A Bayesian Classifier Learning Algorithm Based on Optimization Model

Algorithm 1

BC-OM.

(1)  Input: Data set 𝐷; Variable set 𝐕 = (𝑉₁, 𝑉₂,…, 𝑉_𝑛) (𝑉₁ is the class node and others are attribute

     nodes).

(2) For any pair of variable 𝑉_𝑖 and 𝑉_𝑗 contained in 𝐕, calculate the dependence coefficient 𝑐_𝑖𝑗 by

    Definition 2;

(3) Solve the mathematical programming (OM) and obtain the optimal solution 𝑋^∗=(𝑥_𝑖𝑗);

(4) Build the classifier structure 𝐺^∗ = (𝐕, 𝐄^∗) by 𝑋^∗=(𝑥_𝑖𝑗);

(5) For any variable 𝑉_𝑖 ∈ 𝐕, 𝑖≠1, if there is a subset 𝐙⊂𝐕⧵{𝑉₁, 𝑉_𝑖} such that 𝐙 d-separates 𝑉_𝑖 and

    𝑉₁, then delete 𝑉_𝑖 in 𝐺^∗, update 𝐺^∗ as 𝐕=𝐕⧵{𝑉_𝑖}, 𝐄^∗=𝐄^∗⧵{𝑉_𝑖→𝑉_𝑗 or 𝑉_𝑗→𝑉_𝑖, 𝑉_𝑗 ∈ adj(𝑉_𝑖)};

(6)  Output: The built classifier 𝐺^∗ = (𝐕, 𝐄^∗).