Symbolic Probabilistic Inference with Continuous Variables

Research on Symbolic Probabilistic Inference (SPI) [2, 3) has provided an algorithm for re­ solving general queries in Bayesian networks. SPI applies the concept of dependency­ directed backward search to probabilistic in­ ference, and is incremental with respect to both queries and observations. Unlike tra­ ditional Bayesian network inferencing algo­ rithms, SPI algorithm is goal directed, per­ forming only those calculations that are re­ quired to respond to queries. Research to date on SPI applies to Bayesian networks with discrete-valued variables and does not address variables with continuous values. In this paper1, we extend the SPI algorithm to handle Bayesian networks made up of continuous variables where the relationships between the variables are restricted to be "linear gaussian". We call this variation of the SPI algorithm, SPI Continuous (SPIC). SPIC modifies the three basic SPI opera­ tions: multiplication, summation, and sub­ stitution. However, SPIC retains the frame­ work of the SPI algorithm, namely building the search tree and recursive query mecha­ nism and therefore retains the goal-directed and incrementality features of SPI.