Nonparametric and high-dimensional functional graphical models

TL;DR

This paper introduces a flexible nonparametric approach for constructing high-dimensional functional graphical models using additive forms and functional principal components, with proven statistical guarantees and demonstrated empirical effectiveness.

Contribution

It relaxes linearity assumptions in functional graphical models by employing additive forms and group lasso, providing theoretical guarantees and practical algorithms.

Findings

Establishes statistical consistency for the proposed estimators.

Demonstrates superior empirical performance in simulations.

Applies method successfully to real data.

Abstract

We consider the problem of constructing nonparametric undirected graphical models for high-dimensional functional data. Most existing statistical methods in this context assume either a Gaussian distribution on the vertices or linear conditional means. In this article we provide a more flexible model which relaxes the linearity assumption by replacing it by an arbitrary additive form. The use of functional principal components offers an estimation strategy that uses a group lasso penalty to estimate the relevant edges of the graph. We establish statistical guarantees for the resulting estimators, which can be used to prove consistency if the dimension and the number of functional principal components diverge to infinity with the sample size. We also investigate the empirical performance of our method through simulation studies and a real data application.