A New Look at Causal Independence
This work addresses the problem of computational efficiency in belief-network inference for researchers and practitioners in probabilistic graphical models, but it is incremental as it builds on existing definitions.
The paper tackles the problem of inefficient inference in belief networks by introducing an equivalent a-temporal characterization of causal independence, which results in more efficient representations for inference.
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.