Learning essential graphs

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aGrUM

interactive online version

In [1]:
from pylab import *
import matplotlib.pyplot as plt

import os

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


Compare learning algorithms

Essentially MIIC and 3off2 computes the essential graph (CPDAG) from data. Essential graphs are PDAGs (Partially Directed Acyclic Graphs).

In [2]:
learner=gum.BNLearner("res/sample_asia.csv")
learner.use3off2()
learner.useNMLCorrection()
print(learner)
Filename       : res/sample_asia.csv
Size           : (50000,8)
Variables      : visit_to_Asia[2], lung_cancer[2], tuberculosis[2], bronchitis[2], positive_XraY[2], smoking[2], tuberculos_or_cancer[2], dyspnoea[2]
Induced types  : True
Missing values : False
Algorithm      : 3off2
Score          : BDeu
Correction     : NML  (Not used for score-based algorithms)
Prior          : -

In [3]:
ge3off2=learner.learnEssentialGraph()
print(ge3off2)
<pyAgrum.pyAgrum.EssentialGraph; proxy of <Swig Object of type 'gum::EssentialGraph *' at 0x1097be970> >
In [4]:
gnb.show(ge3off2)
../_images/notebooks_33-Learning_LearningAndEssentialGraphs_6_0.svg
In [5]:
learner=gum.BNLearner("res/sample_asia.csv")
learner.useMIIC()
learner.useNMLCorrection()
print(learner)
gemiic=learner.learnEssentialGraph()
gemiic
Filename       : res/sample_asia.csv
Size           : (50000,8)
Variables      : visit_to_Asia[2], lung_cancer[2], tuberculosis[2], bronchitis[2], positive_XraY[2], smoking[2], tuberculos_or_cancer[2], dyspnoea[2]
Induced types  : True
Missing values : False
Algorithm      : MIIC
Score          : BDeu
Correction     : NML  (Not used for score-based algorithms)
Prior          : -

Out[5]:
no_name 0 visit_to_Asia 2 tuberculosis 0->2 1 lung_cancer 5 smoking 1->5 6 tuberculos_or_cancer 1->6 2->6 3 bronchitis 3->5 7 dyspnoea 3->7 4 positive_XraY 6->4 6->7

For the others methods, it is possible to obtain the essential graph from the learned BN.

In [7]:
learner=gum.BNLearner("res/sample_asia.csv")
learner.useGreedyHillClimbing()
bnHC=learner.learnBN()
print(learner)
geHC=gum.EssentialGraph(bnHC)
geHC
gnb.sideBySide(bnHC,geHC)
Filename       : res/sample_asia.csv
Size           : (50000,8)
Variables      : visit_to_Asia[2], lung_cancer[2], tuberculosis[2], bronchitis[2], positive_XraY[2], smoking[2], tuberculos_or_cancer[2], dyspnoea[2]
Induced types  : True
Missing values : False
Algorithm      : Greedy Hill Climbing
Score          : BDeu
Correction     : MDL  (Not used for score-based algorithms)
Prior          : -

G tuberculosis tuberculosis visit_to_Asia visit_to_Asia tuberculosis->visit_to_Asia tuberculos_or_cancer tuberculos_or_cancer tuberculosis->tuberculos_or_cancer positive_XraY positive_XraY bronchitis bronchitis smoking smoking bronchitis->smoking dyspnoea dyspnoea bronchitis->dyspnoea lung_cancer lung_cancer lung_cancer->bronchitis lung_cancer->smoking lung_cancer->tuberculos_or_cancer tuberculos_or_cancer->positive_XraY tuberculos_or_cancer->dyspnoea
no_name 0 visit_to_Asia 2 tuberculosis 0->2 1 lung_cancer 3 bronchitis 1->3 5 smoking 1->5 6 tuberculos_or_cancer 1->6 2->6 3->5 7 dyspnoea 3->7 4 positive_XraY 6->4 6->7
In [8]:
learner=gum.BNLearner("res/sample_asia.csv")
learner.useLocalSearchWithTabuList()
print(learner)
bnTL=learner.learnBN()
geTL=gum.EssentialGraph(bnTL)
geTL
gnb.sideBySide(bnTL,geTL)
Filename       : res/sample_asia.csv
Size           : (50000,8)
Variables      : visit_to_Asia[2], lung_cancer[2], tuberculosis[2], bronchitis[2], positive_XraY[2], smoking[2], tuberculos_or_cancer[2], dyspnoea[2]
Induced types  : True
Missing values : False
Algorithm      : Local Search with Tabu List
Tabu list size : 2
Score          : BDeu
Correction     : MDL  (Not used for score-based algorithms)
Prior          : -

G tuberculosis tuberculosis lung_cancer lung_cancer tuberculosis->lung_cancer visit_to_Asia visit_to_Asia tuberculosis->visit_to_Asia positive_XraY positive_XraY tuberculos_or_cancer tuberculos_or_cancer positive_XraY->tuberculos_or_cancer bronchitis bronchitis dyspnoea dyspnoea bronchitis->dyspnoea smoking smoking lung_cancer->smoking smoking->bronchitis tuberculos_or_cancer->tuberculosis tuberculos_or_cancer->lung_cancer tuberculos_or_cancer->dyspnoea
no_name 0 visit_to_Asia 2 tuberculosis 0->2 1 lung_cancer 1->2 5 smoking 1->5 6 tuberculos_or_cancer 1->6 2->6 3 bronchitis 3->5 7 dyspnoea 3->7 4 positive_XraY 4->6 6->7

Hence we can compare the 4 algorithms.

In [9]:
(
  gnb.flow.clear()
  .add(ge3off2,"Essential graph from 3off2")
  .add(gemiic,"Essential graph from miic")
  .add(bnHC,"BayesNet from GHC")
  .add(geHC,"Essential graph from GHC")
  .add(bnTL,"BayesNet from TabuList")
  .add(geTL,"Essential graph from TabuList")
  .display()
)
no_name 0 visit_to_Asia 2 tuberculosis 0->2 1 lung_cancer 5 smoking 1->5 6 tuberculos_or_cancer 1->6 2->6 3 bronchitis 3->5 7 dyspnoea 3->7 4 positive_XraY 6->4 6->7
Essential graph from 3off2
no_name 0 visit_to_Asia 2 tuberculosis 0->2 1 lung_cancer 5 smoking 1->5 6 tuberculos_or_cancer 1->6 2->6 3 bronchitis 3->5 7 dyspnoea 3->7 4 positive_XraY 6->4 6->7
Essential graph from miic
G tuberculosis tuberculosis visit_to_Asia visit_to_Asia tuberculosis->visit_to_Asia tuberculos_or_cancer tuberculos_or_cancer tuberculosis->tuberculos_or_cancer positive_XraY positive_XraY bronchitis bronchitis smoking smoking bronchitis->smoking dyspnoea dyspnoea bronchitis->dyspnoea lung_cancer lung_cancer lung_cancer->bronchitis lung_cancer->smoking lung_cancer->tuberculos_or_cancer tuberculos_or_cancer->positive_XraY tuberculos_or_cancer->dyspnoea
BayesNet from GHC
no_name 0 visit_to_Asia 2 tuberculosis 0->2 1 lung_cancer 3 bronchitis 1->3 5 smoking 1->5 6 tuberculos_or_cancer 1->6 2->6 3->5 7 dyspnoea 3->7 4 positive_XraY 6->4 6->7
Essential graph from GHC
G tuberculosis tuberculosis lung_cancer lung_cancer tuberculosis->lung_cancer visit_to_Asia visit_to_Asia tuberculosis->visit_to_Asia positive_XraY positive_XraY tuberculos_or_cancer tuberculos_or_cancer positive_XraY->tuberculos_or_cancer bronchitis bronchitis dyspnoea dyspnoea bronchitis->dyspnoea smoking smoking lung_cancer->smoking smoking->bronchitis tuberculos_or_cancer->tuberculosis tuberculos_or_cancer->lung_cancer tuberculos_or_cancer->dyspnoea
BayesNet from TabuList
no_name 0 visit_to_Asia 2 tuberculosis 0->2 1 lung_cancer 1->2 5 smoking 1->5 6 tuberculos_or_cancer 1->6 2->6 3 bronchitis 3->5 7 dyspnoea 3->7 4 positive_XraY 4->6 6->7
Essential graph from TabuList
In [ ]: