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.
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Smirnov, E., Nalbantov, G., Nikolaev, N. (2010). k-Version-Space Multi-class Classification Based on k-Consistency Tests. In: Balcázar, J.L., Bonchi, F., Gionis, A., Sebag, M. (eds) Machine Learning and Knowledge Discovery in Databases. ECML PKDD 2010. Lecture Notes in Computer Science(), vol 6323. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15939-8_18
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