Roy Arkaprava, Borg Jana Schaich, Dunson David B
Department of Biostatistics, University of Florida, Gainnesville, FL 32611, USA.
Social Science Research Institute, Duke University, Durham, NC 27708-0251, USA.
J Mach Learn Res. 2021 Jan-Dec;22.
Many modern data sets require inference methods that can estimate the shared and individual-specific components of variability in collections of matrices that change over time. Promising methods have been developed to analyze these types of data in static cases, but only a few approaches are available for dynamic settings. To address this gap, we consider novel models and inference methods for pairs of matrices in which the columns correspond to multivariate observations at different time points. In order to characterize common and individual features, we propose a Bayesian dynamic factor modeling framework called Time Aligned Common and Individual Factor Analysis (TACIFA) that includes uncertainty in time alignment through an unknown warping function. We provide theoretical support for the proposed model, showing identifiability and posterior concentration. The structure enables efficient computation through a Hamiltonian Monte Carlo (HMC) algorithm. We show excellent performance in simulations, and illustrate the method through application to a social mimicry experiment.
许多现代数据集需要推理方法，这些方法能够估计随时间变化的矩阵集合中变异性的共享部分和个体特定部分。在静态情况下，已经开发出了有前景的方法来分析这类数据，但在动态环境中可用的方法却很少。为了弥补这一差距，我们考虑针对矩阵对的新型模型和推理方法，其中列对应于不同时间点的多变量观测值。为了刻画共同特征和个体特征，我们提出了一种贝叶斯动态因子建模框架，称为时间对齐共同和个体因子分析（TACIFA），该框架通过一个未知的扭曲函数纳入了时间对齐中的不确定性。我们为所提出的模型提供了理论支持，证明了其可识别性和后验集中性。该结构通过哈密顿蒙特卡罗（HMC）算法实现了高效计算。我们在模拟中展示了出色的性能，并通过应用于一个社会模仿实验来说明该方法。
