What is... the VC-Dimension?
نویسندگان
چکیده
منابع مشابه
Teaching Dimension versus VC Dimension
In this report, we give a brief survey of various results relating the Teaching Dimension and VC-Dimension. The concept of Teaching Dimension was first introduced by Goldman and Kearns, 1995 and Sinohara and Miyano, 1991. In this model, an algorithm tries to learn the hidden concept c from examples, called the teaching set, which uniquely identifies c from the rest of the concepts in the concep...
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The very idea of an \EEective Vapnik Chervonenkis (VC) dimension" (Vapnik, Levin and Le Cun, 1993) relies on the hypothesis that the relation between the generalization error and the number of training examples can be expressed by a formula algebraically similar to the VC bound. This hypothesis calls for a serious discussion since the traditional VC bound widely overestimates the generalization...
متن کاملHints and the VC Dimension
Learning from hints is a generalization of learning from examples that allows for a variety of information about the unknown function to be used in the learning process. In this paper, we use the VC dimension, an established tool for analyzing learning from examples, to analyze learning from hints. In particular, we show how the VC dimension is affected by the introduction of a hint. We also de...
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We will establish that the vc dimension of the class of d-dimensional ellipsoids is (d +3d)/2, and that maximum likelihood estimate with N -component d-dimensional Gaussian mixture models induces a geometric class having vc dimension at least N(d + 3d)/2.
متن کاملHitting sets when the VC-dimension is small
We present an approximation algorithm for the hitting set problem when the VC-dimension of the set system is small. Our algorithm builds on Pach & Agarwal [7], and we show how it can be parallelized and extended to the minimum cost hitting set problem. The running time of the proposed algorithm is comparable with that of Brönnimann & Goodrich [2], and the approximation ratio is smaller by a con...
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ژورنال
عنوان ژورنال: Notices of the American Mathematical Society
سال: 2021
ISSN: 0002-9920,1088-9477
DOI: 10.1090/noti2260