Evolutionary kernel density regression

Abstract

The Nadaraya–Watson estimator, also known as kernel regression, is a density-based regression technique. It weights output values with the relative densities in input space. The density is measured with kernel functions that depend on bandwidth parameters. In this work we present an evolutionary bandwidth optimizer for kernel regression. The approach is based on a robust loss function, leave-one-out cross-validation, and the CMSA-ES as optimization engine. A variant with local parameterized Nadaraya–Watson models enhances the approach, and allows the adaptation of the model to local data space characteristics. The unsupervised counterpart of kernel regression is an approach to learn principal manifolds. The learning problem of unsupervised kernel regression (UKR) is based on optimizing the latent variables, which is a multimodal problem with many local optima. We propose an evolutionary framework for optimization of UKR based on scaling of initial local linear embedding solutions, and minimization of the cross-validation error. Both methods are analyzed experimentally.