The hidden elegance of causal interaction models

Causal interaction models such as the noisy-or model, are used in Bayesian networks to simplify probability acquisition for variables with large numbers of modelled causes. These models essentially prescribe how to complete an exponentially large probability table from a linear number of parameters. Yet, typically the full probability tables are required for inference with Bayesian networks in which such interaction models are used, although inference algorithms tailored to specific types of network exist that can directly exploit the decomposition properties of the interaction models. In this paper we revisit these decomposition properties in view of general inference algorithms and demonstrate that they allow an alternative representation of causal interaction models that is quite concise, even with large numbers of causes involved. In addition to forestalling the need of tailored algorithms, our alternative representation brings engineering benefits beyond those widely recognised.