Heterogeneous Functional Regression for Subgroup Analysis

With ever increasing number of features of modern datasets, data heterogeneity is gradually becoming the norm rather than the exception. Whereas classical regressions usually assume all the samples follow a common model, it becomes imperative to identify the heterogeneous relationship in different subsamples. In this article, we propose a new approach to model heterogeneous functional regression relations. We target at the association between a response and a predictor, whose relationship can vary across underlying subgroups and is modeled as an unknown functional of an auxiliary predictor. We introduce a procedure which performs simultaneous parameter estimation and subgroup identification through a fusion type group-wise penalization. We establish the statistical guarantees in terms of non-asymptotic convergence of the parameter estimation. We also establish the oracle property and asymptotic normality of the estimators. We carry out intensive simulations, and illustrate with a new dataset from an Alzheimer's disease study. Supplementary materials for this article are available online.