Symbolic Probabilistic Inference with Evidence Potential
  Recent research on the Symbolic Probabilistic Inference (SPI) algorithm[2]
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 features. We call the extension
symbolic evidence potential inference (SEPI). SEPI like SPI can handle generic
queries and is incremental with respect to queries and observations. 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
potential 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 distributions 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 answered at
the clique at which it is directed. The algorithm and the computation are
simple. The SEPI algorithm will be presented in this paper along with several
examples.
