A Decomposition Algorithm for Learning Bayesian Networks Based on Scoring Function

Algorithm 1

Decomposition algorithm for learning BNs.

(1) Input: Data set 𝐷; Variable set 𝑉=(𝑉₁,𝑉₂,…,𝑉_𝑛); Node ordering 𝜌.

(2) Construct the moral graph 𝐺^𝑚=(𝑉,𝐸^𝑚) from the data set 𝐷.

(3) Decompose the moral graph 𝐺^𝑚 into its maximal prime subgraphs 𝐺^𝑚₁,𝐺^𝑚₂,…,𝐺^𝑚_𝑘.

(4) For each sub-graph 𝐺^𝑚_𝑙(𝑙=1,2,…,𝑘) of 𝐺^𝑚, call the K2 algorithm with the local node

 ordering of 𝐺^𝑚_𝑙 to construct a directed acyclic graph 𝐺_𝑙(𝑙=1,2,…,𝑘).

(5) Combine 𝐺₁,𝐺₂,…,𝐺_𝑘 into a directed graph 𝐺=(𝑉,𝐸) where

 𝑉=𝑉(𝐺₁)∪𝑉(𝐺₂)∪⋯∪ 𝑉(𝐺_𝑘) and 𝐸=𝐸(𝐺₁)∪𝐸(𝐺₂)∪⋯∪𝐸(𝐺_𝑘).

(6) Output: A directed acyclic graph 𝐺.