Latent Multimodal Functional Graphical Model Estimation

TL;DR

This paper introduces a new statistical framework for estimating latent connectivity graphs from multimodal functional data, with theoretical guarantees and applications to brain imaging.

Contribution

It develops a novel integrative method that models data generation and estimates transformation operators and latent graphs simultaneously, extending partial correlation operators to functional data.

Findings

Estimator converges to a stationary point with quantifiable error.

Successfully recovers latent graphs under mild conditions.

Demonstrates benefits of joint estimation through simulations and brain imaging data.

Abstract

Joint multimodal functional data acquisition, where functional data from multiple modes are measured simultaneously from the same subject, has emerged as an exciting modern approach enabled by recent engineering breakthroughs in the neurological and biological sciences. One prominent motivation to acquire such data is to enable new discoveries of the underlying connectivity by combining multimodal signals. Despite the scientific interest, there remains a gap in principled statistical methods for estimating the graph underlying multimodal functional data. To this end, we propose a new integrative framework that models the data generation process and identifies operators mapping from the observation space to the latent space. We then develop an estimator that simultaneously estimates the transformation operators and the latent graph. This estimator is based on the partial correlation operator, which we rigorously extend from the multivariate to the functional setting. Our procedure is provably efficient, with the estimator converging to a stationary point with quantifiable statistical error. Furthermore, we show recovery of the latent graph under mild conditions. Our work is applied to analyze simultaneously acquired multimodal brain imaging data where the graph indicates functional connectivity of the brain. We present simulation and empirical results that support the benefits of joint estimation.