Abductive Reasoning in Bayesian Belief Networks Using a Genetic Algorithm

E. S. Gelsema
Pre-proceedings of the Fifth International Workshop on Artificial Intelligence and Statistics, PMLR R0:245-251, 1995.

Abstract

Bayesian belief networks (causal networks) have been extensively studied in the past ten years. It has been shown that they provide a sound formalism for probabilistic reasoning, especially if uncertainty is to be represented. A probability space can be modelled as a Bayesian belief network of propositional variables (nodes) which may be pairwise connected by directed arcs. The interpretation is that if an arc exists from node A to node $B$, the probability of node $B$ assuming a given state $b_{i}$ depends on the actual state of node $A$ ( $A$ is a direct cause of $B$ ). The absence of an arc between two nodes implies that there is no such direct dependence. Thus, in a Bayesian belief network, probabilistic dependencies are modelled as arcs between nodes, independencies are implied by the absence of arcs. If for a given probability space, for all states of the root nodes the prior probabilities are known, and in addition, for all non-root nodes the conditional probabilities, given the parent states, the joint probability distribution is completely known. Textbooks on Bayesian belief networks are [1] and [2].

Cite this Paper

BibTeX
@InProceedings{pmlr-vR0-gelsema95a, title = {Abductive Reasoning in {B}ayesian Belief Networks Using a Genetic Algorithm}, author = {Gelsema, E. S.}, booktitle = {Pre-proceedings of the Fifth International Workshop on Artificial Intelligence and Statistics}, pages = {245--251}, year = {1995}, editor = {Fisher, Doug and Lenz, Hans-Joachim}, volume = {R0}, series = {Proceedings of Machine Learning Research}, month = {04--07 Jan}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/r0/gelsema95a/gelsema95a.pdf}, url = {https://proceedings.mlr.press/r0/gelsema95a.html}, abstract = {Bayesian belief networks (causal networks) have been extensively studied in the past ten years. It has been shown that they provide a sound formalism for probabilistic reasoning, especially if uncertainty is to be represented. A probability space can be modelled as a Bayesian belief network of propositional variables (nodes) which may be pairwise connected by directed arcs. The interpretation is that if an arc exists from node A to node $B$, the probability of node $B$ assuming a given state $b_{i}$ depends on the actual state of node $A$ ( $A$ is a direct cause of $B$ ). The absence of an arc between two nodes implies that there is no such direct dependence. Thus, in a Bayesian belief network, probabilistic dependencies are modelled as arcs between nodes, independencies are implied by the absence of arcs. If for a given probability space, for all states of the root nodes the prior probabilities are known, and in addition, for all non-root nodes the conditional probabilities, given the parent states, the joint probability distribution is completely known. Textbooks on Bayesian belief networks are [1] and [2].}, note = {Reissued by PMLR on 01 May 2022.} }
Endnote
%0 Conference Paper %T Abductive Reasoning in Bayesian Belief Networks Using a Genetic Algorithm %A E. S. Gelsema %B Pre-proceedings of the Fifth International Workshop on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 1995 %E Doug Fisher %E Hans-Joachim Lenz %F pmlr-vR0-gelsema95a %I PMLR %P 245--251 %U https://proceedings.mlr.press/r0/gelsema95a.html %V R0 %X Bayesian belief networks (causal networks) have been extensively studied in the past ten years. It has been shown that they provide a sound formalism for probabilistic reasoning, especially if uncertainty is to be represented. A probability space can be modelled as a Bayesian belief network of propositional variables (nodes) which may be pairwise connected by directed arcs. The interpretation is that if an arc exists from node A to node $B$, the probability of node $B$ assuming a given state $b_{i}$ depends on the actual state of node $A$ ( $A$ is a direct cause of $B$ ). The absence of an arc between two nodes implies that there is no such direct dependence. Thus, in a Bayesian belief network, probabilistic dependencies are modelled as arcs between nodes, independencies are implied by the absence of arcs. If for a given probability space, for all states of the root nodes the prior probabilities are known, and in addition, for all non-root nodes the conditional probabilities, given the parent states, the joint probability distribution is completely known. Textbooks on Bayesian belief networks are [1] and [2]. %Z Reissued by PMLR on 01 May 2022.
APA
Gelsema, E.S.. (1995). Abductive Reasoning in Bayesian Belief Networks Using a Genetic Algorithm. Pre-proceedings of the Fifth International Workshop on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research R0:245-251 Available from https://proceedings.mlr.press/r0/gelsema95a.html. Reissued by PMLR on 01 May 2022.

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