Prevalidated ridge regression is a highly-efficient drop-in replacement
  for logistic regression for high-dimensional data
Angus Dempster Geoffrey I. Webb Daniel F. Schmidt
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 closely matches logistic
regression in terms of classification error and log-loss, particularly for
high-dimensional data, while being significantly more computationally efficient
and having effectively no hyperparameters beyond regularisation. 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
computational expense.