosis Original BN G positive_XraY positive_XraY tuberculosis tuberculosis visit_to_Asia visit_to_Asia tuberculosis->visit_to_Asia tuberculos_or_cancer tuberculos_or_cancer tuberculos_or_cancer->positive_XraY tuberculos_or_cancer->tuberculosis dyspnoea dyspnoea tuberculos_or_cancer->dyspnoea bronchitis bronchitis dyspnoea->bronchitis smoking smoking bronchitis->smoking lung_cancer lung_cancer lung_cancer->tuberculos_or_cancer Learned BN G visit_to_Asia visit_to_Asia tuberculosis tuberculosis tuberculosis->visit_to_Asia tuberculos_or_cancer tuberculos_or_cancer tuberculos_or_cancer->tuberculosis positive_XraY positive_XraY tuberculos_or_cancer->positive_XraY dyspnoea dyspnoea tuberculos_or_cancer->dyspnoea lung_cancer lung_cancer lung_cancer->tuberculos_or_cancer smoking smoking smoking->lung_cancer bronchitis bronchitis bronchitis->smoking dyspnoea->bronchitis Graphical diff G positive_XraY positive_XraY tuberculosis tuberculosis visit_to_Asia visit_to_Asia tuberculosis->visit_to_Asia tuberculos_or_cancer tuberculos_or_cancer tuberculos_or_cancer->positive_XraY tuberculos_or_cancer->tuberculosis dyspnoea dyspnoea tuberculos_or_cancer->dyspnoea bronchitis bronchitis dyspnoea->bronchitis smoking smoking bronchitis->smoking lung_cancer lung_cancer lung_cancer->tuberculos_or_cancer information

### 2. with prior structural knowledge

In [23]:

learner=gum.BNLearner("out/sample_asia.csv",bn) #using bn as template for variables
learner.useGreedyHillClimbing()

# I know that smoking causes cancer
# I know that visit to Asia may change the risk of tuberculosis
print(learner)
bn2=learner.learnBN()
gnb.sideBySide(bn,bn2,gnb.getBNDiff(bn,bn2),explain.getInformation(bn2),captions=["Original BN","Learned BN","Graphical diff","information"])

Filename                  : out/sample_asia.csv
Size                      : (50000,8)
Variables                 : visit_to_Asia[2], tuberculosis[2], tuberculos_or_cancer[2], positive_XraY[2], lung_cancer[2], smoking[2], bronchitis[2], dyspnoea[2]
Induced types             : False
Missing values            : False
Algorithm                 : Greedy Hill Climbing
Score                     : BDeu  (Not used for constraint-based algorithms)
Correction                : MDL  (Not used for score-based algorithms)
Prior                     : -
Constraint Mandatory Arcs : {visit_to_Asia->tuberculosis, smoking->lung_cancer}


 G positive_XraY positive_XraY tuberculosis tuberculosis tuberculos_or_cancer tuberculos_or_cancer tuberculosis->tuberculos_or_cancer tuberculos_or_cancer->positive_XraY dyspnoea dyspnoea tuberculos_or_cancer->dyspnoea bronchitis bronchitis bronchitis->dyspnoea smoking smoking smoking->bronchitis lung_cancer lung_cancer smoking->lung_cancer lung_cancer->tuberculos_or_cancer visit_to_Asia visit_to_Asia visit_to_Asia->tuberculosis Original BN G positive_XraY positive_XraY tuberculosis tuberculosis tuberculos_or_cancer tuberculos_or_cancer tuberculos_or_cancer->positive_XraY tuberculos_or_cancer->tuberculosis visit_to_Asia visit_to_Asia tuberculos_or_cancer->visit_to_Asia dyspnoea dyspnoea dyspnoea->tuberculos_or_cancer bronchitis bronchitis dyspnoea->bronchitis smoking smoking dyspnoea->smoking lung_cancer lung_cancer dyspnoea->lung_cancer bronchitis->tuberculos_or_cancer bronchitis->smoking bronchitis->lung_cancer smoking->lung_cancer lung_cancer->tuberculosis lung_cancer->tuberculos_or_cancer lung_cancer->visit_to_Asia visit_to_Asia->tuberculosis Learned BN G visit_to_Asia visit_to_Asia tuberculosis tuberculosis visit_to_Asia->tuberculosis tuberculos_or_cancer tuberculos_or_cancer tuberculos_or_cancer->visit_to_Asia tuberculos_or_cancer->tuberculosis positive_XraY positive_XraY tuberculos_or_cancer->positive_XraY dyspnoea dyspnoea lung_cancer lung_cancer lung_cancer->visit_to_Asia lung_cancer->tuberculosis lung_cancer->tuberculos_or_cancer smoking smoking smoking->lung_cancer bronchitis bronchitis bronchitis->tuberculos_or_cancer bronchitis->lung_cancer bronchitis->smoking dyspnoea->tuberculos_or_cancer dyspnoea->lung_cancer dyspnoea->smoking dyspnoea->bronchitis Graphical diff G positive_XraY positive_XraY tuberculosis tuberculosis tuberculos_or_cancer tuberculos_or_cancer tuberculos_or_cancer->positive_XraY tuberculos_or_cancer->tuberculosis visit_to_Asia visit_to_Asia tuberculos_or_cancer->visit_to_Asia dyspnoea dyspnoea dyspnoea->tuberculos_or_cancer bronchitis bronchitis dyspnoea->bronchitis smoking smoking dyspnoea->smoking lung_cancer lung_cancer dyspnoea->lung_cancer bronchitis->tuberculos_or_cancer bronchitis->smoking bronchitis->lung_cancer smoking->lung_cancer lung_cancer->tuberculosis lung_cancer->tuberculos_or_cancer lung_cancer->visit_to_Asia visit_to_Asia->tuberculosis information

### 3. changing the scores

By default, a BDEU score is used. But it can be changed.

In [24]:

learner=gum.BNLearner("out/sample_asia.csv",bn) #using bn as template for variables
learner.useGreedyHillClimbing()

# I know that smoking causes cancer

# we prefere a log2likelihood score
learner.useScoreLog2Likelihood()

# in order to control the complexity, we limit the number of parents
learner.setMaxIndegree(1) # no more than 1 parent by node
print(learner)
bn2=learner.learnBN()
kl=gum.ExactBNdistance(bn,bn2)
gnb.sideBySide(bn,bn2,gnb.getBNDiff(bn,bn2),
"<br/>".join(["<b>"+k+"</b> :"+str(v) for k,v in kl.compute().items()]),
captions=["original","learned BN","diff","distances"])

Filename                  : out/sample_asia.csv
Size                      : (50000,8)
Variables                 : visit_to_Asia[2], tuberculosis[2], tuberculos_or_cancer[2], positive_XraY[2], lung_cancer[2], smoking[2], bronchitis[2], dyspnoea[2]
Induced types             : False
Missing values            : False
Algorithm                 : Greedy Hill Climbing
Score                     : Log2Likelihood  (Not used for constraint-based algorithms)
Correction                : MDL  (Not used for score-based algorithms)
Prior                     : -
Constraint Max InDegree   : 1
Constraint Mandatory Arcs : {visit_to_Asia->tuberculosis}


 G positive_XraY positive_XraY tuberculosis tuberculosis tuberculos_or_cancer tuberculos_or_cancer tuberculosis->tuberculos_or_cancer tuberculos_or_cancer->positive_XraY dyspnoea dyspnoea tuberculos_or_cancer->dyspnoea bronchitis bronchitis bronchitis->dyspnoea smoking smoking smoking->bronchitis lung_cancer lung_cancer smoking->lung_cancer lung_cancer->tuberculos_or_cancer visit_to_Asia visit_to_Asia visit_to_Asia->tuberculosis original G positive_XraY positive_XraY tuberculos_or_cancer tuberculos_or_cancer positive_XraY->tuberculos_or_cancer tuberculosis tuberculosis lung_cancer lung_cancer tuberculos_or_cancer->lung_cancer visit_to_Asia visit_to_Asia tuberculos_or_cancer->visit_to_Asia dyspnoea dyspnoea bronchitis bronchitis bronchitis->dyspnoea smoking smoking bronchitis->smoking lung_cancer->bronchitis visit_to_Asia->tuberculosis learned BN G visit_to_Asia visit_to_Asia tuberculosis tuberculosis visit_to_Asia->tuberculosis tuberculos_or_cancer tuberculos_or_cancer tuberculosis->tuberculos_or_cancer tuberculos_or_cancer->visit_to_Asia positive_XraY positive_XraY lung_cancer lung_cancer tuberculos_or_cancer->lung_cancer dyspnoea dyspnoea tuberculos_or_cancer->dyspnoea positive_XraY->tuberculos_or_cancer bronchitis bronchitis lung_cancer->bronchitis smoking smoking smoking->lung_cancer bronchitis->smoking bronchitis->dyspnoea diff klPQ :0.14959060082593612errorPQ :0klQP :0.055813027902177785errorQP :64hellinger :0.22242449813301346bhattacharya :0.025047406641408764jensen-shannon :0.028780860049918425distances

### 4. comparing BNs

There are multiple ways to compare Bayes net…

In [25]:

help(gnb.getBNDiff)

Help on function getBNDiff in module pyAgrum.lib.notebook:

getBNDiff(bn1, bn2, size=None, noStyle=False)
get a HTML string representation of a graphical diff between the arcs of _bn1 (reference) with those of _bn2.

if noStyle is False use 4 styles (fixed in pyAgrum.config) :
- the arc is common for both
- the arc is common but inverted in bn2
- the arc is added in bn2
- the arc is removed in bn2

Parameters
----------
bn1: pyAgrum.BayesNet
the reference
bn2: pyAgrum.BayesNet
the compared one
size: float|str
size (for graphviz) of the rendered graph
noStyle: bool
with style or not.

Returns
-------
str
the HTML representation of the comparison


In [26]:

gnb.showBNDiff(bn,bn2)

In [27]:

import pyAgrum.lib.bn_vs_bn as gbnbn
help(gbnbn.graphDiff)

Help on function graphDiff in module pyAgrum.lib.bn_vs_bn:

graphDiff(bnref, bncmp, noStyle=False)
Return a pydot graph that compares the arcs of bnref to bncmp.
graphDiff allows bncmp to have less nodes than bnref. (this is not the case in GraphicalBNComparator.dotDiff())

if noStyle is False use 4 styles (fixed in pyAgrum.config) :
- the arc is common for both
- the arc is common but inverted in _bn2
- the arc is added in _bn2
- the arc is removed in _bn2

See graphDiffLegend() to add a legend to the graph.
Warning
-------
if pydot is not installed, this function just returns None

Returns
-------
pydot.Dot
the result dot graph or None if pydot can not be imported


In [28]:

gbnbn.GraphicalBNComparator?

Init signature: gbnbn.GraphicalBNComparator(name1, name2, delta=1e-06)
Docstring:
BNGraphicalComparator allows to compare in multiple way 2 BNs...The smallest assumption is that the names of the variables are the same in the 2 BNs. But some comparisons will have also to check the type and domainSize of the variables. The bns have not exactly the  same role : _bn1 is rather the referent model for the comparison whereas _bn2 is the compared one to the referent model.

Parameters
----------
name1 : str or pyAgrum.BayesNet
a BN or a filename for reference
name2 : str or pyAgrum.BayesNet
another BN or antoher filename for comparison
File:           ~/.virtualenvs/devAgrum/lib/python3.12/site-packages/pyAgrum/lib/bn_vs_bn.py
Type:           type
Subclasses:

In [29]:

gcmp=gbnbn.GraphicalBNComparator(bn,bn2)
gnb.sideBySide(bn,bn2,gcmp.dotDiff(),gbnbn.graphDiffLegend(),
bn2,bn,gbnbn.graphDiff(bn2,bn),gbnbn.graphDiffLegend(),
ncols=4)

 G positive_XraY positive_XraY tuberculosis tuberculosis tuberculos_or_cancer tuberculos_or_cancer tuberculosis->tuberculos_or_cancer tuberculos_or_cancer->positive_XraY dyspnoea dyspnoea tuberculos_or_cancer->dyspnoea bronchitis bronchitis bronchitis->dyspnoea smoking smoking smoking->bronchitis lung_cancer lung_cancer smoking->lung_cancer lung_cancer->tuberculos_or_cancer visit_to_Asia visit_to_Asia visit_to_Asia->tuberculosis G positive_XraY positive_XraY tuberculos_or_cancer tuberculos_or_cancer positive_XraY->tuberculos_or_cancer tuberculosis tuberculosis lung_cancer lung_cancer tuberculos_or_cancer->lung_cancer visit_to_Asia visit_to_Asia tuberculos_or_cancer->visit_to_Asia dyspnoea dyspnoea bronchitis bronchitis bronchitis->dyspnoea smoking smoking bronchitis->smoking lung_cancer->bronchitis visit_to_Asia->tuberculosis G visit_to_Asia visit_to_Asia tuberculosis tuberculosis visit_to_Asia->tuberculosis tuberculos_or_cancer tuberculos_or_cancer tuberculosis->tuberculos_or_cancer tuberculos_or_cancer->visit_to_Asia positive_XraY positive_XraY lung_cancer lung_cancer tuberculos_or_cancer->lung_cancer dyspnoea dyspnoea tuberculos_or_cancer->dyspnoea positive_XraY->tuberculos_or_cancer bronchitis bronchitis lung_cancer->bronchitis smoking smoking smoking->lung_cancer bronchitis->smoking bronchitis->dyspnoea G a->b overflow c->d Missing e->f reversed g->h Correct G positive_XraY positive_XraY tuberculos_or_cancer tuberculos_or_cancer positive_XraY->tuberculos_or_cancer tuberculosis tuberculosis lung_cancer lung_cancer tuberculos_or_cancer->lung_cancer visit_to_Asia visit_to_Asia tuberculos_or_cancer->visit_to_Asia dyspnoea dyspnoea bronchitis bronchitis bronchitis->dyspnoea smoking smoking bronchitis->smoking lung_cancer->bronchitis visit_to_Asia->tuberculosis G positive_XraY positive_XraY tuberculosis tuberculosis tuberculos_or_cancer tuberculos_or_cancer tuberculosis->tuberculos_or_cancer tuberculos_or_cancer->positive_XraY dyspnoea dyspnoea tuberculos_or_cancer->dyspnoea bronchitis bronchitis bronchitis->dyspnoea smoking smoking smoking->bronchitis lung_cancer lung_cancer smoking->lung_cancer lung_cancer->tuberculos_or_cancer visit_to_Asia visit_to_Asia visit_to_Asia->tuberculosis G visit_to_Asia visit_to_Asia tuberculosis tuberculosis visit_to_Asia->tuberculosis tuberculos_or_cancer tuberculos_or_cancer tuberculosis->tuberculos_or_cancer tuberculos_or_cancer->visit_to_Asia positive_XraY positive_XraY tuberculos_or_cancer->positive_XraY lung_cancer lung_cancer dyspnoea dyspnoea tuberculos_or_cancer->dyspnoea lung_cancer->tuberculos_or_cancer bronchitis bronchitis lung_cancer->bronchitis smoking smoking smoking->lung_cancer smoking->bronchitis bronchitis->dyspnoea G a->b overflow c->d Missing e->f reversed g->h Correct
In [30]:

print("But also gives access to different scores :")
print(gcmp.scores())
print(gcmp.skeletonScores())
print(gcmp.hamming())

But also gives access to different scores :
{'count': {'tp': 2, 'tn': 43, 'fp': 5, 'fn': 6}, 'recall': 0.25, 'precision': 0.2857142857142857, 'fscore': 0.26666666666666666, 'dist2opt': 1.0357142857142856}
{'count': {'tp': 5, 'tn': 18, 'fp': 2, 'fn': 3}, 'recall': 0.625, 'precision': 0.7142857142857143, 'fscore': 0.6666666666666666, 'dist2opt': 0.471442099373003}
{'hamming': 5, 'structural hamming': 8}

In [31]:

print("KL divergence can be computed")
kl=gum.ExactBNdistance (bn,bn2)
kl.compute()

KL divergence can be computed

Out[31]:

{'klPQ': 0.14959060082593612,
'errorPQ': 0,
'klQP': 0.055813027902177785,
'errorQP': 64,
'hellinger': 0.22242449813301346,
'bhattacharya': 0.025047406641408764,
'jensen-shannon': 0.028780860049918425}


### 5. Mixing algorithms

First we learn a structure with HillClimbing (faster ?)

In [32]:

learner=gum.BNLearner("out/sample_asia.csv",bn) #using bn as template for variables
learner.useGreedyHillClimbing()
bn2=learner.learnBN()
kl=gum.ExactBNdistance(bn,bn2)
gnb.sideBySide(bn,bn2,gnb.getBNDiff(bn,bn2),
"<br/>".join(["<b>"+k+"</b> :"+str(v) for k,v in kl.compute().items()]),
captions=["original","learned BN","diff","distances"])

 G positive_XraY positive_XraY tuberculosis tuberculosis tuberculos_or_cancer tuberculos_or_cancer tuberculosis->tuberculos_or_cancer tuberculos_or_cancer->positive_XraY dyspnoea dyspnoea tuberculos_or_cancer->dyspnoea bronchitis bronchitis bronchitis->dyspnoea smoking smoking smoking->bronchitis lung_cancer lung_cancer smoking->lung_cancer lung_cancer->tuberculos_or_cancer visit_to_Asia visit_to_Asia visit_to_Asia->tuberculosis original G positive_XraY positive_XraY tuberculosis tuberculosis tuberculos_or_cancer tuberculos_or_cancer tuberculos_or_cancer->positive_XraY tuberculos_or_cancer->tuberculosis dyspnoea dyspnoea tuberculos_or_cancer->dyspnoea bronchitis bronchitis bronchitis->dyspnoea smoking smoking smoking->bronchitis lung_cancer lung_cancer lung_cancer->tuberculosis lung_cancer->tuberculos_or_cancer lung_cancer->smoking visit_to_Asia visit_to_Asia visit_to_Asia->tuberculosis visit_to_Asia->tuberculos_or_cancer learned BN G visit_to_Asia visit_to_Asia tuberculosis tuberculosis visit_to_Asia->tuberculosis tuberculos_or_cancer tuberculos_or_cancer visit_to_Asia->tuberculos_or_cancer tuberculos_or_cancer->tuberculosis positive_XraY positive_XraY tuberculos_or_cancer->positive_XraY dyspnoea dyspnoea tuberculos_or_cancer->dyspnoea lung_cancer lung_cancer lung_cancer->tuberculosis lung_cancer->tuberculos_or_cancer smoking smoking lung_cancer->smoking bronchitis bronchitis smoking->bronchitis bronchitis->dyspnoea diff klPQ :0.00019860298907722882errorPQ :0klQP :0.00016824945390611122errorQP :128hellinger :0.008580785291602801bhattacharya :3.6809973723158954e-05jensen-shannon :5.088171483007349e-05distances

And then we refine with tabuList

In [33]:

learner=gum.BNLearner("out/sample_asia.csv",bn) #using bn as template for variables
learner.useLocalSearchWithTabuList()

learner.setInitialDAG(bn2.dag())
print(learner)
bn3=learner.learnBN()
kl=gum.ExactBNdistance(bn,bn3)
gnb.sideBySide(bn,bn2,gnb.getBNDiff(bn,bn2),
"<br/>".join(["<b>"+k+"</b> :"+str(v) for k,v in kl.compute().items()]),
captions=["original","learned BN","diff","distances"])

Filename       : out/sample_asia.csv
Size           : (50000,8)
Variables      : visit_to_Asia[2], tuberculosis[2], tuberculos_or_cancer[2], positive_XraY[2], lung_cancer[2], smoking[2], bronchitis[2], dyspnoea[2]
Induced types  : False
Missing values : False
Algorithm      : Local Search with Tabu List
Tabu list size : 2
Score          : BDeu  (Not used for constraint-based algorithms)
Correction     : MDL  (Not used for score-based algorithms)
Prior          : -
Initial DAG    : True  (digraph {
0;
1;
2;
3;
4;
5;
6;
7;

0 -> 1;
2 -> 3;
2 -> 1;
2 -> 7;
4 -> 1;
4 -> 5;
6 -> 7;
4 -> 2;
0 -> 2;
5 -> 6;
}

)


 G positive_XraY positive_XraY tuberculosis tuberculosis tuberculos_or_cancer tuberculos_or_cancer tuberculosis->tuberculos_or_cancer tuberculos_or_cancer->positive_XraY dyspnoea dyspnoea tuberculos_or_cancer->dyspnoea bronchitis bronchitis bronchitis->dyspnoea smoking smoking smoking->bronchitis lung_cancer lung_cancer smoking->lung_cancer lung_cancer->tuberculos_or_cancer visit_to_Asia visit_to_Asia visit_to_Asia->tuberculosis original G positive_XraY positive_XraY tuberculosis tuberculosis tuberculos_or_cancer tuberculos_or_cancer tuberculos_or_cancer->positive_XraY tuberculos_or_cancer->tuberculosis dyspnoea dyspnoea tuberculos_or_cancer->dyspnoea bronchitis bronchitis bronchitis->dyspnoea smoking smoking smoking->bronchitis lung_cancer lung_cancer lung_cancer->tuberculosis lung_cancer->tuberculos_or_cancer lung_cancer->smoking visit_to_Asia visit_to_Asia visit_to_Asia->tuberculosis visit_to_Asia->tuberculos_or_cancer learned BN G visit_to_Asia visit_to_Asia tuberculosis tuberculosis visit_to_Asia->tuberculosis tuberculos_or_cancer tuberculos_or_cancer visit_to_Asia->tuberculos_or_cancer tuberculos_or_cancer->tuberculosis positive_XraY positive_XraY tuberculos_or_cancer->positive_XraY dyspnoea dyspnoea tuberculos_or_cancer->dyspnoea lung_cancer lung_cancer lung_cancer->tuberculosis lung_cancer->tuberculos_or_cancer smoking smoking lung_cancer->smoking bronchitis bronchitis smoking->bronchitis bronchitis->dyspnoea diff klPQ :0.00022946466786724943errorPQ :0klQP :0.00018732565493151892errorQP :128hellinger :0.009049706157565618bhattacharya :4.094378708885513e-05jensen-shannon :5.659279968128039e-05distances

## Impact of the size of the database for the learning

In [34]:

rows=3
sizes=[400,500,700,1000,2000,5000,
10000,50000,75000,
100000,150000,175000,
200000,300000,500000]

def extract_asia(n):
"""
extract n line from asia.csv to extract.csv
"""
with open("out/sample_asia.csv","r") as src:
with open("out/extract_asia.csv","w") as dst:
for _ in range(n+1):

In [35]:

gnb.flow.clear()
nbr=0
l=[]
for i in sizes:
extract_asia(i)
learner=gum.BNLearner("out/extract_asia.csv",bn) # using bn as template for variables
learner.useGreedyHillClimbing()
print(learner.state()["Size"][0])
bn2=learner.learnBN()

kl=gum.ExactBNdistance(bn,bn2)
r=kl.compute()
l.append(log(r['klPQ']))

gnb.flow.display()
plot(sizes,l)
print(f"final value computed : {l[-1]}")

(400,8)
(500,8)
(700,8)
(1000,8)
(2000,8)
(5000,8)
(10000,8)
(50000,8)
(50000,8)
(50000,8)
(50000,8)
(50000,8)
(50000,8)
(50000,8)
(50000,8)


size=400

size=500

size=700

size=1000

size=2000

size=5000

size=10000

size=50000

size=75000

size=100000

size=150000

size=175000

size=200000

size=300000

size=500000
final value computed : -8.531506652322214

In [36]:

gnb.flow.clear()
nbr=0
l=[]
for i in sizes:
extract_asia(i)
learner=gum.BNLearner("out/extract_asia.csv",bn) #using bn as template for variables
learner.useLocalSearchWithTabuList()
print(learner.state()["Size"][0])
bn2=learner.learnBN()

kl=gum.ExactBNdistance(bn,bn2)
r=kl.compute()
l.append(log(r['klPQ']))

gnb.flow.display()
plot(sizes,l)
print(l[-1])

(400,8)
(500,8)
(700,8)
(1000,8)
(2000,8)
(5000,8)
(10000,8)
(50000,8)
(50000,8)
(50000,8)
(50000,8)
(50000,8)
(50000,8)
(50000,8)
(50000,8)


size=400

size=500

size=700

size=1000

size=2000

size=5000

size=10000

size=50000

size=75000

size=100000

size=150000

size=175000

size=200000

size=300000

size=500000
-8.239398044165032