具有延迟Granger因果关系的Hawkes过程
Hawkes Processes with Delayed Granger Causality
AI总结：
本文提出在多元Hawkes过程中显式建模延迟Granger因果效应，证明延迟参数可识别，并用VAE推断时间滞后后验分布，在合成与真实数据上验证了事件预测和滞后推断的有效性。
摘要：
我们旨在基于多元Hawkes过程显式建模延迟的Granger因果效应。这一想法源于一个事实：一个因果事件通常需要一段时间才能产生影响，而研究这一时间滞后本身具有意义。在所提出的模型下，我们首先证明了在温和条件下延迟参数的可识别性。我们进一步研究了一种复杂场景下的模型估计方法，在该场景中我们希望推断时间滞后的后验分布，并理解该分布如何在不同场景下变化。我们将时间滞后视为隐变量，并构建了一个Variational Auto-Encoder (VAE)算法来近似时间滞后的后验分布。通过在Hawkes过程中显式建模时间滞后，我们为模型增加了灵活性。推断出的时间滞后后验分布具有科学意义，并有助于追溯原始因果时间，从而支持根因分析。我们在合成数据和真实数据上实证评估了模型的事件预测和时间滞后推断准确性，取得了有前景的结果。
英文摘要：
We aim to explicitly model the delayed Granger causal effects based on multivariate Hawkes processes. The idea is inspired by the fact that a causal event usually takes some time to exert an effect. Studying this time lag itself is of interest. Given the proposed model, we first prove the identifiability of the delay parameter under mild conditions. We further investigate a model estimation method under a complex setting, where we want to infer the posterior distribution of the time lags and understand how this distribution varies across different scenarios. We treat the time lags as latent variables and formulate a Variational Auto-Encoder (VAE) algorithm to approximate the posterior distribution of the time lags. By explicitly modeling the time lags in Hawkes processes, we add flexibility to the model. The inferred time-lag posterior distributions are of scientific meaning and help trace the original causal time that supports the root cause analysis. We empirically evaluate our model's event prediction and time-lag inference accuracy on synthetic and real data, achieving promising results.
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