论文标题
多模式数据整合的通用液体关联分析
Generalized Liquid Association Analysis for Multimodal Data Integration
论文作者
论文摘要
现在，多模式数据在科学研究中占上风。多模式集成分析中的一个核心问题是了解两种数据模式如何相关并彼此相互作用给定另一个模态或人口统计学变量。该问题可以被提出为研究三组随机变量之间的关联，这个问题在文献中受到了相对较少的关注。在本文中，我们提出了一种新型的广义液体结合分析方法，该方法为研究三向关联的这一重要类别提供了一个新的独特角度。我们将\ citet {li2002la}的液体关联概念从单变量设置扩展到稀疏，多变量和高维设置。我们建立了种群减少模型，将问题转化为三向张量的稀疏塔克分解，并为参数估计开发高阶正交迭代算法。我们得出所提出的估计量的非反应误差结合和渐近一致性，同时允许可变尺寸大于样本量的差异和差异。我们通过模拟和对阿尔茨海默氏病研究的多模式神经成像应用的疗效证明了该方法的功效。
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.
