Learning causal structure among event types from discrete-time event
sequences is a particularly important but challenging task. Existing methods,
such as the multivariate Hawkes processes based methods, mostly boil down to
learning the so-called Granger causality which assumes that the cause event
happens strictly prior to its effect event. Such an assumption is often
untenable beyond applications, especially when dealing with discrete-time event
sequences in low-resolution; and typical discrete Hawkes processes mainly
suffer from identifiability issues raised by the instantaneous effect, i.e.,
the causal relationship that occurred simultaneously due to the low-resolution
data will not be captured by Granger causality. In this work, we propose
Structure Hawkes Processes (SHPs) that leverage the instantaneous effect for
learning the causal structure among events type in discrete-time event
sequence. The proposed method is featured with the minorization-maximization of
the likelihood function and a sparse optimization scheme. Theoretical results
show that the instantaneous effect is a blessing rather than a curse, and the
causal structure is identifiable under the existence of the instantaneous
effect. Experiments on synthetic and real-world data verify the effectiveness
of the proposed method.

本文提出了 Structure Hawkes Processes (SHPs) 用于从离散时间事件序列中学习事件类型之间的因果结构，利用瞬时效应解决因果关系同步发生的识别问题，并通过理论和实验结果验证了该方法的有效性。

用结构霍克斯过程从离散时间事件序列中学习因果结构

Structural Hawkes Processes for Learning Causal Structure from  Discrete-Time Event Sequences

Gaussian processes models are widely adopted for
nonparameteric/semi-parametric modeling. Identifiability issues occur when the
mean model contains polynomials with unknown coefficients. Though resulting
prediction is unaffected, this leads to poor estimation of the coefficients in
the mean model, and thus the estimated mean model loses interpretability. This
paper introduces a new Gaussian process model whose stochastic part is
orthogonal to the mean part to address this issue. This paper also discusses
applications to multi-fidelity simulations using data examples.

本文提出一种新的高斯过程模型，其随机部分与均值部分正交，以解决均值模型包含具有未知系数的多项式时出现的可识别性问题，并探讨其在多保真度模拟中的应用。