Testing and learning Boolean functions

Abstract

Given a function f on n inputs, we consider the problem of testing whether f belongs to a concept class C, or is far from every member of C. An algorithm that achieves this goal for a particular C is called a property testing algorithm, and can be viewed as relaxation of a proper learning algorithm, which must also return an approximation to f if it is in C. We give property testing algorithms for many different classes C, with a focus on those that are fundamental to machine learning, such as halfspaces, decision trees, DNF formulas, and sparse polynomials. In almost all cases, the property testing algorithm has query complexity independent of n, better than the best possible learning algorithm.