Kernel partial least squares for stationary data

TL;DR

This paper analyzes the convergence of kernel partial least squares for stationary dependent data, showing how dependence affects rates and demonstrating high predictive power in protein dynamics.

Contribution

It provides probabilistic convergence rates for kernel partial least squares with stationary data, including the impact of long-range dependence, supported by theoretical and simulation results.

Findings

Long-range dependence slows convergence rates.

Kernel partial least squares has high predictive power in protein dynamics.

Convergence rates depend on source and effective dimensionality conditions.

Abstract

We consider the kernel partial least squares algorithm for non-parametric regression with stationary dependent data. Probabilistic convergence rates of the kernel partial least squares estimator to the true regression function are established under a source and an effective dimensionality condition. It is shown both theoretically and in simulations that long range dependence results in slower convergence rates. A protein dynamics example shows high predictive power of kernel partial least squares.