Linear Algebra Approach to Separable Bayesian Networks
This work addresses complexity reduction in dynamic Bayesian networks for researchers in probabilistic modeling, but appears incremental as it builds on existing concepts of separability.
The paper tackles the problem of modeling separable Bayesian networks by connecting arbitrary Conditional Probability Tables to separable systems using linear algebra, and presents a computational method for testing separability.
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 neighbors, instead of the joint distributions. In terms of modeling, separable networks has rendered possible siginificant reduction in complexity, as the state space is only linear in the number of variables on the network, in contrast to a typical state space which is exponential. In this work, We describe the connection between an arbitrary Conditional Probability Table (CPT) and separable systems using linear algebra. We give an alternate proof on the equivalence of sufficiency and separability. We present a computational method for testing whether a given CPT is separable.