Graph neural networks (GNNs) have been widely applied in multi-variate
time-series forecasting (MTSF) tasks because of their capability in capturing
the correlations among different time-series. These graph-based learning
approaches improve the forecasting performance by discovering and understanding
the underlying graph structures, which represent the data correlation. When the
explicit prior graph structures are not available, most existing works cannot
guarantee the sparsity of the generated graphs that make the overall model
computational expensive and less interpretable. In this work, we propose a
decoupled training method, which includes a graph generating module and a GNNs
forecasting module. First, we use Graphical Lasso (or GraphLASSO) to directly
exploit the sparsity pattern from data to build graph structures in both static
and time-varying cases. Second, we fit these graph structures and the input
data into a Graph Convolutional Recurrent Network (GCRN) to train a forecasting
model. The experimental results on three real-world datasets show that our
novel approach has competitive performance against existing state-of-the-art
forecasting algorithms while providing sparse, meaningful and explainable graph
structures and reducing training time by approximately 40%. Our PyTorch
implementation is publicly available at this https URL

本文提出了一种分离式训练方法，利用 GraphLASSO 算法生成稀疏图结构，使用 Graph Convolutional Recurrent Network 模型进行多元时间序列预测，实验结果表明，该方法可以在保证模型性能的同时，生成稀疏，有意义且易于解释的图结构，并且训练时间减少了约 40%。

多元时间序列预测中发现图模型的稀疏性利用

Sparsity exploitation via discovering graphical models in multi-variate  time-series forecasting

Traffic forecasting is one of the most fundamental problems in transportation
science and artificial intelligence. The key challenge is to effectively model
complex spatial-temporal dependencies and correlations in modern traffic data.
Existing methods, however, cannot accurately model both long-term and
short-term temporal correlations simultaneously, limiting their expressive
power on complex spatial-temporal patterns. In this paper, we propose a novel
spatial-temporal neural network framework: Attention-based Spatial-Temporal
Graph Convolutional Recurrent Network (ASTGCRN), which consists of a graph
convolutional recurrent module (GCRN) and a global attention module. In
particular, GCRN integrates gated recurrent units and adaptive graph
convolutional networks for dynamically learning graph structures and capturing
spatial dependencies and local temporal relationships. To effectively extract
global temporal dependencies, we design a temporal attention layer and
implement it as three independent modules based on multi-head self-attention,
transformer, and informer respectively. Extensive experiments on five real
traffic datasets have demonstrated the excellent predictive performance of all
our three models with all their average MAE, RMSE and MAPE across the test
datasets lower than the baseline methods.

本文提出了一种新的空间 - 时间神经网络框架 ASTGCRN，其中包括图卷积循环模块 GCRN 和全局注意力模块，以有效地对运输数据进行复杂的时空依赖性和相关性建模，并采用三个独立模块的时间关注层来实现对全局时间依赖性的有效提取。实验结果表明，这三个模型均具有极佳的预测表现优于基准方法。

基于注意力机制的时空图卷积循环神经网络用于交通预测

Attention-based Spatial-Temporal Graph Convolutional Recurrent Networks for Traffic Forecasting

This paper introduces Graph Convolutional Recurrent Network (GCRN), a deep
learning model able to predict structured sequences of data. Precisely, GCRN is
a generalization of classical recurrent neural networks (RNN) to data
structured by an arbitrary graph. Such structured sequences can represent
series of frames in videos, spatio-temporal measurements on a network of
sensors, or random walks on a vocabulary graph for natural language modeling.
The proposed model combines convolutional neural networks (CNN) on graphs to
identify spatial structures and RNN to find dynamic patterns. We study two
possible architectures of GCRN, and apply the models to two practical problems:
predicting moving MNIST data, and modeling natural language with the Penn
Treebank dataset. Experiments show that exploiting simultaneously graph spatial
and dynamic information about data can improve both precision and learning
speed.

本文介绍了图卷积循环网络（GCRN），这是一种深度学习模型，能够预测结构化数据序列。GCRN 是经典递归神经网络（RNN）在任意图结构数据上的泛化。该模型将图上的卷积神经网络 (CNN) 与 RNN 相结合，以找出动态模式和空间结构，并将其应用于 MNIST 数据预测和 Penn Treebank 数据集的自然语言建模。实验表明，同时利用数据的图空间和动态信息可以提高精度和学习速度。