Journal ArticleDOI
Learnability and the Vapnik-Chervonenkis dimension
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TLDR
This paper shows that the essential condition for distribution-free learnability is finiteness of the Vapnik-Chervonenkis dimension, a simple combinatorial parameter of the class of concepts to be learned.Abstract:
Valiant's learnability model is extended to learning classes of concepts defined by regions in Euclidean space En. The methods in this paper lead to a unified treatment of some of Valiant's results, along with previous results on distribution-free convergence of certain pattern recognition algorithms. It is shown that the essential condition for distribution-free learnability is finiteness of the Vapnik-Chervonenkis dimension, a simple combinatorial parameter of the class of concepts to be learned. Using this parameter, the complexity and closure properties of learnable classes are analyzed, and the necessary and sufficient conditions are provided for feasible learnability.read more
Citations
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Journal ArticleDOI
Mean Estimation and Regression Under Heavy-Tailed Distributions: A Survey
TL;DR: This work describes sub-Gaussian mean estimators for possibly heavy-tailed data in both the univariate and multivariate settings and focuses on estimators based on median-of-means techniques, but other methods such as the trimmed-mean and Catoni's estimators are also reviewed.
Journal ArticleDOI
Equivalences and Separations Between Quantum and Classical Learnability
TL;DR: These results contrast known results that show that testing black-box functions for various properties, as opposed to learning, can require exponentially more classical queries than quantum queries.
Proceedings ArticleDOI
On the complexity of teaching
Sally A. Goldman,Michael Kearns +1 more
TL;DR: This paper considers a variant of the on-line learning model in which a helpful teacher selects the instances, and measures the complexity of teaching by considering the teaching dimension, which is the minimum number of instances a teacher must reveal to uniquely identify any target concept chosen from the class.
Proceedings ArticleDOI
Mechanism design via machine learning
TL;DR: These reductions imply that for a wide variety of revenue-maximizing pricing problems, given an optimal algorithm for the standard algorithmic problem, it can be converted into a (1 + /spl epsi/)-approximation for the incentive-compatible mechanism design problem, so long as the number of bidders is sufficiently large.
Journal ArticleDOI
Deep learning: a statistical viewpoint
TL;DR: In particular, this article showed that simple gradient methods easily find near-optimal solutions to non-convex optimization problems, and despite giving a near-perfect fit to training data without any explicit effort to control model complexity, these methods exhibit excellent predictive accuracy.
References
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Book
Computers and Intractability: A Guide to the Theory of NP-Completeness
TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
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The Art of Computer Programming
TL;DR: The arrangement of this invention provides a strong vibration free hold-down mechanism while avoiding a large pressure drop to the flow of coolant fluid.
Journal ArticleDOI
Pattern Classification and Scene Analysis.
Book
Pattern classification and scene analysis
Richard O. Duda,Peter E. Hart +1 more
TL;DR: In this article, a unified, comprehensive and up-to-date treatment of both statistical and descriptive methods for pattern recognition is provided, including Bayesian decision theory, supervised and unsupervised learning, nonparametric techniques, discriminant analysis, clustering, preprosessing of pictorial data, spatial filtering, shape description techniques, perspective transformations, projective invariants, linguistic procedures, and artificial intelligence techniques for scene analysis.