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.

翻译：逻辑回归是概率分类中广泛应用的方法。然而，逻辑回归的有效性依赖于谨慎且计算成本相对较高的调参过程，特别是在正则化超参数选择和面对高维数据时更为显著。本文提出一种预验证岭回归模型，该模型在分类误差和对数损失方面与逻辑回归高度吻合（尤其适用于高维数据），同时计算效率显著提升，且除正则化外几乎无需调整超参数。我们通过最小化基于留一交叉验证估计误差的预验证预测集的对数损失来缩放模型系数。该方法利用岭回归模型拟合过程中已计算的数值，以极低的附加计算成本确定缩放参数。