An elementary analysis of ridge regression with random design

TL;DR

This paper offers a simple, self-contained analysis of ridge regression's prediction error with random design, avoiding complex inequalities and using elementary mathematical tools.

Contribution

It introduces an elementary proof technique for understanding ridge regression prediction error, bypassing advanced covariance deviation inequalities.

Findings

Provides a short, self-contained proof of ridge regression error bounds.

Uses exchangeability, matrix perturbation, and operator convexity in analysis.

Simplifies understanding of ridge regression performance with random data.

Abstract

In this note, we provide an elementary analysis of the prediction error of ridge regression with random design. The proof is short and self-contained. In particular, it bypasses the use of Rudelson's deviation inequality for covariance matrices, through a combination of exchangeability arguments, matrix perturbation and operator convexity.