Ridge Regression: Structure, Cross-Validation, and Sketching
Abstract
We study the following three fundamental problems about ridge regression: (1) what is the structure of the estimator? (2) how to correctly use cross-validation to choose the regularization parameter? and (3) how to accelerate computation without losing too much accuracy? We consider the three problems in a unified large-data linear model. We give a precise representation of ridge regression as a covariance matrix-dependent linear combination of the true parameter and the noise. We study the bias of $K$-fold cross-validation for choosing the regularization parameter, and propose a simple bias-correction. We analyze the accuracy of primal and dual sketching for ridge regression, showing they are surprisingly accurate. Our results are illustrated by simulations and by analyzing empirical data.
BibTeX
@inproceedings{
Liu2020Ridge,
title={Ridge Regression: Structure, Cross-Validation, and Sketching},
author={Sifan Liu and Edgar Dobriban},
booktitle={International Conference on Learning Representations},
year={2020},
url={https://openreview.net/forum?id=HklRwaEKwB}
}