a study on comparison of bayesian network structure learning algorithms for selecting appropriate...
TRANSCRIPT
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
A Study on Comparison ofBayesian Network Structure Learning Algorithms
for Selecting Appropriate Models
Jae-seong Yoo
Dept. of Statistics
January 19, 2015
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
Title1 Introduction
GoalBayesian Network๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ํน์ง
๋ค๋ฅธ ๊ธฐ๋ฒ๊ณผ์ ์ฅ๋จ์ ๋น๊ต
๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ๋ค์ํ ์ ํ
Bayesian Network Structure Learning2 Structure Learning Algorithms in bnlearn
Available Constraint-based Learning AlgorithmsAvailable Score-based Learning AlgorithmsAvailable Hybrid Learning Algorithms
3 The Comparison MethodologyThe Number of Graphical Errors in the Learnt StructureNetwork Scores
4 Data Generation with BN Data Generator in R5 Simulation
Real DatasetsSynthetic Data According to Topologies
6 Discussion
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
GoalBayesian Network๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ํน์ง๋ค๋ฅธ ๊ธฐ๋ฒ๊ณผ์ ์ฅ๋จ์ ๋น๊ต๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ๋ค์ํ ์ ํBayesian Network Structure Learning
Goal
In this paper, we compare the performance between the Bayesian network structurelearning algorithms provided by bnlearn package in R.
The performance is evaluated by
using a scoreorcomparing between the target network and the learnt network.
In this paper, it was confirmed that algorithm specific performance test results usingfore-mentioned methods are different.
A data generator based on Bayesian network model using R is built and introduced.
The aim of this paper is to provide objective guidance of selecting suitable algorithm inaccordance to target network using synthetic data generated based on topology.
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
GoalBayesian Network๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ํน์ง๋ค๋ฅธ ๊ธฐ๋ฒ๊ณผ์ ์ฅ๋จ์ ๋น๊ต๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ๋ค์ํ ์ ํBayesian Network Structure Learning
Bayesian Network
A BN defines a unique joint probability distribution over X given by
PB (X1, ยท ยท ยท ,Xn) =n
โi=1
PB (Xi |โXi
).
A BN encodes the independence assumptions over the component random variables ofX .An edge (j , i) in E represents a direct dependency of Xi from Xj .The set of all Bayesian networks with n variables is denotes by Bn.
Figure: P(A,B,C ,D,E ) = P(A)P(B |A)P(C |A)P(D|B,C )P(E |D)
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
GoalBayesian Network๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ํน์ง๋ค๋ฅธ ๊ธฐ๋ฒ๊ณผ์ ์ฅ๋จ์ ๋น๊ต๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ๋ค์ํ ์ ํBayesian Network Structure Learning
๊ธฐ๋ณธ ๊ฐ๋
๋ฒ ์ด์ง์ ๋คํธ์ํฌ(์ดํ BN)๋ ํ๋ฅ ๊ฐ์ด ๋ชจ์ธ ์งํฉ์ ๊ฒฐํฉํ๋ฅ ๋ถํฌ์ ๊ฒฐ์ ๋ชจ๋ธ์ด๋ค.
ํน์ ๋ถ์ผ์ ์์ญ์ง์์ ํ๋ฅ ์ ์ผ๋ก ํํํ๋ ์๋จ
๋ณ์๋ค๊ฐ์ ํ๋ฅ ์ ์์กด ๊ด๊ณ๋ฅผ ๋ํ๋ด๋ ๊ทธ๋ํ์, ๊ฐ ๋ณ์๋ณ ์กฐ๊ฑด๋ถ ํ๋ฅ ๋ก ๊ตฌ์ฑ๋๋ค.
ํ๋์ BN์ ๊ฐ ๋ ธ๋๋ง๋ค ํ๋์ ์กฐ๊ฑด๋ถ ํ๋ฅ ํ(CPT ; Conditional Probability Table)๋ฅผ ๊ฐ๋ ๋น์ํ์ ํฅ๊ทธ๋ํ(DAG ; Directed Acycle Graph)๋ก ์ ์ํ ์ ์๋ค.
๋ ธ๋์ ๋ ธ๋๋ฅผ ์ฐ๊ฒฐํ๋ ํธ(arc or edge)๋ ๋ ธ๋ ์ฌ์ด์ ๊ด๊ณ๋ฅผ ๋ํ๋ด๋ฉฐ, ๋ณ์์ํ๋ฅ ์ ์ธ ์ธ๊ณผ๊ด๊ณ๋ก ๋คํธ์ํฌ๋ฅผ ๊ตฌ์ฑํ๊ณ ์กฐ๊ฑด๋ถํ๋ฅ ํ(CPT)๋ฅผ ๊ฐ์ง๊ณ ๋ค์์ ์๊ณผ๊ฐ์ ๋ฒ ์ด์ฆ ์ ๋ฆฌ(Bayes Theorem)์ ์ด์ฉํ์ฌ ๊ฒฐ๊ณผ๋ฅผ ์ถ๋ก ํ ์ ์๋ค.
P(A|B) =P(A,B)
P(B)
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
GoalBayesian Network๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ํน์ง๋ค๋ฅธ ๊ธฐ๋ฒ๊ณผ์ ์ฅ๋จ์ ๋น๊ต๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ๋ค์ํ ์ ํBayesian Network Structure Learning
๊ธฐ๋ณธ ๊ฐ๋
Figure: Nodes
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
GoalBayesian Network๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ํน์ง๋ค๋ฅธ ๊ธฐ๋ฒ๊ณผ์ ์ฅ๋จ์ ๋น๊ต๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ๋ค์ํ ์ ํBayesian Network Structure Learning
๊ธฐ๋ณธ ๊ฐ๋
Figure: Edges
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
GoalBayesian Network๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ํน์ง๋ค๋ฅธ ๊ธฐ๋ฒ๊ณผ์ ์ฅ๋จ์ ๋น๊ต๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ๋ค์ํ ์ ํBayesian Network Structure Learning
๊ธฐ๋ณธ ๊ฐ๋
Figure: Edges = directed, (No cycles!)
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
GoalBayesian Network๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ํน์ง๋ค๋ฅธ ๊ธฐ๋ฒ๊ณผ์ ์ฅ๋จ์ ๋น๊ต๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ๋ค์ํ ์ ํBayesian Network Structure Learning
๊ธฐ๋ณธ ๊ฐ๋
์ผ๋ฐ์ ์ธ ๋ฒ ์ด์ง์ ๋คํธ์ํฌ๋ ๋ฒ ์ด์ฆ ์ ๋ฆฌ, ๊ณฑ์ ๊ท์น, ์ฒด์ธ ๊ท์น(chain rule)์ ์ํ์ฌ๋ค์๊ณผ ๊ฐ์ ์์ด ๋ง๋ค์ด์ง๋ค.
P(A,B,C ,D,E ) = โi
P(xi |parenti )
์ฌ๊ธฐ์ x1, ยท ยท ยท , xn์ ํน์ ๋ฐ์ดํฐ์ ์์ฑ ์งํฉ
parent(xi )๋ xi์ ๋ถ๋ชจ ๋ ธ๋๋ค์ ์งํฉ
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
GoalBayesian Network๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ํน์ง๋ค๋ฅธ ๊ธฐ๋ฒ๊ณผ์ ์ฅ๋จ์ ๋น๊ต๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ๋ค์ํ ์ ํBayesian Network Structure Learning
๊ธฐ๋ณธ ๊ฐ๋
Figure: P(A,B,C ,D,E ) = โi P(nodei |parentsi )
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
GoalBayesian Network๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ํน์ง๋ค๋ฅธ ๊ธฐ๋ฒ๊ณผ์ ์ฅ๋จ์ ๋น๊ต๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ๋ค์ํ ์ ํBayesian Network Structure Learning
๊ธฐ๋ณธ ๊ฐ๋
Figure: P(A,B,C ,D,E ) = P(A)
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
GoalBayesian Network๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ํน์ง๋ค๋ฅธ ๊ธฐ๋ฒ๊ณผ์ ์ฅ๋จ์ ๋น๊ต๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ๋ค์ํ ์ ํBayesian Network Structure Learning
๊ธฐ๋ณธ ๊ฐ๋
Figure: P(A,B,C ,D,E ) = P(A)P(B |A)
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
GoalBayesian Network๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ํน์ง๋ค๋ฅธ ๊ธฐ๋ฒ๊ณผ์ ์ฅ๋จ์ ๋น๊ต๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ๋ค์ํ ์ ํBayesian Network Structure Learning
๊ธฐ๋ณธ ๊ฐ๋
Figure: P(A,B,C ,D,E ) = P(A)P(B |A)P(C |A)
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
GoalBayesian Network๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ํน์ง๋ค๋ฅธ ๊ธฐ๋ฒ๊ณผ์ ์ฅ๋จ์ ๋น๊ต๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ๋ค์ํ ์ ํBayesian Network Structure Learning
๊ธฐ๋ณธ ๊ฐ๋
Figure: P(A,B,C ,D,E ) = P(A)P(B |A)P(C |A)P(D|B,C )
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
GoalBayesian Network๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ํน์ง๋ค๋ฅธ ๊ธฐ๋ฒ๊ณผ์ ์ฅ๋จ์ ๋น๊ต๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ๋ค์ํ ์ ํBayesian Network Structure Learning
๊ธฐ๋ณธ ๊ฐ๋
Figure: P(A,B,C ,D,E ) = P(A)P(B |A)P(C |A)P(D|B,C )P(E |D)
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
GoalBayesian Network๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ํน์ง๋ค๋ฅธ ๊ธฐ๋ฒ๊ณผ์ ์ฅ๋จ์ ๋น๊ต๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ๋ค์ํ ์ ํBayesian Network Structure Learning
S. L. Lauritzen and D. J. Spiegelhalter (1988)
S. L. Lauritzen and D. J. Spiegelhalter (1988),
โLocal Computations with Probabilities on Graphical Structures
and Their Application to Expert Systemsโ,
Journal of the Royal Statistical Society. Series B (Methodological), Vol. 50, No. 2, pp. 157-224
Abstract
Casual Network๋ ๋ณ์ set์ ํฌํจ๋์ด์๋ ์ํฅ๋ ฅ์ ํจํด์ ์์ ํ๋ ๊ฒ์ ๋งํ๋ฉฐ, ๋ง์๋ถ์ผ์์ ์ฌ์ฉ๋๊ณ ์๋ค. ์ด๋ ์ ๋ฌธ๊ฐ ์์คํ ์ผ๋ก๋ถํฐ ํฌ์ง๋ง(large) ํฌ์(sparse) ๋คํธ์ํฌ๋ฅผ์ด์ฉํด ๊ตญ์ง์ ๊ณ์ฐ์ ํ์ฌ ๊ตฌํด์ง ํ๊ท ์ ํตํด ์ด ์ํฅ๋ ฅ์ ์ถ๋ก ํ๋ ๊ฒ์ด ๋ณดํต์ด๋ค. ์ด๋์ ํํ ํ๋ฅ ์ ์ธ ๋ฐฉ๋ฒ์ ์ด์ฉํ๋ ๊ฒ์ด ๋ถ๊ฐ๋ฅํ์๋ค.
์ด ๋ ผ๋ฌธ์์๋ original network์ ์์ ๋ณํ๋ฅผ ์ฃผ์ด ์ผ๋ถ ๋ฒ์๋ฅผ ๊ฒฐํฉ ํ๋ฅ ๋ถํฌ๋ก ๋ํ๋ผ ์
์๊ณ , ์ด๋ฅผ ์ด์ฉํด์ ๋ณ์ ์ฌ์ด์ ๊ตญ์ง์ ์ํฅ๋ ฅ์ ์ถ๋ก ํ ์ ์๋ค๊ณ ์ค๋ช ํ๊ณ ์๋ค.
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
GoalBayesian Network๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ํน์ง๋ค๋ฅธ ๊ธฐ๋ฒ๊ณผ์ ์ฅ๋จ์ ๋น๊ต๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ๋ค์ํ ์ ํBayesian Network Structure Learning
S. L. Lauritzen and D. J. Spiegelhalter (1988)
Figure: ์์์ ๋ฐฉ๋ฌธ ์ฌ๋ถ, ํก์ฐ ์ฌ๋ถ์ ํ์งํ๊ณผ์ ๊ด๊ณ๋ฅผ ๋์ํํ ๋ฒ ์ด์ง์ ๋คํธ์ํฌ ๋ชจํ
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
GoalBayesian Network๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ํน์ง๋ค๋ฅธ ๊ธฐ๋ฒ๊ณผ์ ์ฅ๋จ์ ๋น๊ต๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ๋ค์ํ ์ ํBayesian Network Structure Learning
S. L. Lauritzen and D. J. Spiegelhalter (1988)
Figure: ์ค์ ๋ฐ์ดํฐ์ ๋ชจ์ต๊ณผ, ์ด์ ๋ฒ ์ด์ง์ ๋คํธ์ํฌ ๊ทธ๋ํ ๋ชจํ
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
GoalBayesian Network๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ํน์ง๋ค๋ฅธ ๊ธฐ๋ฒ๊ณผ์ ์ฅ๋จ์ ๋น๊ต๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ๋ค์ํ ์ ํBayesian Network Structure Learning
S. L. Lauritzen and D. J. Spiegelhalter (1988)
Unit Test : ํ์ 1์ด ์๋๋ฐ, ๊ทธ์ ๋ํ ์ ๋ณด๊ฐ ์๋ฌด๊ฒ๋ ์๋ค. P(T = 1), P(L = 1), P(B = 1)
๊ฒฐ๋ก : ๊ฒฐํต์ผ ๊ฐ๋ฅ์ฑ์ ์ฝ 1%, ํ์์ผ ๊ฐ๋ฅ์ฑ์ ์ฝ 5%, ๊ธฐ๊ด์ง์ผ์ด ์์ ๊ฐ๋ฅ์ฑ์ ์ฝ 46%
์ด๋ค.
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
GoalBayesian Network๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ํน์ง๋ค๋ฅธ ๊ธฐ๋ฒ๊ณผ์ ์ฅ๋จ์ ๋น๊ต๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ๋ค์ํ ์ ํBayesian Network Structure Learning
S. L. Lauritzen and D. J. Spiegelhalter (1988)
Question 1 : ํ์ 2๋ ์ต๊ทผ ์์์๋ฅผ ๋ฐฉ๋ฌธํ๊ณ , ๋นํก์ฐ์์ด๋ค. P(T = 1|A = 1,S = 0)
๊ฒฐ๋ก : ๊ธฐ๊ด์ง์ผ์ด ์์ ๊ฐ๋ฅ์ฑ์ด ์ฝ 34% ์ด๋ค.
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
GoalBayesian Network๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ํน์ง๋ค๋ฅธ ๊ธฐ๋ฒ๊ณผ์ ์ฅ๋จ์ ๋น๊ต๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ๋ค์ํ ์ ํBayesian Network Structure Learning
S. L. Lauritzen and D. J. Spiegelhalter (1988)
Question 2 : ํ์ 3์ ์ต๊ทผ ์์์๋ฅผ ๋ฐฉ๋ฌธํ๊ณ ๋นํก์ฐ์์ด๋ค. ํธํก ๊ณค๋๋ ๊ฒช์ง ์๊ณ ์์ง๋ง,
X-Ray ํ ์คํธ ๊ฒฐ๊ณผ ์์ฑ ๋ฐ์์ ๋ณด์๋ค. P(T = 1|A = 1,S = 0,D = 0,X = 1)
๊ฒฐ๋ก : ํ์์๊ฒ ๊ฒฐํต๊ณผ ๊ธฐ๊ด์ง์ผ์ด ์์ ๊ฐ๋ฅ์ฑ์ด ๊ฐ๊ฐ ์ฝ 33%์ด๋ค.
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
GoalBayesian Network๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ํน์ง๋ค๋ฅธ ๊ธฐ๋ฒ๊ณผ์ ์ฅ๋จ์ ๋น๊ต๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ๋ค์ํ ์ ํBayesian Network Structure Learning
๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ํน์ง
์ฅ์
ํน์ ๋ถ์ผ์ ์์ญ ์ง์์ ํ๋ฅ ์ ์ผ๋ก ํํํ๋ ๋ํ์ ์ธ ์๋จ
๋ณ์๋ค ๊ฐ์ ํ๋ฅ ์ ์์กด ๊ด๊ณ๋ฅผ ๋ํ๋ด๋ ๊ทธ๋ํ์ ๊ฐ ๋ณ์๋ณ ์กฐ๊ฑด๋ถ ํ๋ฅ ๋ก ๊ตฌ์ฑ
๋ถ๋ฅ ํด๋์ค ๋ ธ๋์ ์ฌํ ํ๋ฅ ๋ถํฌ๋ฅผ ๊ตฌํด์ค์ผ๋ก์จ ๊ฐ์ฒด๋ค์ ๋ํ ํ๋์ ์๋๋ถ๋ฅ๊ธฐ๋ก
์ด์ฉ ๊ฐ๋ฅ
์ํ์ด ์ด๋ค ๋ถ๋ฅ๋ก ๋ถ๋ฅ๋์์ ๋ ์ ๊ทธ๋ฐ ๊ฒฐ์ ์ด ๋ด๋ ค์ก๋์ง ํด์ ๊ฐ๋ฅ
๋จ์
์ ๋ ฅ๊ฐ์ผ๋ก ์์นํ์ด ์๋ ๋ฒ์ฃผํ์ ์ฌ์ฉ
๋ ธ๋ ์๊ฐ ๋ฐฉ๋ํด์ง๋ฉด ์๊ฐ์ด ์ค๋ ์์๋ ์ ์์
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
GoalBayesian Network๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ํน์ง๋ค๋ฅธ ๊ธฐ๋ฒ๊ณผ์ ์ฅ๋จ์ ๋น๊ต๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ๋ค์ํ ์ ํBayesian Network Structure Learning
๋ค๋ฅธ ๊ธฐ๋ฒ๊ณผ์ ๋น๊ต - ๋ก์ง์คํฑ ํ๊ท๋ถ์
์ฅ์
๋ค๋ณ๋ ๋ถ์์ผ๋ก ๋ง์ด ์ฐ์
๋ค๋ณ๋ ๋ณ์๋ฅผ ๋ ๋ฆฝ๋ณ์๋กํ์ฌ ์ข ์๋ณ์์ ๋ฏธ์น๋ ์ํฅ์ ํ์ ๊ฐ๋ฅ
์ ๋ ฅ๊ฐ์ผ๋ก ์์นํ๊ณผ ๋ฒ์ฃผํ ๋ชจ๋ ์ทจ๊ธ ๊ฐ๋ฅ
๋จ์
์ํ์ด ์ด๋ค ๋ถ๋ฅ๋ก ๋ถ๋ฅ๋์์ ๋ ์ ๊ทธ๋ฐ ๊ฒฐ์ ์ด ๋ด๋ ค์ก๋์ง ํด์ํ๊ธฐ๊ฐ ์ด๋ ค์
๋ถ์์๋ฃ์ ๊ฐ์ฅ ์ ํฉํ ๋ชจ๋ธ์ ์ ์ ํ๋ ๋ฐ ์๊ฐ ํฌ์๊ฐ ํ์
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
GoalBayesian Network๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ํน์ง๋ค๋ฅธ ๊ธฐ๋ฒ๊ณผ์ ์ฅ๋จ์ ๋น๊ต๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ๋ค์ํ ์ ํBayesian Network Structure Learning
๋ค๋ฅธ ๊ธฐ๋ฒ๊ณผ์ ๋น๊ต - ์ ๊ฒฝ๋ง
์ฅ์
๋ถ๋ฅ๋ฌธ์ ๋ฟ๋ง ์๋๋ผ ์์ธก, ํ๊ฐ, ํฉ์ฑ, ์ ์ด ๋ฑ์ ๋ค์ํ ๋ถ์ผ์ ์ ์ฉ ๊ฐ๋ฅ
ํ์ต๋ฅ๋ ฅ์ ๊ฐ์ถ๊ณ ์ผ๋ฐํ ๋ฅ๋ ฅ์ด ๋ฐ์ด๋๊ณ ๊ตฌํ์ด ์ฌ์
๋ค์ธต ํผ์ ํธ๋ก ์ ์ ํ๋ถ๋ฆฌ๊ฐ ๋ถ๊ฐ๋ฅํ ๊ฒฝ์ฐ์๋ ๋์ ์ฑ๋ฅ์ ๋ณด์ฌ์ฃผ๋ ํ ๋จ๊ณ ์ง๋ณดํ
์ ๊ฒฝ๋ง
๋จ์
์ํ์ด ์ด๋ค ๋ถ๋ฅ๋ก ๋ถ๋ฅ๋์์ ๋ ์ ๊ทธ๋ฐ ๊ฒฐ์ ์ด ๋ด๋ ค์ก๋์ง ์ด์ ๋ฅผ ๋ถ์ํ๊ธฐ๊ฐ
์ด๋ ค์
์ ๋ ฅ๊ฐ์ผ๋ก ์์นํ์ด ์๋ ๋ฒ์ฃผํ์ ์ฌ์ฉ
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
GoalBayesian Network๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ํน์ง๋ค๋ฅธ ๊ธฐ๋ฒ๊ณผ์ ์ฅ๋จ์ ๋น๊ต๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ๋ค์ํ ์ ํBayesian Network Structure Learning
๋ค๋ฅธ ๊ธฐ๋ฒ๊ณผ์ ๋น๊ต - ์์ฌ ๊ฒฐ์ ํธ๋ฆฌ
์ฅ์
์์ฌ๊ฒฐ์ ๊ท์น์ ๋ํํํ์ฌ ๊ด์ฌ๋์์ ํด๋นํ๋ ์ง๋จ์ ๋ช ๊ฐ์ ์์ง๋จ์ผ๋ก
๋ถ๋ฅํ๊ฑฐ๋ ์์ธก์ ์ํํ๋ ๊ณ๋์ ๋ถ์ ๋ฐฉ๋ฒ
์ํ์ด ์ด๋ค ๋ถ๋ฅ๋ก ๋ถ๋ฅ๋์์ ๋ ์ ๊ทธ๋ฐ ๊ฒฐ์ ์ด ๋ด๋ ค์ก๋์ง ํด์ ๊ฐ๋ฅ
์ ๋ ฅ๊ฐ์ผ๋ก ์์นํ, ๋ฒ์ฃผํ ๋ชจ๋ ์ทจ๊ธ ๊ฐ๋ฅ
๋จ์
๋ฐ์๋ณ์๊ฐ ์์นํ์ธ ํ๊ท๋ชจํ์์๋ ๊ทธ ์์ธก๋ ฅ์ด ๋จ์ด์ง
๋๋ฌด๊ฐ ๋๋ฌด ๊น์ ๊ฒฝ์ฐ์๋ ์์ธก๋ ฅ ์ ํ์ ํด์์ด ์ฝ์ง ์์
๊ฐ์ง๊ฐ ๋ง์ ๊ฒฝ์ฐ ์๋ก์ด ์๋ฃ์ ์ ์ฉํ ๋ ์์ธก ์ค์ฐจ๊ฐ ํผ
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
GoalBayesian Network๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ํน์ง๋ค๋ฅธ ๊ธฐ๋ฒ๊ณผ์ ์ฅ๋จ์ ๋น๊ต๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ๋ค์ํ ์ ํBayesian Network Structure Learning
๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ๋ค์ํ ์ ํ
๋์ด๋ธ ๋ฒ ์ด์ง์ ๋คํธ์ํฌ (NBN)
๊ฐ์ ์ ๋จ์ํจ์๋ ๋ถ๊ตฌํ๊ณ ๋ง์ ์ฐ๊ตฌ๋ฅผ ํตํด ๋น๊ต์ ๋์ ๋ถ๋ฅ์ฑ๋ฅ์ ๋ณด์ฌ์ค๋ค.
์ผ๋ฐ ๋ฒ ์ด์ง์ ๋คํธ์ํฌ (GBN)
ํด๋์ค ๋ ธ๋์กฐ์ฐจ ์ผ๋ฐ ์์ฑ ๋ ธ๋์์ ์ฐจ์ด๋ฅผ ๋์ง ์๊ณ ๋ชจ๋ ๋ ธ๋๋ค ๊ฐ์ ์ํธ์์กด๋๋ฅผ
ํ๋์ ๋ฒ ์ด์ง์ ๋คํธ์ํฌ๋ก ํํํ๋ค.
ํธ๋ฆฌ-ํ์ฅ ๋์ด๋ธ ๋ฒ ์ด์ง์ ๋คํธ์ํฌ (TAN)
์์ฑ ๋ ธ๋๋ค ๊ฐ์๋ ์ํธ์์กด๋๊ฐ ์กด์ฌํ๋ค๊ณ ๊ฐ์ ํ๊ณ , ์ด๋ฌํ ์์ฑ ๊ฐ ์ํธ์์กด๋๋ฅผํ๋์ ์ผ๋ฐ ๋ฒ ์ด์ง์ ๋คํธ์ํฌ ํํ๋ก ํํ ๊ฐ๋ฅํ๋๋ก NBN์ ํ์ฅํ ๊ฒ์ด๋ค.
๋์ ๋ฒ ์ด์ง์ ๋คํธ์ํฌ (DBN)
์๊ณ์ด ๋ถ์์ ์ํด ํ์ฌ ๋ณ์์ ํ๋ฅ ์ ๊ณ์ฐํ ๋, ์ด์ ์์ ์ ์ ๋ณด๋ฅผ ํจ๊ป ๊ณ ๋ คํ๋๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ด๋ค.
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
GoalBayesian Network๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ํน์ง๋ค๋ฅธ ๊ธฐ๋ฒ๊ณผ์ ์ฅ๋จ์ ๋น๊ต๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ๋ค์ํ ์ ํBayesian Network Structure Learning
๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ๋ค์ํ ์ ํ
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
GoalBayesian Network๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ํน์ง๋ค๋ฅธ ๊ธฐ๋ฒ๊ณผ์ ์ฅ๋จ์ ๋น๊ต๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ๋ค์ํ ์ ํBayesian Network Structure Learning
๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ๋ค์ํ ์ ํ
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
GoalBayesian Network๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ํน์ง๋ค๋ฅธ ๊ธฐ๋ฒ๊ณผ์ ์ฅ๋จ์ ๋น๊ต๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ๋ค์ํ ์ ํBayesian Network Structure Learning
Bayesian Network Structure Learning
Learning a Bayesian network is as follows:
Given a data T = {y1, ยท ยท ยท , yn} and a scoring function ฯ, the problem of learning a Bayesiannetwork is to find a Bayesian network B โ Bn that maximizes the value ฯ(B,T ).
Figure: A model before learning structure
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
Available Constraint-based Learning AlgorithmsAvailable Score-based Learning AlgorithmsAvailable Hybrid Learning Algorithms
Available constraint-based learning algorithms
Grow-Shrink (GS) based on the Grow-Shrink Markov Blanket, the first (and simplest) Markovblanket detection algorithm used in a structure learning algorithm.
Incremental Association (IAMB) based on the Markov blanket detection algorithm of thesame name, which is based on a two-phase selection scheme (a forwardselection followed by an attempt to remove false positives).
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
Available Constraint-based Learning AlgorithmsAvailable Score-based Learning AlgorithmsAvailable Hybrid Learning Algorithms
Available Score-based Learning Algorithms
Hill-Climbing (HC) a hill climbing greedy search on the space of the directed graphs. Theoptimized implementation uses score caching, score decomposability andscore equivalence to reduce the number of duplicated tests.
Tabu Search (TABU) a modified hill climbing able to escape local optima by selecting anetwork that minimally decreases the score function.
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
Available Constraint-based Learning AlgorithmsAvailable Score-based Learning AlgorithmsAvailable Hybrid Learning Algorithms
Available Hybrid Learning Algorithms
Max-Min Hill-Climbing (MHHC) a hybrid algorithm which combines the Max-Min Parentsand Children algorithm (to restrict the search space) and the Hill-Climbingalgorithm (to find the optimal network structure in the restricted space).
Restricted Maximization (RSMAX2) a more general implementation of the Max-MinHill-Climbing, which can use any combination of constraint-based andscore-based algorithms.
IntroductionStructure Learning Algorithms in bnlearn
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SimulationDiscussion
The Number of Graphical Errors in the Learnt StructureNetwork Scores
The Number of Graphical Errors in the LearntStructure
In terms of the number of graphical errors in the learnt structure.
Target Network Learnt Network DirectionC (Correct Arcs) exist exist correctM (Missing Arcs) exist not existWO (Wrongly Oriented Arcs) exist exist wrongWC (Wrongly Corrected Arcs) not exist exist
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
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The Number of Graphical Errors in the Learnt StructureNetwork Scores
Network Scores
In all four cases, the higher the value of the metric, the better the network.
BDe BDe(B,T ) = P(B,T ) = P(B)รโni=1 โqi
j=1(ฮ(N โฒij )
ฮ(Nij+N โฒij )รโri
k=1
ฮ(Nijk+N โฒijk )
ฮ(N โฒijk ))
ฯ(B |T ) = LL(B |T )โ f (N)|B |,
Log-Likelihood(LL) If f (N) = 0, we have the LL score.
AIC If f(N) = 1, we have the AIC scoring function:
BIC If f (N) = 12 log(N), we have the BIC score.
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
Data Generation with BN Data Generator in R
BN Data Generator {BNDataGenerator}
Description It based on a Bayesian network model to generates synthetic data.
Usage BN Data Generator (arcs, Probs, n, node names)
Suppose bnlearn
Repository CRAN (Submitted at 2014-12-28)
URL https://github.com/praster1/BN Data Generator
Arguments
arcs (matrix) A matrix that determines the arcs.Probs (list) The conditional probabilities.
n (constant) Data Sizenode names (vector) Node names
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
Data Generation with BN Data Generator in R
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
Data Generation with BN Data Generator in R
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
Real DatasetsSynthetic Data According to Topologies
Outline1 Introduction
GoalBayesian Network๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ํน์ง
๋ค๋ฅธ ๊ธฐ๋ฒ๊ณผ์ ์ฅ๋จ์ ๋น๊ต
๋ฒ ์ด์ง์ ๋คํธ์ํฌ์ ๋ค์ํ ์ ํ
Bayesian Network Structure Learning2 Structure Learning Algorithms in bnlearn
Available Constraint-based Learning AlgorithmsAvailable Score-based Learning AlgorithmsAvailable Hybrid Learning Algorithms
3 The Comparison MethodologyThe Number of Graphical Errors in the Learnt StructureNetwork Scores
4 Data Generation with BN Data Generator in R5 Simulation
Real DatasetsSynthetic Data According to Topologies
6 Discussion
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
Real DatasetsSynthetic Data According to Topologies
Asia DataSet
Description Small synthetic data set from Lauritzen and Spiegelhalter (1988) about lungdiseases (tuberculosis, lung cancer or bronchitis) and visits to Asia.
Number of nodes 8
Number of arcs 8
Number of parameters 18
Source Lauritzen S, Spiegelhalter D (1988).โLocal Computation with Probabilities on Graphical Structures and theirApplication to Expert Systems (with discussion)โ.Journal of the Royal Statistical Society: Series B (Statistical Methodology),50(2), 157-224.
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
Real DatasetsSynthetic Data According to Topologies
Asia DataSet
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
Real DatasetsSynthetic Data According to Topologies
Insurance DataSet
Description Insurance is a network for evaluating car insurance risks.
Number of nodes 27
Number of arcs 52
Number of parameters 984
Source Binder J, Koller D, Russell S, Kanazawa K (1997).โAdaptive Probabilistic Networks with Hidden Variablesโ.Machine Learning, 29(2-3), 213-244.
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
Real DatasetsSynthetic Data According to Topologies
Insurance DataSet
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
Real DatasetsSynthetic Data According to Topologies
Alarm DataSet
Description The ALARM (โA Logical Alarm Reduction Mechanismโ) is a Bayesiannetwork designed to provide an alarm message system for patient monitoring.
Number of nodes 37
Number of arcs 46
Number of parameters 509
Source Beinlich I, Suermondt HJ, Chavez RM, Cooper GF (1989).โThe ALARM Monitoring System: A Case Study with Two ProbabilisticInference Techniques for Belief Networks.โIn โProceedings of the 2nd European Conference on Artificial Intelligence inMedicineโ, pp. 247-256. Springer-Verlag.
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
Real DatasetsSynthetic Data According to Topologies
Alarm DataSet
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
Real DatasetsSynthetic Data According to Topologies
HailFinder DataSet
Description Hailfinder is a Bayesian network designed to forecast severe summer hail innortheastern Colorado.
Number of nodes 56
Number of arcs 66
Number of parameters 2656
Source Abramson B, Brown J, Edwards W, Murphy A, Winkler RL (1996).โHailfinder: A Bayesian system for forecasting severe weatherโ.International Journal of Forecasting, 12(1), 57-71.
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
Real DatasetsSynthetic Data According to Topologies
HailFinder DataSet
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
Real DatasetsSynthetic Data According to Topologies
Summary
IntroductionStructure Learning Algorithms in bnlearn
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SimulationDiscussion
Real DatasetsSynthetic Data According to Topologies
Varying topologies and number of nodes
Eitel J. M. Laurฤฑa,โAn Information-Geometric Approach to Learning Bayesian Network Topologies from Dataโ,Innovations in Bayesian Networks Studies in Computational Intelligence Volume 156, 2008, pp 187-217
IntroductionStructure Learning Algorithms in bnlearn
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Real DatasetsSynthetic Data According to Topologies
Prerequisite
Cardinality was limited to two.
The probability value, which is imparted optionally under U(0, 1) distribution.
All experiments are repeated 100 times, and overall results are reported.
Constraint-based Learning Algorithms often makes undirected arcs. So, this has beenexcluded from comparison.
IntroductionStructure Learning Algorithms in bnlearn
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Real DatasetsSynthetic Data According to Topologies
Collapse
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
Real DatasetsSynthetic Data According to Topologies
Collapse (Score)
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
Real DatasetsSynthetic Data According to Topologies
Collapse (Arcs)
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
Real DatasetsSynthetic Data According to Topologies
Collapse
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
Real DatasetsSynthetic Data According to Topologies
Line
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
Real DatasetsSynthetic Data According to Topologies
Line (Score)
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
Real DatasetsSynthetic Data According to Topologies
Line (Arcs)
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
Real DatasetsSynthetic Data According to Topologies
Line
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
Real DatasetsSynthetic Data According to Topologies
Star
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
Real DatasetsSynthetic Data According to Topologies
Star (Score)
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
Real DatasetsSynthetic Data According to Topologies
Star (Arcs)
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
Real DatasetsSynthetic Data According to Topologies
Star
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
Real DatasetsSynthetic Data According to Topologies
PseudoLoop
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
Real DatasetsSynthetic Data According to Topologies
PseudoLoop (Score)
IntroductionStructure Learning Algorithms in bnlearn
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Real DatasetsSynthetic Data According to Topologies
PseudoLoop (Arc)
IntroductionStructure Learning Algorithms in bnlearn
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SimulationDiscussion
Real DatasetsSynthetic Data According to Topologies
PseudoLoop
IntroductionStructure Learning Algorithms in bnlearn
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Real DatasetsSynthetic Data According to Topologies
Diamond
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Real DatasetsSynthetic Data According to Topologies
Diamond (Score)
IntroductionStructure Learning Algorithms in bnlearn
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Real DatasetsSynthetic Data According to Topologies
Diamond (Arc)
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
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Real DatasetsSynthetic Data According to Topologies
Diamond
IntroductionStructure Learning Algorithms in bnlearn
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SimulationDiscussion
Real DatasetsSynthetic Data According to Topologies
Rhombus
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
Real DatasetsSynthetic Data According to Topologies
Rhombus (Score)
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
Real DatasetsSynthetic Data According to Topologies
Rhombus (Arc)
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
Real DatasetsSynthetic Data According to Topologies
Rhombus
IntroductionStructure Learning Algorithms in bnlearn
The Comparison MethodologyData Generation with BN Data Generator in R
SimulationDiscussion
Discussion
In most cases using synthetic data according to topology,If comparing by score, then TABU search has good performance.But comparing by reference to โWhat C is the lot?โ, then HC has also goodperformance.
Hybrid algorithm compared to Score-based algorithm is found to be that draw the arcmore conservative.
About Line and Star form, the performance difference due to relatively algorithm wasnot large compared to other topology.