Learning essential graphs

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aGrUM

interactive online version

In [1]:
%matplotlib inline
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 mixed graphs.

In [2]:
learner=gum.BNLearner("out/sample_asia.csv")
learner.use3off2()
learner.useNMLCorrection()
print(learner)
ge3off2=learner.learnEssentialGraph()
Filename       : out/sample_asia.csv
Size           : (500000,8)
Variables      : tuberculosis[2], smoking[2], tuberculos_or_cancer[2], visit_to_Asia[2], positive_XraY[2], bronchitis[2], lung_cancer[2], dyspnoea[2]
Induced types  : True
Missing values : False
Algorithm      : 3off2
Correction     : NML
Prior          : -

In [3]:
gnb.showDot(ge3off2.toDot());
../_images/notebooks_33-Learning_LearningAndEssentialGraphs_5_0.svg
In [4]:
learner=gum.BNLearner("out/sample_asia.csv")
learner.useMIIC()
learner.useNMLCorrection()
print(learner)
gemiic=learner.learnEssentialGraph()
gemiic
Filename       : out/sample_asia.csv
Size           : (500000,8)
Variables      : tuberculosis[2], smoking[2], tuberculos_or_cancer[2], visit_to_Asia[2], positive_XraY[2], bronchitis[2], lung_cancer[2], dyspnoea[2]
Induced types  : True
Missing values : False
Algorithm      : MIIC
Correction     : NML
Prior          : -

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

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

In [5]:
learner=gum.BNLearner("out/sample_asia.csv")
learner.useGreedyHillClimbing()
bnHC=learner.learnBN()
print(learner)
geHC=gum.EssentialGraph(bnHC)
geHC
gnb.sideBySide(bnHC,geHC)
Filename       : out/sample_asia.csv
Size           : (500000,8)
Variables      : tuberculosis[2], smoking[2], tuberculos_or_cancer[2], visit_to_Asia[2], positive_XraY[2], bronchitis[2], lung_cancer[2], dyspnoea[2]
Induced types  : True
Missing values : False
Algorithm      : Greedy Hill Climbing
Score          : BDeu
Prior          : -

G tuberculos_or_cancer tuberculos_or_cancer dyspnoea dyspnoea tuberculos_or_cancer->dyspnoea positive_XraY positive_XraY tuberculos_or_cancer->positive_XraY bronchitis bronchitis tuberculos_or_cancer->bronchitis dyspnoea->bronchitis smoking smoking bronchitis->smoking tuberculosis tuberculosis tuberculosis->tuberculos_or_cancer tuberculosis->dyspnoea visit_to_Asia visit_to_Asia tuberculosis->visit_to_Asia lung_cancer lung_cancer lung_cancer->tuberculos_or_cancer lung_cancer->smoking lung_cancer->bronchitis
no_name 0 tuberculosis 2 tuberculos_or_cancer 0->2 3 visit_to_Asia 0->3 7 dyspnoea 0->7 1 smoking 4 positive_XraY 2->4 5 bronchitis 2->5 2->7 5->1 6 lung_cancer 6->1 6->2 6->5 7->5
In [6]:
learner=gum.BNLearner("out/sample_asia.csv")
learner.useLocalSearchWithTabuList()
print(learner)
bnTL=learner.learnBN()
geTL=gum.EssentialGraph(bnTL)
geTL
gnb.sideBySide(bnTL,geTL)
Filename       : out/sample_asia.csv
Size           : (500000,8)
Variables      : tuberculosis[2], smoking[2], tuberculos_or_cancer[2], visit_to_Asia[2], positive_XraY[2], bronchitis[2], lung_cancer[2], dyspnoea[2]
Induced types  : True
Missing values : False
Algorithm      : Local Search with Tabu List
Tabu list size : 2
Score          : BDeu
Prior          : -

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

Hence we can compare the 4 algorithms.

In [7]:
(
  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 tuberculosis 2 tuberculos_or_cancer 0->2 3 visit_to_Asia 0->3 1 smoking 5 bronchitis 1->5 6 lung_cancer 1->6 4 positive_XraY 2->4 7 dyspnoea 2->7 5->7 6->2
Essential graph from 3off2
no_name 0 tuberculosis 2 tuberculos_or_cancer 0->2 3 visit_to_Asia 0->3 1 smoking 5 bronchitis 1->5 6 lung_cancer 1->6 4 positive_XraY 2->4 7 dyspnoea 2->7 5->7 6->2
Essential graph from miic
G tuberculos_or_cancer tuberculos_or_cancer dyspnoea dyspnoea tuberculos_or_cancer->dyspnoea positive_XraY positive_XraY tuberculos_or_cancer->positive_XraY bronchitis bronchitis tuberculos_or_cancer->bronchitis dyspnoea->bronchitis smoking smoking bronchitis->smoking tuberculosis tuberculosis tuberculosis->tuberculos_or_cancer tuberculosis->dyspnoea visit_to_Asia visit_to_Asia tuberculosis->visit_to_Asia lung_cancer lung_cancer lung_cancer->tuberculos_or_cancer lung_cancer->smoking lung_cancer->bronchitis
BayesNet from GHC
no_name 0 tuberculosis 2 tuberculos_or_cancer 0->2 3 visit_to_Asia 0->3 7 dyspnoea 0->7 1 smoking 4 positive_XraY 2->4 5 bronchitis 2->5 2->7 5->1 6 lung_cancer 6->1 6->2 6->5 7->5
Essential graph from GHC
G tuberculos_or_cancer tuberculos_or_cancer dyspnoea dyspnoea tuberculos_or_cancer->dyspnoea positive_XraY positive_XraY smoking smoking smoking->dyspnoea bronchitis bronchitis smoking->bronchitis bronchitis->dyspnoea tuberculosis tuberculosis tuberculosis->tuberculos_or_cancer tuberculosis->positive_XraY visit_to_Asia visit_to_Asia tuberculosis->visit_to_Asia lung_cancer lung_cancer lung_cancer->tuberculos_or_cancer lung_cancer->positive_XraY lung_cancer->smoking
BayesNet from TabuList
no_name 0 tuberculosis 2 tuberculos_or_cancer 0->2 3 visit_to_Asia 0->3 4 positive_XraY 0->4 1 smoking 5 bronchitis 1->5 6 lung_cancer 1->6 7 dyspnoea 1->7 2->7 5->7 6->2 6->4
Essential graph from TabuList
In [ ]: