Lanczos Approximations for the Speedup of Kernel Partial Least Squares Regression

Details Lanczos Approximations for the Speedup of Kernel Partial Least Squares Regression Lanczos Approximations for the Speedup of Kernel Partial Least Squares Regression

2009-02-19

arxiv.org/abs/0902.3347v1

JMLR Workshop and Conference Proceedings 5 (AISTATS 2009), p 288-295, 2009

Statistics

Machine Learning

to appear in Proceedings of the 12th International Conference on Artificial Intelligence and Statistics (AISTATS 09)

Scientific paper

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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