A New Characterization of Probabilities in Bayesian Networks

We characterize probabilities in Bayesian networks in terms of algebraic expressions called quasi-probabilities. These are arrived at by casting Bayesian networks as noisy AND-OR-NOT networks, and viewing the subnetworks that lead to a node as arguments for or against a node. Quasiprobabilities are in a sense the "natural" algebra of Bayesian networks: we can easily compute the marginal quasi-probability of any node recursively, in a compact form; and we can obtain the joint quasi-probability of any set of nodes by multiplying their marginals (using an idempotent product operator). Quasi-probabilities are easily manipulated to improve the efficiency of probabilistic inference. They also turn out to be representable as square-wave pulse trains, and joint and marginal distributions can be computed by multiplication and complementation of pulse trains.

• Type: Conference
• Year: 2004
• Where: UAI
• Authors: Lenhart K. Schubert
• Keywords: Bayesian Networks, Expressions Called Quasi-probabilities, Noisy And-or-not Networks, UAI 2004, UAI 2008