Learning Functional Graphs with Nonlinear Sufficient Dimension Reduction

TL;DR

This paper introduces a nonparametric functional graphical model using functional sufficient dimension reduction, improving estimation accuracy and relaxing Gaussian assumptions while preserving probabilistic conditional independence.

Contribution

It presents a novel nonparametric approach based on functional sufficient dimension reduction that avoids the curse of dimensionality and maintains probabilistic conditional independence.

Findings

Demonstrates improved estimation accuracy through simulations.

Shows advantages on f-MRI dataset analysis.

Relaxes Gaussian assumptions in functional graphical models.

Abstract

Functional graphical models have undergone extensive development during the recent years, leading to a variety models such as the functional Gaussian graphical model, the functional copula Gaussian graphical model, the functional Bayesian graphical model, the nonparametric functional additive graphical model, and the conditional functional graphical model. These models rely either on some parametric form of distributions on random functions, or on additive conditional independence, a criterion that is different from probabilistic conditional independence. In this paper we introduce a nonparametric functional graphical model based on functional sufficient dimension reduction. Our method not only relaxes the Gaussian or copula Gaussian assumptions, but also enhances estimation accuracy by avoiding the ``curse of dimensionality''. Moreover, it retains the probabilistic conditional independence as the criterion to determine the absence of edges. By doing simulation study and analysis of the f-MRI dataset, we demonstrate the advantages of our method.