Short-term Temporal Dependency Detection under Heterogeneous Event Dynamic with Hawkes Processes
This addresses the challenge of distinguishing mutual interactions from intensity fluctuations in event data, with applications in neuroscience, though it is incremental as it modifies existing MLE approaches.
The paper tackled the problem of detecting short-term temporal dependencies in event sequences under heterogeneous intensity, showing that maximum likelihood estimation errors can be reduced by an order of magnitude using interacting Hawkes processes, and proposed a robust method that outperforms existing ones by notable margins in experiments.
Many event sequence data exhibit mutually exciting or inhibiting patterns. Reliable detection of such temporal dependency is crucial for scientific investigation. The de facto 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 direct or nonlinear transform of standard MHP intensity with constant baseline, inconsistent with real-world data. Under irregular and unknown heterogeneous intensity, capturing temporal dependency is hard as one struggles to distinguish the effect of mutual interaction from that of intensity fluctuation. In this paper, we address the short-term temporal dependency detection issue. We show the maximum likelihood estimation (MLE) for cross-impact from MHP has an error that can not be eliminated but may be reduced by order of magnitude, using heterogeneous intensity not of the target HP but of the interacting HP. Then we proposed a robust and computationally-efficient method modified from 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, no repeated observations). Extensive experiments on various datasets show that our method outperforms existing ones by notable margins, with highlighted novel applications in neuroscience.