Detection of Short-Term Temporal Dependencies in Hawkes Processes with Heterogeneous Background Dynamics

Abstract

Many kinds of simultaneously-observed event sequences exhibit mutually exciting or inhibiting patterns. Reliable detection of such temporal dependencies is crucial for scientific investigation. A common model is the Multivariate Hawkes Process (MHP), whose impact function naturally encodes a causal structure in Granger causality. However, the vast majority of existing methods use a transformed standard MHP intensity with a constant baseline, which may be inconsistent with real-world data. On the other hand, modeling irregular and unknown background dynamics directly is a challenge, as one struggles to distinguish the effect of mutual interaction from that of fluctuations in background dynamics. In this paper, we address the short-term temporal dependency detection issue. We show that maximum likelihood estimation (MLE) for cross-impact from MHP has an error that can not be eliminated, but may be reduced by an order of magnitude using a heterogeneous intensity not for the target HP but for the interacting HP. Then we propose a robust and computationally-efficient modification of MLE that does not rely on the prior estimation of the heterogeneous intensity and is thus applicable in a data-limited regime (e.g., few-shot, unrepeated observations). Extensive experiments on various datasets show that our method outperforms existing ones by notable margins, with highlighted novel applications in neuroscience.