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Learning-Related Complexity of Linear Ranking Functions

  • Atsuyoshi Nakamura
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4264)

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.

Keywords

Function Class Collaborative Filter Ordinal Regression Graph Dimension Decision List 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Atsuyoshi Nakamura
    • 1
  1. 1.Graduate School of Information Science and TechnologyHokkaido UniversitySapporoJapan

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