Identifying causal relations among multi-variate time series is one of the
most important elements towards understanding the complex mechanisms underlying
the dynamic system. It provides critical tools for forecasting, simulations and
interventions in science and business analytics. In this paper, we proposed a
graph neural network approach with score-based method aiming at learning a
sparse DAG that captures the causal dependencies in a discretized time temporal
graph. We demonstrate methods with graph neural network significantly
outperformed other state-of-the-art methods with dynamic bayesian networking
inference. In addition, from the experiments, the structural causal model can
be more accurate than a linear SCM discovered by the methods such as Notears.

本文提出了一种基于得分的图神经网络方法，旨在学习离散时间时间图中捕捉因果依赖的稀疏 DAG，结果表明该方法较其他现有方法如动态贝叶斯网络推断等表现更好，得到的结构因果模型也比诸如 Notears 等方法发现的线性 SCM 更准确。

GDBN：一种动态贝叶斯网络的图神经网络方法

GDBN: a Graph Neural Network Approach to Dynamic Bayesian Network

We revisit the structure learning problem for dynamic Bayesian networks and
propose a method that simultaneously estimates contemporaneous (intra-slice)
and time-lagged (inter-slice) relationships between variables in a time-series.
Our approach is score-based, and revolves around minimizing a penalized loss
subject to an acyclicity constraint. To solve this problem, we leverage a
recent algebraic result characterizing the acyclicity constraint as a smooth
equality constraint. The resulting algorithm, which we call DYNOTEARS,
outperforms other methods on simulated data, especially in high-dimensions as
the number of variables increases. We also apply this algorithm on real
datasets from two different domains, finance and molecular biology, and analyze
the resulting output. Compared to state-of-the-art methods for learning dynamic
Bayesian networks, our method is both scalable and accurate on real data. The
simple formulation and competitive performance of our method make it suitable
for a variety of problems where one seeks to learn connections between
variables across time.

利用一种基于得分的方法来解决动态贝叶斯网络中的结构学习问题，该方法同时估计时间序列中变量之间的同步和时间滞后关系，并且在模拟数据和真实数据方面都具有较高的准确性和可扩展性，特别适用于需要学习变量间时间关系的多个问题。