Symbolic Probabilistic Inference with Continuous Variables

TL;DR

This paper extends the Symbolic Probabilistic Inference (SPI) algorithm to handle Bayesian networks with continuous variables, specifically linear Gaussian relationships, maintaining its goal-directed and incremental features.

Contribution

The paper introduces SPI Continuous (SPIC), adapting SPI for continuous variables with linear Gaussian relationships while preserving its core properties.

Findings

Successfully extended SPI to continuous variables

Retains goal-directed and incremental inference capabilities

Applicable to linear Gaussian Bayesian networks

Abstract

Research on Symbolic Probabilistic Inference (SPI) [2, 3] has provided an algorithm for 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. Unlike traditional Bayesian network inferencing algorithms, SPI algorithm is goal directed, performing only those calculations that are required 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 papers, 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 operations: multiplication, summation, and substitution. However, SPIC retains the framework of the SPI algorithm, namely building the search tree and recursive query mechanism and therefore retains the goal-directed and incrementality features of SPI.