A New Characterization of Probabilities in Bayesian Networks
Lenhart Schubert
Abstract:
We characterize probabilities in Bayesian networks in terms of algebraic expressions called quasiprobabilities. These are arrived at by casting Bayesian networks as noisy ANDORNOT 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 quasiprobability of any node recursively, in a compact form; and we can obtain the joint quasiprobability of any set of nodes by multiplying their marginals (using an idempotent product operator). Quasiprobabilities are easily manipulated to improve the efficiency of probabilistic inference. They also turn out to be representable as squarewave pulse trains, and joint and marginal distributions can be computed by multiplication and complementation of pulse trains.
Keywords:
Pages: 495503
PS Link:
PDF Link: /papers/04/p495schubert.pdf
BibTex:
@INPROCEEDINGS{Schubert04,
AUTHOR = "Lenhart Schubert
",
TITLE = "A New Characterization of Probabilities in Bayesian Networks",
BOOKTITLE = "Proceedings of the Twentieth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI04)",
PUBLISHER = "AUAI Press",
ADDRESS = "Arlington, Virginia",
YEAR = "2004",
PAGES = "495503"
}

