Integrative Factor Regression and Its Inference for Multimodal Data Analysis

• Activity Number: 402 - Integrative Inference with Data from Multiple Sources: Challenges and New Developments
• Type: Topic-Contributed
• Date/Time: Thursday, August 12, 2021 : 2:00 PM to 3:50 PM
• Sponsor: ENAR
• Author(s): Quefeng Li* and Lexin Li
• Companies: University of North Carolina at Chapel Hill and University of California, Berkeley
• Keywords: Date integration; Dimension reduction; Factor analysis; High-dimensional inference

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.