Theory of linear and integer programming
Theory of linear and integer programming
Learnability and the Vapnik-Chervonenkis dimension
Journal of the ACM (JACM)
COLT '91 Proceedings of the fourth annual workshop on Computational learning theory
Fast identification of geometric objects with membership queries
COLT '91 Proceedings of the fourth annual workshop on Computational learning theory
On-line learning of rectangles
COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
On exact specification by examples
COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
Lower Bound Methods and Separation Results for On-Line Learning Models
Machine Learning - Computational learning theory
COLT '93 Proceedings of the sixth annual conference on Computational learning theory
On training simple neural networks and small-weight neurons
Euro-COLT '93 Proceedings of the first European conference on Computational learning theory
Machine Learning
Machine Learning
Generalized teaching dimensions and the query complexity of learning
COLT '95 Proceedings of the eighth annual conference on Computational learning theory
PAC learning intersections of halfspaces with membership queries (extended abstract)
COLT '96 Proceedings of the ninth annual conference on Computational learning theory
Lower Bounds for the Complexity of Learning Half-Spaces with Membership Queries
ALT '98 Proceedings of the 9th International Conference on Algorithmic Learning Theory
Intrinsic Complexity of Learning Geometrical Concepts from Positive Data
COLT '01/EuroCOLT '01 Proceedings of the 14th Annual Conference on Computational Learning Theory and and 5th European Conference on Computational Learning Theory
Intrinsic complexity of learning geometrical concepts from positive data
Journal of Computer and System Sciences
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We consider exact identification of geometrical objects over the domain {0,1,…,n−1}d, d≥1 fixed. We give efficient implementations of the general incremental scheme “identify the target concept by constructing its convex hull” for learning convex concepts. This approach is of interest for intersections of half-spaces over the considered domain, as the convex hull of a concept of this type is known to have “few” vertices. In this case we obtain positive results on learning intersections of halfspaces with superset/disjointedness queries, and on learning single halfspaces with membership queries. We believe that the presented paradigm may become important for neural networks with a fixed number of discrete inputs.