Local Expression Languages for Probabilistic Dependence: a Preliminary Report

TL;DR

This paper introduces an extended local expression language for belief networks that allows for more flexible representation and inference of probabilistic dependencies, exemplified by the 'noisy or' relationship.

Contribution

It generalizes the local expression language in SPI, enabling the combination of partial distributions and capturing complex dependencies like 'noisy or'.

Findings

Extended language supports operators for combining distributions.

Captures semantics and complexity advantages of 'noisy or'.

Enhances inference capabilities in belief networks.

Abstract

We present a generalization of the local expression language used in the Symbolic Probabilistic Inference (SPI) approach to inference in belief nets [1l, [8]. The local expression language in SPI is the language in which the dependence of a node on its antecedents is described. The original language represented the dependence as a single monolithic conditional probability distribution. The extended language provides a set of operators (*, +, and -) which can be used to specify methods for combining partial conditional distributions. As one instance of the utility of this extension, we show how this extended language can be used to capture the semantics, representational advantages, and inferential complexity advantages of the "noisy or" relationship.