Latent Multimodal Functional Graphical Model Estimation

• 成果类型: Article
• 署名作者: Tsai, Katherine; Zhao, Boxin; Koyejo, Sanmi; Kolar, Mladen
• 署名单位: University of Illinois System; University of Illinois Urbana-Champaign; University of Chicago; Stanford University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2023.2252142
• 发表日期: 2024
• 页码: 2217-2229
• 关键词: integrated analysis; brain networks; joint; connectivity; regression; selection

摘要

Joint multimodal functional data acquisition, where functional data from multiple modes are measured simultaneously from the same subject, has emerged as an exciting modern approach enabled by recent engineering breakthroughs in the neurological and biological sciences. One prominent motivation to acquire such data is to enable new discoveries of the underlying connectivity by combining multimodal signals. Despite the scientific interest, there remains a gap in principled statistical methods for estimating the graph underlying multimodal functional data. To this end, we propose a new integrative framework that models the data generation process and identifies operators mapping from the observation space to the latent space. We then develop an estimator that simultaneously estimates the transformation operators and the latent graph. This estimator is based on the partial correlation operator, which we rigorously extend from the multivariate to the functional setting. Our procedure is provably efficient, with the estimator converging to a stationary point with quantifiable statistical error. Furthermore, we show recovery of the latent graph under mild conditions. Our work is applied to analyze simultaneously acquired multimodal brain imaging data where the graph indicates functional connectivity of the brain. We present simulation and empirical results that support the benefits of joint estimation. Supplementary materials for this article are available online including a standardized description of the materials available for reproducing the work.