Gradient-based kernel dimension reduction for supervised learning

TL;DR

This paper introduces a kernel-based gradient method for supervised linear dimension reduction, effectively identifying important input directions with simple computation and broad applicability.

Contribution

It presents a novel kernel approach using gradient estimators for dimension reduction that requires minimal assumptions and is computationally efficient.

Findings

Successfully identifies effective directions in input space

Demonstrates computational efficiency over existing methods

Applicable to diverse data distributions and variable types

Abstract

This paper proposes a novel kernel approach to linear dimension reduction for supervised learning. The purpose of the dimension reduction is to find directions in the input space to explain the output as effectively as possible. The proposed method uses an estimator for the gradient of regression function, based on the covariance operators on reproducing kernel Hilbert spaces. In comparison with other existing methods, the proposed one has wide applicability without strong assumptions on the distributions or the type of variables, and uses computationally simple eigendecomposition. Experimental results show that the proposed method successfully finds the effective directions with efficient computation.