A New Characterization of Probabilities in Bayesian Networks
This work addresses a fundamental challenge in machine learning for researchers and practitioners dealing with Bayesian networks, offering a novel algebraic framework that could improve inference efficiency, though it appears incremental as it builds on existing network representations.
The paper tackles the problem of probabilistic inference in Bayesian networks by characterizing probabilities using algebraic expressions called quasi-probabilities, which enable efficient computation of marginal and joint distributions through recursive and multiplicative operations.
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. Quasi-probabilities 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.