多模态数据集成的广义液体关联分析
Generalized Liquid Association Analysis for Multimodal Data Integration
摘要：
多模态数据现在在科学研究中很流行。多模态综合分析中的一个核心问题是了解两种数据模态如何在给定另一种模态或人口统计变量的情况下相互关联和相互作用。该问题可以表述为研究三组随机变量之间的关联，这是一个在文献中受到相对较少关注的问题。在本文中，我们提出了一种新的广义液体关联分析方法，这提供了一个新的和独特的角度来研究这类重要的问题的三向关联。我们将\citet{li2002LA}的液体关联的概念从单变量设置扩展到稀疏、多变量和高维设置。建立了种群降维模型，将问题转化为三向张量的稀疏Tucker分解，并提出了一种高阶正交迭代算法进行参数估计.在变量维数大于样本量且随样本量的变化而发散的情况下，我们得到了估计量的非渐近误差界和渐近相合性。我们证明了该方法的有效性，通过模拟和多模态神经成像应用于阿尔茨海默病的研究。
英文摘要：
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.
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