# Learning, Bayesian Probability, Graphical Models, and Abduction

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

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