PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Lanczos Approximations for the Speedup of Kernel Partial Least Squares Regression
Nicole Krämer, Masashi Sugiyama and Mikio braun
In: AISTATS 2009, 16-18 Apr 2009, Clearwater Beach, USA.


The runtime for Kernel Partial Least Squares (KPLS) to compute the fit is quadratic in the number of examples. However, the necessity of obtaining sensitivity measures as degrees of freedom for model selection or confidence intervals for more detailed analysis requires cubic runtime, and thus constitutes a computational bottleneck in real-world data analysis. We propose a novel algorithm for KPLS which not only computes (a) the fit, but also (b) its approximate degrees of freedom and (c) error bars in quadratic runtime. The algorithm exploits a close connection between Kernel PLS and the Lanczos algorithm for approximating the eigenvalues of symmetric matrices, and uses this approximation to compute the trace of powers of the kernel matrix in quadratic runtime.

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EPrint Type:Conference or Workshop Item (Paper)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:4355
Deposited By:Nicole Krämer
Deposited On:13 March 2009