Communications of the ACM
Learning k-DNF with noise in the attributes
COLT '88 Proceedings of the first annual workshop on Computational learning theory
Learning with restricted focus of attention
COLT '93 Proceedings of the sixth annual conference on Computational learning theory
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
Toward Efficient Agnostic Learning
Machine Learning - Special issue on computational learning theory, COLT'92
Uniform-distribution attribute noise learnability
Information and Computation
Agnostically Learning Halfspaces
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Learning disjunction of conjunctions
IJCAI'85 Proceedings of the 9th international joint conference on Artificial intelligence - Volume 1
Agnostically learning decision trees
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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Recently, Kalai et al. [1] have shown (among other things) that linear threshold functions over the Boolean cube and unit sphere are agnostically learnable with respect to the uniform distribution using the hypothesis class of polynomial threshold functions. Their primary algorithm computes monomials of large constant degree, although they also analyze a low-degree algorithm for learning origin-centered halfspaces over the unit sphere. This paper explores noise-tolerant learnability of linear thresholds over the cube when the learner sees a very limited portion of each instance. Uniform-distribution weak learnability results are derived for the agnostic, unknown attribute noise, and malicious noise models. The noise rates that can be tolerated vary: the rate is essentially optimal for attribute noise, constant (roughly 1/8) for agnostic learning, and non-trivial ($\Omega(1/\sqrt{n})$) for malicious noise. In addition, a new model that lies between the product attribute and malicious noise models is introduced, and in this stronger model results similar to those for the standard attribute noise model are obtained for learning homogeneous linear thresholds with respect to the uniform distribution over the cube. The learning algorithms presented are simple and have small-polynomial running times.