A New Characterization of Probabilities in Bayesian Networks

Lenhart Schubert

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arXiv · 1207.4168

A New Characterization of Probabilities in Bayesian Networks

Lenhart Schubert

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Abstract

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.

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Lenhart Schubert. 2012-07-11. A New Characterization of Probabilities in Bayesian Networks. https://arxiv.org/abs/1207.4168

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