Adaptive Sparse PLS for Logistic Regression

Since few years, data analysis struggles with statistical issues related to the "curse of high dimensionality". In this context, meaning when the number of considered variables is far larger than the number of observations in the sample, standard methods for classification are inappropriate, calling for the development of specific methodologies. We hereby propose a new approach suitable for classification in the high dimensional case. It uses sparse Partial Least Squares (sparse PLS) performing compression and variable selection combined to Ridge penalized logistic regression. In particular, we developed an adaptive version of sparse PLS to improve the dimension reduction process. Simulations show the accuracy of our method, compared with other state-of-the-art approaches. The particular combination of the iterative optimization of logistic regression and sparse PLS in our procedure appears to ensure convergence and stability concerning the hyper-parameters tuning, contrary to other methods processing classification with sparse PLS. Our results are confirmed on a real data set, using expression levels of thousands of genes concerning less than three hundred patients to predict the relapse for breast cancer. Eventually, our approach is implemented in the plsgenomics R-package.