Journal ArticleDOI
Learnability and the Vapnik-Chervonenkis dimension
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
More filters
Book ChapterDOI
Verification as Learning Geometric Concepts
TL;DR: It is shown that invariants in program verification can be regarded as geometric concepts in machine learning, and the learning algorithm is extended to obtain a sound procedure that can generate proofs containing invariants that are arbitrary boolean combinations of polynomial inequalities.
Theoretical foundations of active learning
TL;DR: Borders on the rates of convergence achievable by active learning are derived, under various noise models and under general conditions on the hypothesis class.
Proceedings Article
Neural Networks with Quadratic VC Dimension
Pascal Koiran,Eduardo D. Sontag +1 more
TL;DR: This paper showed that neural networks with continuous activation functions have VC dimension at least as large as the square of the number of weights w. This result settles a long-standing open question, namely whether the well-known O(w log w) bound, known for hard-threshold nets, also held for more general sigmoidal nets.
Journal ArticleDOI
Queries revisited
TL;DR: A brief tutorial on the problem of learning a finite concept class over a finite domain using membership queries and/or equivalence queries, focusing on the various notions of combinatorial dimension that have been employed.
Proceedings ArticleDOI
Stability and Generalization of Graph Convolutional Neural Networks
Saurabh Verma,Zhi-Li Zhang +1 more
TL;DR: This paper is the first to study stability bounds on graph learning in a semi-supervised setting and derive generalization bounds for GCNN models and shows that the algorithmic stability of a GCNN model depends upon the largest absolute eigenvalue of its graph convolution filter.
References
More filters
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.
Book
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.