A New Look at Causal Independence

TL;DR

This paper introduces a new temporal and functional characterization of causal independence, enabling more efficient belief-network inference by exploiting causal structure.

Contribution

It provides an equivalent temporal and functional framework for causal independence, improving inference efficiency in belief networks.

Findings

Empirical results demonstrate improved inference efficiency.

Functional representation simplifies causal interactions.

Nested decomposition of functions captures causal independence effectively.

Abstract

Heckerman (1993) defined causal independence in terms of a set of temporal conditional independence statements. These statements formalized certain types of causal interaction where (1) the effect is independent of the order that causes are introduced and (2) the impact of a single cause on the effect does not depend on what other causes have previously been applied. In this paper, we introduce an equivalent a temporal characterization of causal independence based on a functional representation of the relationship between causes and the effect. In this representation, the interaction between causes and effect can be written as a nested decomposition of functions. Causal independence can be exploited by representing this decomposition in the belief network, resulting in representations that are more efficient for inference than general causal models. We present empirical results showing the benefits of a causal-independence representation for belief-network inference.