Double fused Lasso regularized regression with both matrix and vector valued predictors

Abstract

In many contemporary applications such as longitudinal studies, neuroimaging or civil engineering, a dataset can contain high dimensional measurements on both matrix-valued and vector-valued variables. Such structure demands statistical tools that can extract information from both types of measurements. In this paper, we propose a double fused Lasso regularized method to handle both matrix-valued and vector-valued predictors under the context of linear regression and logistic regression. An efficient and scalable sGS-ADMM (symmetric Gauss-Seidel based alternating direction method of multipliers) algorithm is derived to obtain the estimator. Global convergence and the Q-linear rate of convergence for the algorithm is established. Consistency of the double fused Lasso estimators holds under mild conditions. Numerical experiments and examples show that the double fused Lasso estimators achieve efficient gains in estimation and better prediction performance compared to existing estimators.