Regularized logistic regression without a penalty term: An application to cancer classification with microarray data

Regularized logistic regression is a useful classification method for problems with few samples and a huge number of variables. This regression needs to determine the regularization term, which amounts to searching for the optimal penalty parameter and the norm of the regression coefficient vector. This paper presents a new regularized logistic regression method based on the evolution of the regression coefficients using estimation of distribution algorithms. The main novelty is that it avoids the determination of the regularization term. The chosen simulation method of new coefficients at each step of the evolutionary process guarantees their shrinkage as an intrinsic regularization. Experimental results comparing the behavior of the proposed method with Lasso and ridge logistic regression in three cancer classification problems with microarray data are shown. (C) 2010 Elsevier Ltd. All rights reserved.