Communications of the ACM
Average case complete problems
SIAM Journal on Computing
Learnability and the Vapnik-Chervonenkis dimension
Journal of the ACM (JACM)
The Strength of Weak Learnability
Machine Learning
Boosting a weak learning algorithm by majority
COLT '90 Proceedings of the third annual workshop on Computational learning theory
An improved boosting algorithm and its implications on learning complexity
COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
Amplification of weak learning under the uniform distribution
COLT '93 Proceedings of the sixth annual conference on Computational learning theory
Cryptographic limitations on learning Boolean formulae and finite automata
Journal of the ACM (JACM)
Journal of Computer and System Sciences
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
BPP has subexponential time simulations unless EXPTIME has publishable proofs
Computational Complexity
Boosting a weak learning algorithm by majority
Information and Computation
The harmonic sieve: a novel application of Fourier analysis to machine learning theory and practice
The harmonic sieve: a novel application of Fourier analysis to machine learning theory and practice
P = BPP if E requires exponential circuits: derandomizing the XOR lemma
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
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
Improved boosting algorithms using confidence-rated predictions
COLT' 98 Proceedings of the eleventh annual conference on Computational learning theory
More efficient PAC-learning of DNF with membership queries under the uniform distribution
COLT '99 Proceedings of the twelfth annual conference on Computational learning theory
Bounds to Complexities of Networks for Sorting and for Switching
Journal of the ACM (JACM)
Pseudorandom generators without the XOR lemma
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Improving Performance in Neural Networks Using a Boosting Algorithm
Advances in Neural Information Processing Systems 5, [NIPS Conference]
Hard-core distributions for somewhat hard problems
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Towards Proving Strong Direct Product Theorems
CCC '01 Proceedings of the 16th Annual Conference on Computational Complexity
Using nondeterminism to amplify hardness
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Hardness amplification proofs require majority
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
The uniform hardcore lemma via approximate Bregman projections
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Hardness Amplification Proofs Require Majority
SIAM Journal on Computing
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Query complexity in errorless hardness amplification
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Computational randomness from generalized hardcore sets
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
On attribute efficient and non-adaptive learning of parities and DNF expressions
COLT'05 Proceedings of the 18th annual conference on Learning Theory
A complete characterization of statistical query learning with applications to evolvability
Journal of Computer and System Sciences
On the complexity of hard-core set constructions
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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This paper connects hard-core set construction, a type of hardness amplification from computational complexity, and boosting, a technique from computational learning theory. Using this connection we give fruitful applications of complexity-theoretic techniques to learning theory and vice versa. We show that the hard-core set construction of Impagliazzo (1995), which establishes the existence of distributions under which boolean functions are highly inapproximable, may be viewed as a boosting algorithm. Using alternate boosting methods we give an improved bound for hard-core set construction which matches known lower bounds from boosting and thus is optimal within this class of techniques. We then show how to apply techniques from Impagliazzo (1995) to give a new version of Jackson's celebrated Harmonic Sieve algorithm for learning DNF formulae under the uniform distribution using membership queries. Our new version has a significant asymptotic improvement in running time. Critical to our arguments is a careful analysis of the distributions which are employed in both boosting and hard-core set constructions.