Communications of the ACM
Learnability and the Vapnik-Chervonenkis dimension
Journal of the ACM (JACM)
Learning monotone ku DNF formulas on product distributions
COLT '91 Proceedings of the fourth annual workshop on Computational learning theory
Improved learning of AC0 functions
COLT '91 Proceedings of the fourth annual workshop on Computational learning theory
Lower bounds for PAC learning with queries
COLT '93 Proceedings of the sixth annual conference on Computational learning theory
Learning Boolean concepts in the presence of many irrelevant features
Artificial Intelligence
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 learnability of discrete distributions
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)
Selection of relevant features and examples in machine learning
Artificial Intelligence - Special issue on relevance
Efficient noise-tolerant learning from statistical queries
Journal of the ACM (JACM)
A Spectral Algorithm for Learning Mixtures of Distributions
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
On using extended statistical queries to avoid membership queries
The Journal of Machine Learning Research
Multiple instance learning of real valued data
The Journal of Machine Learning Research
On learning monotone DNF under product distributions
Information and Computation
Learning functions of k relevant variables
Journal of Computer and System Sciences - Special issue: STOC 2003
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
Learning mixtures of product distributions over discrete domains
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Discovering Classification from Data of Multiple Sources
Data Mining and Knowledge Discovery
Quantum Algorithms for Learning and Testing Juntas
Quantum Information Processing
Exploiting Product Distributions to Identify Relevant Variables of Correlation Immune Functions
The Journal of Machine Learning Research
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We study the problem of learning k-juntas given access to examples drawn from a number of different product distributions. Thus we wish to learn a function f: {−1, 1}n → {−1, 1} that depends on k (unknown) coordinates. While the best-known algorithms for the general problem of learning a k-junta require running times of nk poly(n, 2k), we show that, given access to k different product distributions with biases separated by γ 0, the functions may be learned in time poly(n, 2k, γ−k). More generally, given access to t ≤ k different product distributions, the functions may be learned in time nk/tpoly(n, 2k, γ−k). Our techniques involve novel results in Fourier analysis, relating Fourier expansions with respect to different biases, and a generalization of Russo's formula.