Robust penalized logistic regression with truncated loss functions

The penalized logistic regression (PLR) is a powerful statistical tool for classification. It has been commonly used in many practical problems. Despite its success, since the loss function of the PLR is unbounded, resulting classifiers can be sensitive to outliers. To build more robust classifiers, we propose the robust PLR (RPLR) which uses truncated logistic loss functions, and suggest three schemes to estimate conditional class probabilities. Connections of the RPLR with some other existing work on robust logistic regression have been discussed. Our theoretical results indicate that the RPLR is Fisher consistent and more robust to outliers. Moreover, we develop estimated generalized approximate cross validation (EGACV) for the tuning parameter selection. Through numerical examples, we demonstrate that truncating the loss function indeed yields better performance in terms of classification accuracy and class probability estimation.