Exploiting Causal Independence in Bayesian Network Inference

TL;DR

This paper introduces a novel approach to Bayesian network inference by exploiting causal independence, enabling finer factorization of probabilities and improving computational efficiency in larger networks.

Contribution

The paper presents a new formulation of causal independence that allows for more efficient exact inference in Bayesian networks by further factorizing conditional probabilities.

Findings

More efficient inference in larger networks

Empirical validation on medical diagnosis networks

Outperforms previous methods in speed and scalability

Abstract

A new method is proposed for exploiting causal independencies in exact Bayesian network inference. A Bayesian network can be viewed as representing a factorization of a joint probability into the multiplication of a set of conditional probabilities. We present a notion of causal independence that enables one to further factorize the conditional probabilities into a combination of even smaller factors and consequently obtain a finer-grain factorization of the joint probability. The new formulation of causal independence lets us specify the conditional probability of a variable given its parents in terms of an associative and commutative operator, such as ``or'', ``sum'' or ``max'', on the contribution of each parent. We start with a simple algorithm VE for Bayesian network inference that, given evidence and a query variable, uses the factorization to find the posterior distribution of the query. We show how this algorithm can be extended to exploit causal independence. Empirical studies, based on the CPCS networks for medical diagnosis, show that this method is more efficient than previous methods and allows for inference in larger networks than previous algorithms.