Variable selection for multivariate functional data via conditional correlation learning

Variable selection involves selecting truly important predictors from p-dimensional multivariate functional predictors in functional predictive models. In this paper, a variable selection method is designed for scalar-on-function predictions entangled with nonlinear joint associations among scalar response and multiple functional predictors. First, a nonparametric functional nonlinear conditional correlation coefficient, namely, the FunNCC coefficient, is proposed to measure complex dependencies, including the nonmonotonic marginal dependence, along with the conditional associations of redundancy, complement, and interaction. Then, a model-free feature ordering and selection method is designed, where the FunNCC is utilized to rank relevance, enabling the selection of a subset of predictors with the strongest joint dependence. Since this method allows for quantitatively evaluating the contributions of predictors in explaining responses, it achieves moderate model interpretability. Finally, extensive simulation studies and two real-data cases involving air pollution regression and hand gesture recognition are conducted to evaluate the finite sample performance of the proposed method, and the results show that the proposed FunNCC and variable selection methods outperform state-of-the-art baselines.