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：多模态功能数据联合采集（即从同一受试者同时测量多种模态的功能数据）已成为神经和生物科学领域工程突破催生的新兴现代方法。此类数据采集的核心动机在于通过融合多模态信号揭示潜在连接模式的新发现。尽管具有重要科学意义，但目前仍缺乏用于估计多模态功能数据底层图结构的严谨统计方法。为此，我们提出一个新的整合框架：首先对数据生成过程进行建模，识别从观测空间到隐空间的映射算子，进而开发可同时估计变换算子与隐图的估计器。该估计基于偏相关算子，我们将其从多元场景严格推广至函数型场景。所提方法具有可证明的高效性：估计量可收敛至具有可量化统计误差的驻点。此外，我们证明了在温和条件下可恢复隐图。本工作应用于分析同步采集的多模态脑成像数据，其中图结构表征脑功能连接。仿真与实证结果均支持联合估计的优越性。