Performance analysis of a greedy algorithm for inferring boolean functions

Abstract

A simple greedy algorithm has been known as an approximation algorithm for inference of a Boolean function from positive and negative examples, which is a fundamental problem in discovery science. It was conjectured from results of computational experiments that the greedy algorithm can find an exact (or optimal) solution with high probability if input data for each function are generated uniformly at random. This conjecture was proved only for AND/OR of literals. This paper gives a proof of the conjecture for more general Boolean functions which we call unbalanced functions. We also proved that unbalanced functions account for more than half of all Boolean functions, and the ratio of d-input unbalanced functions to all d-input Boolean functions converges to 1 as d grows. This means that the greedy algorithm can find the exact solution with high probability for most Boolean functions if input data are generated uniformly at random. In order to improve the performance for cases of small d, we develop a variant of the greedy algorithm. The theoretical results on the greedy algorithm and the effectiveness of the variant were confirmed through computational experiments. © Springer-Verlag Berlin Heidelberg 2003.