Sparse regularization for multivariate linear models for functional data

The Global COE Program Mathematics-for-Industry Education & Research HubグローバルCOEプログラム「マス･フォア･インダストリ教育研究拠点」We consider the variable selection problem in multivariate linear models where the predictors are given as functions and the responses are scalars, with the help of sparse regularization. Observations corresponding to the predictors are supposed to be measured repeatedly at discrete time points, and then they are treated as smooth functional data. Parameters included in the functional multivariate linear model are estimated by the penalized least squared method with the l_1/l_2 type penalty. We construct a blockwise coordinate descent algorithm for deriving the estimates of the functional multivariate linear model. A tuning parameter which control the degree of the regularization is decided by information criteria. In order to investigate the effectiveness of the proposed method we apply it to the analysis of simulated data and real data