A1927
Title: Graphical modeling of multivariate Cox process
Authors: Jiehuan Sun - University of Illinois at Chicago (United States)
Tianxi Cai - Harvard School of Public Health (United States)
Lexin Li - University of California Berkeley (United States)
Kuang-Yao Lee - Temple University (United States) [presenting]
Abstract: A central question in the analysis of multivariate temporal point process data that are simultaneously recorded for multiple subjects is to model the inter-dependency among different point processes. A novel hidden point process graphical model is proposed to address this question. Built on a log Gaussian multivariate Cox process, the model hinges on random intensity functions to wholly determine the point process distribution, and the conditional dependency among the intensity functions characterizes the network's edges. The approach distinguishes itself from most existing vectorial or functional graphical models by dealing with entirely unobserved and non-Hilbertian random intensity functions. A precision operator is introduced, and a one-to-one correspondence between the zero element of this operator and the conditional independence of the intensity function is established. A hard thresholding-based estimation procedure is developed, and its asymptotic consistency is established. The empirical performance of the method is investigated through both simulations and the analysis of electronic health records (EHR) data, which infers relatedness of different EHR encounters and reconstructs the healthcare knowledge network for patients with type 2 diabetes.
