Extraction of Belief Knowledge from a Relational Database for Quantitative Bayesian Network Inference

Algorithm 3

Input: Training set 𝑇, attribute set 𝑋=𝑋₁,…,𝑋_𝑛, and class 𝐶.

Output: TAN constructed by conditional mutual information metric.

Step 1. Compute the conditional mutual information 𝐼𝑋_𝑖;𝑋_𝑗∣𝐶 between

each pair of attributes 𝑋_𝑖,𝑋_𝑗, 𝑖≠𝑗.

Step 2. Build a complete undirected graph wherein the vertices are attributes 𝑋₁,…,𝑋_𝑛.

Annotate the weight of an edge connecting 𝑋_𝑖 to 𝑋_𝑗 by 𝐼𝑋_𝑖;𝑋_𝑗,∣𝐶.

Step 3. Build a maximum weighted spanning tree.

Step 4. Transform the resulting undirected tree to a directed tree by choosing a root node

and setting the direction of all edges outward from the directed tree.

Step 5. Build a TAN model by adding a vertex labeled by 𝐶 and adding an arc from 𝐶 to each 𝑋_𝑖.