Statistically and Computationally Efficient Variance Estimator for Kernel Ridge Regression

TL;DR

This paper introduces a random projection-based variance estimator for kernel ridge regression that is both statistically consistent and computationally efficient, applicable to various kernels including Gaussian and cubic splines.

Contribution

The paper presents a novel variance estimation method using random projections that improves efficiency while maintaining consistency across multiple kernel types.

Findings

Estimator is statistically consistent and computationally efficient.

Method is optimal for a broad class of kernels including Gaussian and cubic splines.

Simulation results support theoretical claims.

Abstract

In this paper, we propose a random projection approach to estimate variance in kernel ridge regression. Our approach leads to a consistent estimator of the true variance, while being computationally more efficient. Our variance estimator is optimal for a large family of kernels, including cubic splines and Gaussian kernels. Simulation analysis is conducted to support our theory.