Abstract

Multimodal data, where different types of data are collected from the same subjects, are fast emerging in a large variety of scientific applications. Factor analysis is commonly used in integrative analysis of multimodal data, and is particularly useful to overcome the curse of high dimensionality and high correlations. However, there is little work on statistical inference for factor analysis-based supervised modeling of multimodal data. In this article, we consider an integrative linear regression model that is built upon the latent factors extracted from multimodal data. We address three important questions: how to infer the significance of one data modality given the other modalities in the model; how to infer the significance of a combination of variables from one modality or across different modalities; and how to quantify the contribution, measured by the goodness of fit, of one data modality given the others. When answering each question, we explicitly characterize both the benefit and the extra cost of factor analysis. Those questions, to our knowledge, have not yet been addressed despite wide use of factor analysis in integrative multimodal analysis, and our proposal bridges an important gap. We study the empirical performance of our methods through simulations, and further illustrate with a multimodal neuroimaging analysis.

摘要

多模态数据，即从同一主题收集不同类型的数据，正迅速出现在各种科学应用中。因子分析常用于多模态数据的综合分析，对克服高维、高相关的诅咒特别有用。然而，关于基于因子分析的多模态数据监督建模的统计推断的工作很少。在本文中，我们考虑了一个综合线性回归模型，该模型建立在从多模态数据中提取的潜在因素之上。我们解决了三个重要问题：如何在给定模型中其他模式的情况下推断一种数据模式的重要性；如何从一种模态或不同模态中推断变量组合的重要性；以及如何量化贡献，由一种数据模式给定其他数据模式的拟合优度来衡量。在回答每个问题时，我们明确描述了因子分析的好处和额外成本。据我们所知，尽管在综合多模态分析中广泛使用因子分析，但这些问题尚未得到解决，而我们的提议弥合了一个重要的差距。我们通过模拟研究我们方法的经验性能，并通过多模态神经影像分析进一步说明。