Approximating Hyper-Rectangles: Learning and Pseudorandom Sets

Peter Auer, Philip M. Long, Aravind Srinivasan

Abstract: The PAC learning of rectangles has been studied because they have been found experimentally to yield excellent hypotheses for several applied learning problems. Also, pseudorandom sets for rectangles have been actively studied recently because (i) they are a subproblem common to the derandomization of depth-2 (DNF) circuits and derandomizing randomized logspace, and (ii) they approximate the distribution of n independent multivalued random variables. We present improved upper bounds for a class of such problems of “approximating” high-dimensional rectangles that arise in PAC learning and pseudo- randomness.