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
On the computational power of depth 2 circuits with threshold and modulo gates
STOC '94 Proceedings of the twenty-sixth 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
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
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
Boosting and other ensemble methods
Neural Computation
Theory and application of trapdoor functions
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
An efficient membership-query algorithm for learning DNF with respect to the uniform distribution
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Hardness amplification within NP
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Quantum DNF Learnability Revisited
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
Proclaiming Dictators and Juntas or Testing Boolean Formulae
APPROX '01/RANDOM '01 Proceedings of the 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems and 5th International Workshop on Randomization and Approximation Techniques in Computer Science: Approximation, Randomization and Combinatorial Optimization
Optimally-Smooth Adaptive Boosting and Application to Agnostic Learning
ALT '02 Proceedings of the 13th International Conference on Algorithmic Learning Theory
On Boosting with Optimal Poly-Bounded Distributions
COLT '01/EuroCOLT '01 Proceedings of the 14th Annual Conference on Computational Learning Theory and and 5th European Conference on Computational Learning Theory
Smooth Boosting and Learning with Malicious Noise
COLT '01/EuroCOLT '01 Proceedings of the 14th Annual Conference on Computational Learning Theory and and 5th European Conference on Computational Learning Theory
On Learning Monotone DNF under Product Distributions
COLT '01/EuroCOLT '01 Proceedings of the 14th Annual Conference on Computational Learning Theory and and 5th European Conference on Computational Learning Theory
On the Derandomization of Constant Depth Circuits
APPROX '01/RANDOM '01 Proceedings of the 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems and 5th International Workshop on Randomization and Approximation Techniques in Computer Science: Approximation, Randomization and Combinatorial Optimization
On using extended statistical queries to avoid membership queries
The Journal of Machine Learning Research
On boosting with polynomially bounded distributions
The Journal of Machine Learning Research
Optimally-smooth adaptive boosting and application to agnostic learning
The Journal of Machine Learning Research
Smooth boosting and learning with malicious noise
The Journal of Machine Learning Research
More efficient PAC-learning of DNF with membership queries under the uniform distribution
Journal of Computer and System Sciences
Learning intersections and thresholds of halfspaces
Journal of Computer and System Sciences - Special issue on FOCS 2002
Hardness amplification within NP
Journal of Computer and System Sciences - Special issue on computational complexity 2002
On learning monotone DNF under product distributions
Information and Computation
Key agreement from weak bit agreement
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Learning DNF from random walks
Journal of Computer and System Sciences - Special issue: Learning theory 2003
Property Testing: A Learning Theory Perspective
Foundations and Trends® in Machine Learning
General hardness amplification of predicates and puzzles
TCC'11 Proceedings of the 8th conference on Theory of cryptography
Characterizing pseudoentropy and simplifying pseudorandom generator constructions
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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This paper connects two fundamental ideas from theoretical computer science: 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 [15], 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 [15] 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.