Preface to the special issue

Abstract

The series “International Symposium on Artificial Intelligence and Mathematics” is held every two years in Fort Lauderdale. While the general scope of the series is broad, and even includes the interaction of AI with Operations Research, each meeting typically includes a special focus on one or two particular topics. In the 2010 meeting, about half the papers were in the track Boolean and pseudo-Boolean functions which was organized by Endre Boros and Yves Crama, another four were in the track Constraint programming and hybrid methods organized by John Hooker, and the remaining papers covered a wide range of topics that tie AI to mathematics. This special issue of AMAI contains four papers from the third track and one from the first track, chosen by the organizers to be expanded and polished into journal versions by their excellence in written and oral presentation. Two papers are on Bayesian updating, one on the multi-armed bandit problem, one on concept analysis in data mining, and one on minimizing clausal data bases. In what follows, we try to set the context for each of these papers. A Bayesian network is a probabilistic directed acyclic graph for modeling a set of random variables and their conditional dependencies, for example, between a set of diseases and symptoms. Bayesian networks may be used to generate explanations for given evidence, such as finding the most likely instantiation of a set of target variables given partial evidence on the remaining variables. Most Relevant Explanation (MRE) is the problem of generating an explanation that emphasizes the role of the most relevant target variables: if e is a set of observed variable values and if y1, y2, ... are all possible instantiations of all possible subsets of target variables, then MRE = maxi Pr(e|yi)/Pr(e|¬yi). In some respects, MRE estimates may be better than other Bayesian estimates. However, in the paper “Most Relevant Explanation: Computational complexity and approximation methods”, Yuan, Lim, and Littman show that MRE is NP-hard. The authors then propose and evaluate