A Decomposition Algorithm for Learning Bayesian Networks Based on Scoring Function

Algorithm 3

MMPC.

(1) Input: Data set 𝐷; Variable set 𝑉=(𝑉₁,𝑉₂,…,𝑉_𝑛); Target variable 𝑇.

(2) CPC=∅;

(3) repeat

(4)  for  𝑉_𝑗∈(𝑉⧵CPC⧵{𝑇})  do

(5)          𝑆(𝑉_𝑗)=argmin_𝑍⊆CPCdep(𝑇,𝑉_𝑗∣𝑍);

(6)  end for

(7)  𝑌=argmax_{𝑉𝑗∈(𝑉⧵CPC⧵{𝑇})}dep(𝑇,𝑉_𝑗∣𝑆(𝑉_𝑗));

(8)  if   ¬Ind(𝑇;𝑌∣𝑆(𝑌))  then

(9)          CPC=CPC∪{𝑌};

(10)        end if

(11) until  CPC has not changed;

(12) for 𝑉_𝑗∈CPC  do

(13)        if  Ind(𝑇;𝑉_𝑗∣𝑍) for some 𝑍⊆CPC⧵{𝑇}  then

(14)         CPC=CPC⧵𝑉_𝑗;

(15)        end if

(16) end for

(17) return  CPC

(18) Output: The parents and children PC(𝑇) of 𝑇.