Proper learning algorithm for functions of k terms under smooth distributions

Authors: Yoshifumi Sakai, Eiji Takimoto, and Akira Maruoka

Source: Information & Computation Vol. 152, No. 2, 1999, 188 - 204.

Abstract. In this paper, we introduce a probabilistic distribution, called a smooth distribution, which is a generalization of variants of the uniform distribution such as q-bounded distribution and product distribution. Then, we give an algorithm that, under the smooth distribution, properly learns the class of functions of k terms given as kkn={g(f1(v),...,fk(v)) | g k, fv,..., fk n} in polynomial time for constant k, where k is the class of all Boolean functions of k variables and n is the class of terms over n variables. Although class kkn was shown by Blum and Singh to be learned using DNF as the hypothesis class, it has remained open whether it is properly learnable under a distribution-free setting.

©Copyright 1999, Academic Press