Prevalidated Ridge Regression is a Highly-Efficient Drop-In Replacement for Logistic Regression for High-dimensional Data

Abstract Logistic regression is a ubiquitous method for probabilistic classification. However, the effectiveness of logistic regression depends upon careful and relatively computationally expensive tuning, especially for the regularisation hyperparameter, and especially in the context of high-dimensional data. We present a prevalidated ridge regression model that in practice closely matches logistic regression in terms of 0–1 loss and log-loss, particularly for high-dimensional data, while being significantly more computationally efficient and having no user-tuned hyperparameters (the regularisation hyperparameter is learned automatically as part of the fitting process). We scale the coefficients of the model so as to minimise log-loss for a set of prevalidated predictions derived from the estimated leave-one-out cross-validation error. This exploits quantities already computed in the course of fitting the ridge regression model in order to find the scaling parameter with nominal additional computation.