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Learning bounds via sample width for classifiers on finite metric spaces

Anthony, Martin and Ratsaby, Joel (2014) Learning bounds via sample width for classifiers on finite metric spaces. Theoretical Computer Science, 529 . pp. 2-10. ISSN 0304-3975

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Abstract

In a recent paper [M. Anthony, J. Ratsaby, Maximal width learning of binary functions, Theoretical Computer Science 411 (2010) 138–147] the notion of sample width for binary classifiers mapping from the real line was introduced, and it was shown that the performance of such classifiers could be quantified in terms of this quantity. This paper considers how to generalize the notion of sample width so that we can apply it where the classifiers map from some finite metric space. By relating the learning problem to one involving the domination numbers of certain graphs, we obtain generalization error bounds that depend on the sample width and on certain measures of ‘density’ of the underlying metric space. We also discuss how to employ a greedy set-covering heuristic to bound generalization error.

Item Type: Article
Official URL: http://www.sciencedirect.com/science/journal/03043...
Additional Information: © 2014 Elsevier B.V.
Library of Congress subject classification: Q Science > QA Mathematics
Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Sets: Departments > Mathematics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 02 Aug 2013 15:23
URL: http://eprints.lse.ac.uk/51375/

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