Generalized Liquid Association Analysis for Multimodal Data Integration

TL;DR

This paper introduces a novel generalized liquid association analysis method for studying complex three-way associations in high-dimensional multimodal data, with theoretical guarantees and applications in neuroimaging for Alzheimer's disease.

Contribution

It extends liquid association to high-dimensional, multivariate settings, formulates a population dimension reduction model, and develops a tensor-based estimation algorithm with theoretical guarantees.

Findings

Effective in high-dimensional simulations

Successfully applied to neuroimaging data for Alzheimer's

Provides non-asymptotic error bounds and consistency

Abstract

Multimodal data are now prevailing in scientific research. A central question in multimodal integrative analysis is to understand how two data modalities associate and interact with each other given another modality or demographic variables. The problem can be formulated as studying the associations among three sets of random variables, a question that has received relatively less attention in the literature. In this article, we propose a novel generalized liquid association analysis method, which offers a new and unique angle to this important class of problems of studying three-way associations. We extend the notion of liquid association of \citet{li2002LA} from the univariate setting to the sparse, multivariate, and high-dimensional setting. We establish a population dimension reduction model, transform the problem to sparse Tucker decomposition of a three-way tensor, and develop a higher-order orthogonal iteration algorithm for parameter estimation. We derive the non-asymptotic error bound and asymptotic consistency of the proposed estimator, while allowing the variable dimensions to be larger than and diverge with the sample size. We demonstrate the efficacy of the method through both simulations and a multimodal neuroimaging application for Alzheimer's disease research.