Learning k-term monotone Boolean formulae

Abstract

Valiant introduced a computational model of learning by examples, and gave a precise definition of learnability based on the model. Since then, much effort has been devoted to characterize learnable classes of concepts on this model. Among such learnable classes is the one, denoted k-term MDNF, consisting of monotone disjunctive normal form formulae with at most k terms. In literature, k-term MDNF is shown to be learnable under the assumption that examples are drawn according to the uniform distribution. In this paper we generalize the result to obtain the statement that k-term MDNF is learnable even if positive examples are drawn according to such distribution that the maximum of the ratio of the probabilities of two positive examples is bounded from above by some polynomial.