PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

An Algebraic Perspective on Boolean Function Learning
Ricard Gavaldà and Denis Thérien
In: 20th Intl. Conf. on Algorithmic Learning Theory (ALT'09), 3-5 Oct 2009, Porto, Portugal.

Abstract

In order to systematize existing results, we propose to analyze the learnability of boolean functions computed by an algebraically defined model, programs over monoids. The expressiveness of the model, hence its learning complexity, depends on the algebraic structure of the chosen monoid. We identify three classes of monoids that can be identified, respectively, from Membership queries alone, Equivalence queries alone, and both types of queries. The algorithms for the first class are new to our knowledge, while those for the other two are combinations or particular cases of known algorithms. Learnability of these three classes captures many previous learning results. Moreover, by using nontrivial taxonomies of monoids, we can argue that using the same techniques to learn larger classes of boolean functions seems to require proving new circuit lower bounds or proving learnability of DNF formulas.

EPrint Type:Conference or Workshop Item (Paper)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Theory & Algorithms
ID Code:6632
Deposited By:Ricard Gavaldà
Deposited On:08 March 2010