k-version-space multi-class classification based on k-consistency tests

Authors:
Evgueni Smirnov;Georgi Nalbantov;Nikolay Nikolaev
Affiliations:
Department of Knowledge Engineering, Maastricht University, Maastricht, The Netherlands;Department of Knowledge Engineering, Maastricht University, Maastricht, The Netherlands;Department of Computing, Goldsmiths College, University of London, London, United Kingdom
Venue:
ECML PKDD'10 Proceedings of the 2010 European conference on Machine learning and knowledge discovery in databases: Part III
Year:
2010

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Abstract

k-Version spaces were introduced in [6] to handle noisy data. They were defined as sets of k-consistent hypotheses; i.e., hypotheses consistent with all but k instances. Although k-version spaces were applied, their implementation was intractable due to the boundary-set representation. This paper argues that to classify with k-version spaces we do not need an explicit representation. Instead we need to solve a general k-consistency problem and a general k0-consistency problem. The general k-consistency problem is to test the hypothesis space for classifier that is k-consistent with the data. The general k0-consistency problem is to test the hypothesis space for classifier that is k-consistent with the data and 0-consistent with a labeled test instance. Hence, our main result is that the k-version-space classification can be (tractably) implemented if we have (tractable) k-consistency-test algorithms and (tractable) k0-consistency-test algorithms. We show how to design these algorithms for any learning algorithm in multi-class classification setting.