Linear Algebra Approach to Separable Bayesian Networks

Separable Bayesian Networks, or the Influence Model, are dynamic Bayesian Networks in which the conditional probability distribution can be separated into a function of only the marginal distribution of a node’s parents, instead of the joint distributions. We describe the connection between an arbitrary Conditional Probability Table (CPT) and separable systems using linear algebra. We give an alternate proof to [Pfeffer00] on the equivalence of sufficiency and separability. We present a computational method for testing whether a given CPT is separable.