  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.
