The Strength of Weak Learnability
Machine Learning
Learning decision trees using the Fourier spectrum
SIAM Journal on Computing
Threshold circuits of bounded depth
Journal of Computer and System Sciences
On using the Fourier transform to learn Disjoint DNF
Information Processing Letters
Learning unions of boxes with membership and equivalence queries
COLT '94 Proceedings of the seventh annual conference on Computational learning theory
On-Line Learning of Rectangles and Unions of Rectangles
Machine Learning - Special issue on computational learning theory, COLT'92
Boosting a weak learning algorithm by majority
Information and Computation
An efficient membership-query algorithm for learning DNF with respect to the uniform distribution
Journal of Computer and System Sciences
Efficient learning with virtual threshold gates
Information and Computation
On Learning Read-k-Satisfy-j DNF
SIAM Journal on Computing
Computing Boolean functions by polynomials and threshold circuits
Computational Complexity
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Smooth boosting and learning with malicious noise
The Journal of Machine Learning Research
Proving Hard-Core Predicates Using List Decoding
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Journal of Computer and System Sciences - STOC 2001
| Hi-index | 5.23 |
We consider the problem of learning unions of rectangles over the domain [b]^n, in the uniform distribution membership query learning setting, where both b and n are ''large''. We obtain poly(n,logb)-time algorithms for the following classes: *poly(nlogb)-way Majority of O(log(nlogb)loglog(nlogb))-dimensional rectangles. *Union of poly(log(nlogb)) many O(log^2(nlogb)(loglog(nlogb)logloglog(nlogb))^2)-dimensional rectangles. *poly(nlogb)-way Majority of poly(nlogb)-Or of disjoint O(log(nlogb)loglog(nlogb)) dimensional rectangles. Our main algorithmic tool is an extension of Jackson's boosting- and Fourier-based Harmonic Sieve algorithm [J.C. Jackson, An efficient membership-query algorithm for learning DNF with respect to the uniform distribution, Journal of Computer and System Sciences 55 (3) (1997) 414-440] to the domain [b]^n, building on work of Akavia et al. [A. Akavia, S. Goldwasser, S. Safra, Proving hard core predicates using list decoding, in: Proc. of the 44th Annual IEEE Symposium on Foundations of Computer Science, FOCS '03, 2003, pp. 146-156]. Other ingredients used to obtain the results stated above are techniques from exact learning [A. Beimel, E. Kushilevitz, Learning boxes in high dimension, Algorithmica 22 (1/2) (1998) 76-90] and ideas from recent work on learning augmented AC^0 circuits [J.C. Jackson, A.R. Klivans, R.A. Servedio, Learnability beyond AC^0, in: Proc. of the 34th Annual ACM Symposium on Theory of Computing, STOC '02, 2002, pp. 776-784] and on representing Boolean functions as thresholds of parities [A.R. Klivans, R.A. Servedio, Learning DNF in time 2^O^@?^(^n^^^1^^^/^^^3^), Journal of Computer and System Sciences 68 (2) (2004) 303-318].