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
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
Randomized algorithms
Learning sparse multivariate polynomials over a field with queries and counterexamples
Journal of Computer and System Sciences
General bounds on statistical query learning and PAC learning with noise via hypothesis boosting
Information and Computation
Efficient noise-tolerant learning from statistical queries
Journal of the ACM (JACM)
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
Quantum lower bounds by quantum arguments
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
On the Efficiency of Noise-Tolerant PAC Algorithms Derived from Statistical Queries
COLT '00 Proceedings of the Thirteenth Annual Conference on Computational Learning Theory
A polynomial-time algorithm for learning noisy linear threshold functions
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Efficient learning from faulty data
Efficient learning from faulty data
A Generalized Birthday Problem
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
New Lower Bounds for Statistical Query Learning
COLT '02 Proceedings of the 15th Annual Conference on Computational Learning Theory
New Lower Bounds for Statistical Query Learning
COLT '02 Proceedings of the 15th Annual Conference on Computational Learning Theory
Uniform-distribution attribute noise learnability
Information and Computation
New lower bounds for statistical query learning
Journal of Computer and System Sciences - Special issue on COLT 2002
Exploiting Product Distributions to Identify Relevant Variables of Correlation Immune Functions
The Journal of Machine Learning Research
Characterizing statistical query learning: simplified notions and proofs
ALT'09 Proceedings of the 20th international conference on Algorithmic learning theory
Spectral norm in learning theory: some selected topics
ALT'06 Proceedings of the 17th international conference on Algorithmic Learning Theory
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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In this paper, we study the problem of using statistical query (SQ) to learn a class of highly correlated boolean functions, namely, a class of functions where any pair agree on significantly more than 1/2 fraction of the inputs. We give an almost-tight bound on how well one can approximate all the functions without making any query, and then we show that beyond this bound, the number of statistical queries the algorithm has to make increases with the "extra" advantage the algorithm gains in learning the functions. Here the advantage is defined to be the probability the algorithm agrees with the target function minus the probability the algorithm doesn't agree.An interesting consequence of our results is that the class of booleanized linear functions over a finite field (f(a(x) = 1 iff 驴(a 驴 x) = 1, where 驴 is an arbitrary boolean function that maps any elements in GFp to 卤1) is not efficiently learnable. This result is useful since the hardness of learning booleanized linear functions over a finite field is related to the security of certain cryptosystems ([B01]). In particular, we prove that the class of linear threshold functions over a finite field (f(a,b(x) = 1 iff a 驴 x 驴 b) cannot be learned efficiently using statistical query. This contrasts with Blum et. al.'s result [BFK+96] that linear threshold functions over reals (perceptions) are learnable using the SQ model.Finally, we describe a PAC-learning algorithm that learns a class of linear threshold functions in time that is provably impossible for statistical query algorithms. With properly chosen parameters, this class of linear threshold functions become an example of PAC-learnable, but not SQlearnable functions that are not parity functions.