Evolvability from learning algorithms
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Separating Models of Learning with Faulty Teachers
ALT '07 Proceedings of the 18th international conference on Algorithmic Learning Theory
ALT '08 Proceedings of the 19th international conference on Algorithmic Learning Theory
Separating models of learning with faulty teachers
Theoretical Computer Science
Almost tight upper bound for finding Fourier coefficients of bounded pseudo-Boolean functions
Journal of Computer and System Sciences
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We consider the problems of attribute-efficient PAC learning of two well-studied concept classes: parity functions and DNF expressions over {0,1}n. We show that attribute-efficient learning of parities with respect to the uniform distribution is equivalent to decoding high-rate random linear codes from low number of errors, a long-standing open problem in coding theory. This is the first evidence that attribute-efficient learning of a natural PAC learnable concept class can be computationally hard. An algorithm is said to use membership queries (MQs) non-adaptively if the points at which the algorithm asks MQs do not depend on the target concept. Using a simple non-adaptive parity learning algorithm and a modification of Levin's algorithm for locating a weakly-correlated parity due to Bshouty et al. (1999), we give the first non-adaptive and attribute-efficient algorithm for learning DNF with respect to the uniform distribution. Our algorithm runs in time Õ(ns4/ε) and uses Õ(s4 · log2n/ε) non-adaptive MQs, where s is the number of terms in the shortest DNF representation of the target concept. The algorithm improves on the best previous algorithm for learning DNF (of Bshouty et al., 1999) and can also be easily modified to tolerate random persistent classification noise in MQs.