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Learning on finite metric spaces

Anthony, Martin and Ratsaby, Joel (2012) Learning on finite metric spaces. RUTCOR research reports, RRR 19-2012. Center for Operations Research, Rutgers University, Piscataway, New Jersey.

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Abstract

In M. Anthony and J. Ratsaby. Maximal width learning of binary functions. Theoretical Computer Science, 411:138–147, 2010, 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: Monograph (Report)
Official URL: http://rutcor.rutgers.edu/2012.html
Additional Information: © 2012 The Authors
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Departments > Mathematics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Identification Number: RRR 19-2012
Date Deposited: 11 Jul 2012 12:13
URL: http://eprints.lse.ac.uk/44782/

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