Year: 2022
Type: article
Abstract: Multimodal data are now prevailing in scientific research. One of the central questions 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 Li (2002) 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.
Authors: Lexin Li, Jing Zeng, Xin Zhang
Institutions: University of California, Berkeley, Florida State University
Language: English
Subfield: Computational Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: CIF: Small: Cluster Analysis for Highly-correlated, Heavy-tailed, and Higher-order Data, Multimodal Integrative Dimension Reduction and Statistical Modeling with Applications to Temporomandibular Joint (TMJ) Morphometry and Biomechanics, New Statistical Methods for Multicenter Multimodal Longitudinal Neuroimaging Analysis, Tensor and Subspace Learning Methods with Applications to Medical Imaging, Mechanisms of Alzheimer's Disease Progression in the Aging Brain, CIF: Small: Collaborative Research: Graphical Modeling of Multivariate Functional Data, Neural and Biochemical Mechanisms of Cognitive Aging
OpenAlex ID: W3047942544