A model for compressing probabilities in belief networks

Probabilistic reasoning with belief (Bayesian) networks is based on conditional probability matrices. Thus it suffers from NP-hard implementations. In particular, the amount of probabilistic information necessary for the computations is often overwhelming. So, compressing the conditional probability table is one of the most important issues faced by the probabilistic reasoning community. Santos suggested an approach (called linear potential functions) for compressing the information from a combinatorial amount to roughly linear in the number of random variable assignments. However, much of the information in Bayesian networks, in which there are no linear potential functions, would be fitted by polynomial approximating functions rather than by reluctantly linear functions. For this reason, we construct a polynomial method to compress the conditional probability table in this paper. We evaluated the proposed technique, and our experimental results demonstrate that the approach is efficient and promising.