Logistic regression with image covariates via the combination of L1 and Sobolev regularizations

The use of image covariates to build a classification model has lots of impact in various fields, such as computer science, medicine, and so on. The aim of this paper is to develop an estimation method for logistic regression model with image covariates. We propose a novel regularized estimation approach, where the regularization is a combination of L1 regularization and Sobolev norm regularization. The L1 penalty can perform variable selection, while the Sobolev norm penalty can capture the shape edges information of image data. We develop an efficient algorithm for the optimization problem. We also establish a nonasymptotic error bound on parameter estimation. Simulated studies and a real data application demonstrate that our proposed method performs very well.