A New Look at Causal Independence
  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.
