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Learning essential graphs

Creative Commons LicenseaGrUMinteractive online version
from pylab import *




import pyagrum as gum
import pyagrum.lib.notebook as gnb

Compare learning algorithms

Section titled “Compare learning algorithms”

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

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
Correction     : NML
Prior          : -
gemiic = learner.learnEssentialGraph()
gnb.show(gemiic)

svg

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

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
Prior          : -
G visit_to_Asia visit_to_Asia positive_XraY positive_XraY lung_cancer lung_cancer smoking smoking lung_cancer->smoking tuberculos_or_cancer tuberculos_or_cancer lung_cancer->tuberculos_or_cancer bronchitis bronchitis lung_cancer->bronchitis tuberculos_or_cancer->positive_XraY dyspnoea dyspnoea tuberculos_or_cancer->dyspnoea bronchitis->smoking bronchitis->dyspnoea tuberculosis tuberculosis tuberculosis->visit_to_Asia tuberculosis->tuberculos_or_cancer
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 
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
Prior          : -
G visit_to_Asia visit_to_Asia positive_XraY positive_XraY tuberculos_or_cancer tuberculos_or_cancer positive_XraY->tuberculos_or_cancer tuberculosis tuberculosis positive_XraY->tuberculosis lung_cancer lung_cancer smoking smoking lung_cancer->smoking bronchitis bronchitis smoking->bronchitis tuberculos_or_cancer->lung_cancer dyspnoea dyspnoea tuberculos_or_cancer->dyspnoea bronchitis->dyspnoea tuberculosis->visit_to_Asia tuberculosis->lung_cancer tuberculosis->tuberculos_or_cancer
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 4 positive_XraY 2->4 2->6 3 bronchitis 3->5 7 dyspnoea 3->7 4->6 6->7

Hence we can compare the 4 algorithms.

(
  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 visit_to_Asia visit_to_Asia positive_XraY positive_XraY lung_cancer lung_cancer smoking smoking lung_cancer->smoking tuberculos_or_cancer tuberculos_or_cancer lung_cancer->tuberculos_or_cancer bronchitis bronchitis lung_cancer->bronchitis tuberculos_or_cancer->positive_XraY dyspnoea dyspnoea tuberculos_or_cancer->dyspnoea bronchitis->smoking bronchitis->dyspnoea tuberculosis tuberculosis tuberculosis->visit_to_Asia tuberculosis->tuberculos_or_cancer
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 visit_to_Asia visit_to_Asia positive_XraY positive_XraY tuberculos_or_cancer tuberculos_or_cancer positive_XraY->tuberculos_or_cancer tuberculosis tuberculosis positive_XraY->tuberculosis lung_cancer lung_cancer smoking smoking lung_cancer->smoking bronchitis bronchitis smoking->bronchitis tuberculos_or_cancer->lung_cancer dyspnoea dyspnoea tuberculos_or_cancer->dyspnoea bronchitis->dyspnoea tuberculosis->visit_to_Asia tuberculosis->lung_cancer tuberculosis->tuberculos_or_cancer
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 4 positive_XraY 2->4 2->6 3 bronchitis 3->5 7 dyspnoea 3->7 4->6 6->7
Essential graph from TabuList