Constructing Kernel Functions for Binary Regression

  • Authors:

  • Masashi Sugiyama;Hidemitsu Ogawa

  • Affiliations:

  • The author is with the Department of Computer Science, Tokyo Institute of Technology, Tokyo, 152--8552 Japan. E-mail: sugi@cs.titech.ac.jp,;The author is with Toray Engineering Co., Ltd., Otsu-shi, 520--2141 Japan. E-mail: hidemitsu-ogawa@kuramae.ne.jp

  • Venue:
  • IEICE - Transactions on Information and Systems
  • Year:
  • 2006

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Abstract

Kernel-based learning algorithms have been successfully applied in various problem domains, given appropriate kernel functions. In this paper, we discuss the problem of designing kernel functions for binary regression and show that using a bell-shaped cosine function as a kernel function is optimal in some sense. The rationale of this result is based on the Karhunen-Loève expansion, i.e., the optimal approximation to a set of functions is given by the principal component of the correlation operator of the functions.