Optimal Classification of Multivariate Functional Data using Deep Neural Networks

Oregon Convention Center 

We propose a new method, which we call Multivariate Functional Deep Neural Network (MFDNN), for classifying multivariate functional data across diverse domains. In contrast to existing approaches limited to Gaussian settings and uniform dimensional domains, MFDNN accommodates non-Gaussian data functions on varying dimensional domains (e.g., functions and images). The proposed classifier attains minimax optimality, substantiated by theoretical justifications. Demonstrations on simulated and real-world datasets underscore the versatility and efficacy of MFDNN. This approach complements recent advancements and extends previous results by exploring deep neural network procedures on multivariate functional data across different domains. Comparisons highlight the favorable performance of our method.

Functional data

Deep neural network

Classification

Multivariate functional data 

Section on Nonparametric Statistics