题目：Learning network-structured dependence from non-stationary multivariate point process data

报告人：张春明 教授（美国威斯康星大学麦迪逊分校）

摘要：Understanding sparse network dependencies among nodes from multivariate point process data has broad applications in information transmission, social science, and computational neuroscience. This paper introduces new continuous-time stochastic models for conditional intensity functions, revealing network structures within non-stationary multivariate counting processes. Our model's stochastic mechanism is crucial for inferring graph parameters relevant to structure recovery, distinct from commonly used processes like the Poisson, Hawkes, queuing, and piecewise deterministic Markov processes. This leads to proposing a novel marked point process for intensity discontinuities. We derive concise representations of their conditional distributions and demonstrate cyclicity of the counting processes driven by recurrence time points. These theoretical properties enable us to establish statistical consistency and convergence properties for proposed penalized M-estimators in graph parameters under mild regularity conditions. Simulation evaluations showcase the method's computational simplicity and improved estimation accuracy compared to existing approaches. Real neuron spike train recordings are analyzed to infer connectivity in neuronal networks.

报告人简介：Chunming Zhang is a Professor in the Department of Statistics at the University of Wisconsin-Madison. She earned her Ph.D. in Statistics from the University of North Carolina at Chapel Hill in 2000. Her research interests encompass statistical methods in computational neuroscience, biostatistics, and financial econometrics, along with the analysis of imaging, spatial, and temporal data. Additionally, her work delves into multiple hypotheses testing, large-scale simultaneous inference, dimension reduction, high-dimensional inference, non-parametric and semi-parametric modeling and inference, functional and longitudinal data analysis, and robust statistics. She is an elected Fellow of the Institute of Mathematical Statistics (IMS) and the American Statistical Association (ASA), and a recipient of the IMS Medallion Award and Lecture in 2024. Dr. Zhang serves on the editorial boards of Annals of Statistics and the Journal of the American Statistical Association.

报告时间：2024年6月24日(周一)上午 10:00-11:00

报告地点：教二楼913

联系人：周洁