Detecting Marginal and Conditional Independencies between Events and Learning Their Causal Structure

Abstract

Consider data given as a sequence of events, where each event has a timestamp and is of a specific type. We introduce a test for detecting marginal independence between events of two given types and for conditional independence when conditioned on one type. The independence test is based on comparing the delays between two successive events of the given types with the delays that would occur in the independent situation. We define a Causal Event Model (CEM) for modeling the event-generating mechanisms. The model is based on the assumption that events are either spontaneous or caused by others and that the causal mechanisms depend on the event type. The causal structure is defined by a directed graph which may contain cycles. Based on the independence test, an algorithm is designed to uncover the causal structure. The results show many similarities with Bayesian network theory, except that the order of events has to be taken into account. Experiments on simulated data show the accuracy of the test and the correctness of the learning algorithm when assumed that the spontaneous events are generated by a Poisson process.