Learning Point Process Network Models with Timing Uncertainty

• Activity Number: 545 - Statistical Advances in Learning Large-Scale Networks from Massive Data Sets
• Type: Topic Contributed
• Date/Time: Thursday, August 11, 2022 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Yao Xie* and Xiuyuan Cheng and Tingnan Gong
• Companies: Georgia Institute of Technology and Duke University and Georgia Institute of Technology
• Keywords: Point processes; Discrete events data; Low-rank models; Influence function estimation; Low-rank ; Estimation algorithm

Abstract

Point processes over networks are becoming a popular topic in statistics and machine learning. The discrete nature of events data observed in social networks, crime data, medical records, etc., poses new challenges to statistical modeling and computation. Each discrete events data point typically consists of the time, location (node index), and marks (additional information about the events). The purpose is to recover the underlying influence networks, which capture the complex interdependence between the event observations. We consider the situation when the timing of each event is uncertain, an important aspect of such data that has been largely ignored in previous models. For instance, in medical records, the lab test results come out with imprecise timing (they are merely the time of lab results released rather than the actual precise time of patient conditions). Our work proposes a new model to tackle the timing uncertainty and present efficient learning algorithms based on optimization, utilizing the underlying low-rank structure of the network influence kernels. We demonstrate the good performance of the proposed model and algorithm using synthetic and real data.