Learning, Bayesian Probability, Graphical Models, and Abduction

David Poole

to appear, Peter Flach and Antonis Kakas, editors, Abduction and Induction: essays on their relation and integration, Kluwer, 1998.


In this chapter I review Bayesian statistics as used for induction and relate it to logic-based abduction. Much reasoning under uncertainty, including induction, is based on Bayes' rule. Bayes' rule is interesting precisely because it provides a mechanism for abduction. I review work of Buntine that argues that much of the work on Bayesian learning can be best viewed in terms of graphical models such as Bayesian networks, and review previous work of Poole that relates Bayesian networks to logic-based abduction. This lets us see how much of the work on induction can be viewed in terms of logic-based abduction. I then explore what this means for extending logic-based abduction to richer representations, such as learning decision trees with probabilities at the leaves. Much of this paper is tutorial in nature; both the probabilistic and logic-based notions of abduction and induction are introduced and motivated.

You can get the pdf. There are also slides (in PDF format) from my invited talk at the IJCAI-97 workshop in induction and abduction.

Related Papers

W. Buntine, "Operations for Learning with Graphical Models", Journal of Artificial Intelligence Research, Volume 2, pages 159-225, 1994.

D. Poole, The Independent Choice Logic for modelling multiple agents under uncertainty, Artificial Intelligence, Volume 94, Numbers 1-2, Special Issue on Economic Principles of Multi-agent Systems, pages 5-56, 1997.

D. Poole, Abducing Through Negation As Failure: Stable models in the Independent Choice Logic, to appear Journal of Logic Programming, 1999.

Last updated 11 June 1998 - David Poole