Learning Granger Causality for Non-stationary Hawkes Processes

Abstract Learning causal relationships from point processes is of great significance to various real-world applications, e.g., user behaviour study, fault diagnosis. Though several methods have been proposed for this problem, the existing methods rely on the stationarity assumption of the point process. Such a stationarity assumption is usually violated due to the influence of latent confounders of the point processes. Based on the study of various real-world point processes, we find that a non-stationary Hawkes process is usually a mixture of several non-overlap and stationary processes. Thus, we propose an adaptive pattern based method for the non-stationary Hawkes Process (named GC-nsHP). In the proposed method, the following two steps are iteratively employed to adaptively partition the non-stationary processes and learn the causal structure for the partitioned sub-processes: 1) we use a dynamic-programming-based algorithm to partition the non-stationary long process into several stationary sub-processes; 2) we use an expectation-maximization-based algorithm (EM) to learn the Granger Causality of each pattern. Experiments on both synthetic and real-world datasets not only show the effectiveness on the non-stationary point process, but also discover some interesting results on the IPTV data set.