On Using Extended Statistical Queries to Avoid Membership Queries

The Kushilevitz-Mansour (KM) algorithm is an algorithm that finds all the “large” Fourier coefficients of a Boolean function. It is the main tool for learning decision trees and DNF expressions in the PAC model with respect to the uniform distribution. The algorithm requires access to the membership query (MQ) oracle. The access is often unavailable in learning applications and thus the KM algorithm cannot be used. We significantly weaken this requirement by producing an analogue of the KM algorithm that uses extended statistical queries (SQ) (SQs in which the expectation is taken with respect to a distribution given by a learning algorithm). We restrict a set of distributions that a learning algorithm may use for its statistical queries to be a set of product distributions with each bit being 1 with probability ρ, 1/2 or 1−ρ for a constant 1/2 > ρ > 0 (we denote the resulting model by SQ–Dρ). Our analogue finds all the “large” Fourier coefficients of degree l...

• Type: Conference
• Year: 2001
• Where: COLT
• Authors: Nader H. Bshouty, Vitaly Feldman
• Keywords: Algorithms, COLT 2001, Decision Trees, Machine Learning, Statistical Queries