Point-to-Point Process Models for Spatio-temporal Networks

University Of California-Davis, Davis CA

Investigators

Abstract

Real-time data collection systems allow researchers to monitor and analyze billions of streaming events. Transportation data often consists of trips, the streaming events, from one location to another. This forms a spatio-temporal network, in which the connections occur between locations. Such spatio-temporal networks are prevalent in econometrics, transportation and infrastructure applications, internet security data, neurology data, and epidemiological networks. The majority of statistical methodology for modelling networks assumes that a single static network is observed. In contrast, this setting presumes that each network connection is an event that happens at specific times, so one must adapt network models to accommodate this novel data modality. Predicting these events is particularly challenging because the event rate can depend on time and the two associated spatial locations, resulting in an explosion of the number of parameters. One can make assumptions, which will depend on the application, that reduce the effective number of parameters in a data adaptive fashion. For example, this research will study spatial community structure in transportation planning applications, temporal trends in internet security data, and complex dependencies between events for financial transactions. This will require a broad probabilistic framework that can accommodate such assumptions, and computationally tractable statistical methodology for predicting connections in spatio-temporal networks. It is natural to model these edge events in such dynamic networks as point processes with conditional intensities, and the resulting model for the entire system will be called a point-to-point process. This novel approach has the advantage of modelling the network in continuous time, so that natural likelihood-based procedures can work directly on transactional dataframes where each row corresponds to an edge event. The research focus is divided into three topics and areas of application. First, for transportation networks, it is natural to segment spatial locations using low rank methods, the study of which will require adapting the stochastic block model to the point-to-point process framework. Secondly, detecting and localizing temporal changepoints in dynamic networks can be accomplished by employing group fusion penalties and trend filtering. Thirdly, for financial transaction networks and epidemiological networks, complex dependencies can be examined by adapting Hawkes models to the point-to-point process framework. The research will examine the theory of these statistical problems and develop computationally tractable algorithms.