Symbolic Probabilistic Inference with Evidence Potential

Recent research on the Symbolic Probabilis­ tic Inference (SPI) algorithm[;:] has focused attention on the importance of resolving general queries in Bayesian networks. SPI applies the concept of dependency-directed backward search to probabilistic inference, and is incremental with respect to both queries and observations. In response to this research we have extended the evidence potential algorithm [3] with the same fea­ tures. We call the extension symbolic evi­ dence potential inference (SEPI). SEPI like SPI can handle generic queries and is incre­ mental with respect to queries and observa­ tions. While in SPI, operations are done on a search tree constructed from the nodes of the original network, in SEPI, a clique-tree structure obtained from the evidence poten­ tial algorithm [3] is the basic framework for recursive query processing. In this paper, we describe the systematic query and caching procedure of SEPI. SEPI begins with finding a clique tree from a Bayesian network the standard procedure of the evidence potential algorithm. With the clique tree, various probability distribu­ tions are computed and stored in each clique. This is the "pre-processing" step of SEPI. Once this step is done, the query can then be computed. To process a query, a recursive process similar to the SPI algorithm is used. The queries are directed to the root clique and decomposed into queries for the clique's subtrees until a particular query can be an­ swered at the clique at which it is directed. The algorithm and the computation are sim­ ple. The SEPI algorithm will be presented in this paper along with several examples.