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The runtime for Kernel Partial Least Squares (KPLS) to compute the fit isquadratic in the number of examples. However, the necessity of obtainingsensitivity measures as degrees of freedom for model selection or confidenceintervals for more detailed analysis requires cubic runtime, and thusconstitutes a computational bottleneck in real-world data analysis. We proposea 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. Thealgorithm exploits a close connection between Kernel PLS and the Lanczosalgorithm for approximating the eigenvalues of symmetric matrices, and usesthis approximation to compute the trace of powers of the kernel matrix inquadratic runtime.

Lanczos Approximations for the Speedup of Kernel Partial Least Squares Regression