The HPBNET Procedure

A Bayesian network is a graphical model that consists of two parts, , where G is a directed acyclic graph (DAG) whose nodes correspond to the random variables in U (U is the set of input variables plus the target variable in PROC HPBNET and P is a set of local probability distributions, one for each node conditional on each value combination of the parents). The joint probability distribution of U can be factorized to the product of the local probability distributions; that is , where are the parents of X. It is assumed that the network structure G and the probability distribution P are faithful to each other; that is, every conditional independence in the structure G is also present in P, and vice versa.

Given a target variable T, a Markov blanket of T is defined as a subset of input variables such that T is conditionally independent of each of the remaining input variables given MB. Under the faithful assumption, the Markov blanket of T is unique. According to the definition of the Markov blanket, the probability distribution of T is completely determined by its Markov blanket; therefore, the Markov blanket can be used for variable selection.

PROC HPBNET supports two types of variable selections: one by independence tests between each input variable and the target (when PRESCREENING=1) and the other by conditional independence tests between each input variable and the target given any subset of other input variables (when VARSELECT=1, 2, or 3).

PROC HPBNET uses specialized data structures to efficiently compute the contingency tables for any variable combinations, and it uses dynamic candidate generation to reduce the false candidates (variable combinations).