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Learning-Related Complexity of Linear Ranking Functions

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Algorithmic Learning Theory (ALT 2006)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4264))

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Abstract

In this paper, we study learning-related complexity of linear ranking functions from n-dimensional Euclidean space to {1,2,...,k}. We show that their graph dimension, a kind of measure for PAC learning complexity in the multiclass classification setting, is Θ(n+k). This graph dimension is significantly smaller than the graph dimension Ω(nk) of the class of {1,2,...,k}-valued decision-list functions naturally defined using k–1 linear discrimination functions. We also show a risk bound of learning linear ranking functions in the ordinal regression setting by a technique similar to that used in the proof of an upper bound of their graph dimension.

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Authors and Affiliations

  1. Graduate School of Information Science and Technology, Hokkaido University, Kita 14, Nishi 9, Kita-ku, Sapporo, 060-0814, Japan

    Atsuyoshi Nakamura

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  1. Atsuyoshi Nakamura
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Editors and Affiliations

  1. Departament de Llenguatges i Sistemes Informàtics Laboratori d’Algorísmica Relacional, Complexitat i Aprenentatge, Universitat Politècnica de Catalunya, Barcelona,  

    José L. Balcázar

  2. Google, 1600 Amphitheatre Parkway, 94043, Mountain View, CA, USA

    Philip M. Long

  3. Department of Computer Science and Department of Mathematics, National University of Singapore, 117543, Singapore, Republic of Singapore

    Frank Stephan

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Nakamura, A. (2006). Learning-Related Complexity of Linear Ranking Functions. In: Balcázar, J.L., Long, P.M., Stephan, F. (eds) Algorithmic Learning Theory. ALT 2006. Lecture Notes in Computer Science(), vol 4264. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11894841_30

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  • DOI: https://doi.org/10.1007/11894841_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-46649-9

  • Online ISBN: 978-3-540-46650-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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