TY - JOUR

T1 - Learning bounds via sample width for classifiers on finite metric spaces

AU - Anthony, Martin

AU - Ratsaby, Joel

N1 - Publisher Copyright:
© 2013 Elsevier B.V.

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - Generalization error

KW - Learning algorithms

KW - Machine learning

UR - http://www.scopus.com/inward/record.url?scp=84898053811&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2013.07.004

DO - 10.1016/j.tcs.2013.07.004

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AN - SCOPUS:84898053811

SN - 0304-3975

VL - 529

SP - 2

EP - 10

JO - Theoretical Computer Science

JF - Theoretical Computer Science

ER -