Upper-Lower Bounds Candidate Sets Searching Algorithm for Bayesian Network Structure Learning

Algorithm 1

UGLA.

(1) Input: Data set D; Variable set ;

(2) Initialization: undirected graph , where ;

(3) Order-0 CI test: for each pair variables , if is hold, then , where

   is an undirected edge;

(4) For each triplet variables

(5)     For each pair variables , and , if , , , and is hold,

    then ,

(6) End for;

(7) Triangulate undirected graph , what results with

(8) Call the junction tree algorithm to obtain maximal prime sub-graphs from ;

(9) Output and as final result.