Exploiting Causal Independence in Bayesian Network Inference

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.

Modelling treatment effects in a clinical Bayesian network using Boolean threshold functions

“…; >g, called an interaction function, an alternative formalisation is possible. Using the interaction function f and the causal parameters Pr ðI j jC j Þ, it follows that [7,3,8]:…”

“…Pr ðS j jC j ; MÞ: (8) There are various choices possible for the conditional probability distributions Pr ðS j jC j ; MÞ…”

An Improved LAZY-AR Approach to Bayesian Network Inference

“…A variable is barren [13], if it is neither an evidence nor a target variable and it only has barren descendants. Probabilistic inference can be conducted directly in the original BN [6,9,12,13,17,18,19]. It can also be performed in a join tree [3,5,7,8,14].…”

“…LAZY-ARVE is built upon the AR Message Identification (ARMI) and VE [17,18,19] algorithms. First, the sub-algorithm ARMI applies AR for the graphical identification of the propagated CPTs.…”

“…A second approach to BN inference is direct computation (DC), which performs inference directly in a BN. The classical DC algorithms are variable elimination (VE) [17,18,19], arc-reversal (AR) [9,13] and symbolic probabilistic inference (SPI) [6,12]. The experimental results provided by Zhang [17] indicate that VE is more efficient than the classical JTP methods when updating twenty or less non-evidence variables, given a set of twenty or fewer evidence variables.…”