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.

翻译：联合多模态功能数据采集（即同时从同一受试者采集多种模态的功能数据）已成为神经科学与生物科学领域工程突破所催生的前沿现代方法。此类数据采集的核心价值在于，通过整合多模态信号能够揭示潜在的功能连接模式。尽管具有重要科学价值，但目前仍缺乏用于估计多模态功能数据潜在图结构的规范性统计方法。为此，我们提出一种新型整合框架：该框架可建模数据生成过程，并识别从观测空间到潜变量空间的映射算子。我们进一步开发了同步估计变换算子与潜变量图的估计器，该估计器基于偏相关算子构建，我们将其从多元场景严格扩展至函数型场景。我们的方法具有可证明的高效性——估计器能收敛至定量统计误差可控的驻点。此外，我们证明了在温和条件下潜变量图的可恢复性。本研究应用于分析同步采集的多模态脑成像数据，其中图结构表征大脑功能连接。仿真与实证结果均支持联合估计的优越性。