Communications of the ACM
Weakly learning DNF and characterizing statistical query learning using Fourier analysis
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Information and Computation
Efficient noise-tolerant learning from statistical queries
Journal of the ACM (JACM)
A General Dimension for Approximately Learning Boolean Functions
ALT '02 Proceedings of the 13th International Conference on Algorithmic Learning Theory
New lower bounds for statistical query learning
Journal of Computer and System Sciences - Special issue on COLT 2002
Spectral norm in learning theory: some selected topics
ALT'06 Proceedings of the 17th international conference on Algorithmic Learning Theory
Characterizing statistical query learning: simplified notions and proofs
ALT'09 Proceedings of the 20th international conference on Algorithmic learning theory
A complete characterization of statistical query learning with applications to evolvability
Journal of Computer and System Sciences
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In this paper, we consider Kearns' [4] Statistical Query Model of learning. It is well known [3] that the number of statistical queries, needed for "weakly learning" an unknown target concept (i.e. for gaining significant advantage over random guessing) is polynomially related to the so-called Statistical Query dimension of the concept class. In this paper, we provide a similar characterization for "strong learning" where the learners final hypothesis is required to approximate the unknown target concept up to a small rate of misclassification. The quantity that characterizes strong learnability in the Statistical Query model is a surprisingly close relative of (though not identical to) the Statistical Query dimension. For the purpose of proving the main result, we provide other characterizations of strong learnability which are given in terms of covering numbers and related notions. These results might find some interest in their own right. All characterizations are purely information-theoretical and ignore computational issues.