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 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.useMIIC()
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      : MIIC
Score          : BDeu  (Not used for constraint-based algorithms)
Correction     : NML  (Not used for score-based algorithms)
Prior          : -


In [3]:

gemiic=learner.learnEssentialGraph()
gnb.show(gemiic)
../_images/notebooks_33-Learning_LearningAndEssentialGraphs_5_0.svg

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

In [4]:

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  (Not used for constraint-based algorithms)
Correction     : MDL  (Not used for score-based algorithms)
Prior          : -
G positive_XraY positive_XraY dyspnoea dyspnoea visit_to_Asia visit_to_Asia tuberculosis tuberculosis tuberculosis->visit_to_Asia tuberculos_or_cancer tuberculos_or_cancer tuberculosis->tuberculos_or_cancer lung_cancer lung_cancer smoking smoking lung_cancer->smoking lung_cancer->tuberculos_or_cancer bronchitis bronchitis lung_cancer->bronchitis tuberculos_or_cancer->positive_XraY tuberculos_or_cancer->dyspnoea bronchitis->dyspnoea bronchitis->smoking
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 [5]:

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  (Not used for constraint-based algorithms)
Correction     : MDL  (Not used for score-based algorithms)
Prior          : -
G positive_XraY positive_XraY tuberculos_or_cancer tuberculos_or_cancer positive_XraY->tuberculos_or_cancer dyspnoea dyspnoea visit_to_Asia visit_to_Asia tuberculosis tuberculosis tuberculosis->visit_to_Asia lung_cancer lung_cancer tuberculosis->lung_cancer smoking smoking lung_cancer->smoking bronchitis bronchitis smoking->bronchitis tuberculos_or_cancer->dyspnoea tuberculos_or_cancer->tuberculosis tuberculos_or_cancer->lung_cancer bronchitis->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 [6]:

(
  gnb.flow.clear()
  .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 miic
G positive_XraY positive_XraY dyspnoea dyspnoea visit_to_Asia visit_to_Asia tuberculosis tuberculosis tuberculosis->visit_to_Asia tuberculos_or_cancer tuberculos_or_cancer tuberculosis->tuberculos_or_cancer lung_cancer lung_cancer smoking smoking lung_cancer->smoking lung_cancer->tuberculos_or_cancer bronchitis bronchitis lung_cancer->bronchitis tuberculos_or_cancer->positive_XraY tuberculos_or_cancer->dyspnoea bronchitis->dyspnoea bronchitis->smoking
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 positive_XraY positive_XraY tuberculos_or_cancer tuberculos_or_cancer positive_XraY->tuberculos_or_cancer dyspnoea dyspnoea visit_to_Asia visit_to_Asia tuberculosis tuberculosis tuberculosis->visit_to_Asia lung_cancer lung_cancer tuberculosis->lung_cancer smoking smoking lung_cancer->smoking bronchitis bronchitis smoking->bronchitis tuberculos_or_cancer->dyspnoea tuberculos_or_cancer->tuberculosis tuberculos_or_cancer->lung_cancer bronchitis->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 [ ]: