Communications of the ACM
A hard-core predicate for all one-way functions
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
A guided tour of Chernoff bounds
Information Processing Letters
The Strength of Weak Learnability
Machine Learning
Learning decision trees using the Fourier spectrum
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Efficient noise-tolerant learning from statistical queries
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Constant depth circuits, Fourier transform, and learnability
Journal of the ACM (JACM)
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
On the Fourier spectrum of monotone functions
Journal of the ACM (JACM)
A decision-theoretic generalization of on-line learning and an application to boosting
Journal of Computer and System Sciences - Special issue: 26th annual ACM symposium on the theory of computing & STOC'94, May 23–25, 1994, and second annual Europe an conference on computational learning theory (EuroCOLT'95), March 13–15, 1995
An efficient membership-query algorithm for learning DNF with respect to the uniform distribution
Journal of Computer and System Sciences
Specification and simulation of statistical query algorithms for efficiency and noise tolerance
Journal of Computer and System Sciences - Special issue on the eighth annual workshop on computational learning theory, July 5–8, 1995
Noise-tolerant learning, the parity problem, and the statistical query model
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Exploiting Product Distributions to Identify Relevant Variables of Correlation Immune Functions
The Journal of Machine Learning Research
Statistical algorithms and a lower bound for detecting planted cliques
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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The Statistical Query (SQ) model provides an elegant means for generating noise-tolerant PAC learning algorithms that run in time inverse polynomial in the noise rate. Whether or not there is an SQ algorithm for every noise-tolerant PAC algorithm that is efficient in this sense remains an open question. However, we show that PAC algorithms derived from the Statistical Query model are not always the most efficient possible. Specifically, we give a general definition of SQ-based algorithm and show that there is a subclass of parity functions for which there is an efficient PAC algorithm requiring asymptotically less running time than any SQ-based algorithm. While it turns out that this result can be derived fairly easily by combining a recent algorithm of Blum, Kalai, and Wasserman with an older lower bound, we also provide alternate, Fourier-based approaches to both the upper and lower bounds that strengthen the results in various ways. The lower bound in particular is stronger than might be expected, and the amortized technique used in deriving this bound may be of independent interest.