Spatiotemporal time series is the foundation of understanding human
activities and their impacts, which is usually collected via monitoring sensors
placed at different locations. The collected data usually contains missing
values due to various failures, which have significant impact on data analysis.
To impute the missing values, a lot of methods have been introduced. When
recovering a specific data point, most existing methods tend to take into
consideration all the information relevant to that point regardless of whether
they have a cause-and-effect relationship. During data collection, it is
inevitable that some unknown confounders are included, e.g., background noise
in time series and non-causal shortcut edges in the constructed sensor network.
These confounders could open backdoor paths between the input and output, in
other words, they establish non-causal correlations between the input and
output. Over-exploiting these non-causal correlations could result in
overfitting and make the model vulnerable to noises. In this paper, we first
revisit spatiotemporal time series imputation from a causal perspective, which
shows the causal relationships among the input, output, embeddings and
confounders. Next, we show how to block the confounders via the frontdoor
adjustment. Based on the results of the frontdoor adjustment, we introduce a
novel Causality-Aware SPatiotEmpoRal graph neural network (CASPER), which
contains a novel Spatiotemporal Causal Attention (SCA) and a Prompt Based
Decoder (PBD). PBD could reduce the impact of confounders and SCA could
discover the sparse causal relationships among embeddings. Theoretical analysis
reveals that SCA discovers causal relationships based on the values of
gradients. We evaluate Casper on three real-world datasets, and the
experimental results show that Casper outperforms the baselines and effectively
discovers causal relationships.

从因果的角度重新审视了时空时间序列的填充，引入了前门调整与一个基于因果感知的时空图神经网络 (CASPER)，它包含了一个新颖的时空因果注意力 (SCA) 和一个基于提示的解码器 (PBD)。PBD 可以减少混淆变量的影响，而 SCA 可以发现嵌入之间的稀疏因果关系。经过理论分析，发现 SCA 是基于梯度值来发现因果关系的。通过在三个真实数据集上的评估，实验证明 Casper 能够胜过基准方法，并有效地发现因果关系。

CASPER: 因果感知的时空图神经网络对时空时间序列插值

CASPER: Causality-Aware Spatiotemporal Graph Neural Networks for  Spatiotemporal Time Series Imputation

Neural forecasting of spatiotemporal time series drives both research and
industrial innovation in several relevant application domains. Graph neural
networks (GNNs) are often the core component of the forecasting architecture.
However, in most spatiotemporal GNNs, the computational complexity scales up to
a quadratic factor with the length of the sequence times the number of links in
the graph, hence hindering the application of these models to large graphs and
long temporal sequences. While methods to improve scalability have been
proposed in the context of static graphs, few research efforts have been
devoted to the spatiotemporal case. To fill this gap, we propose a scalable
architecture that exploits an efficient encoding of both temporal and spatial
dynamics. In particular, we use a randomized recurrent neural network to embed
the history of the input time series into high-dimensional state
representations encompassing multi-scale temporal dynamics. Such
representations are then propagated along the spatial dimension using different
powers of the graph adjacency matrix to generate node embeddings characterized
by a rich pool of spatiotemporal features. The resulting node embeddings can be
efficiently pre-computed in an unsupervised manner, before being fed to a
feed-forward decoder that learns to map the multi-scale spatiotemporal
representations to predictions. The training procedure can then be parallelized
node-wise by sampling the node embeddings without breaking any dependency, thus
enabling scalability to large networks. Empirical results on relevant datasets
show that our approach achieves results competitive with the state of the art,
while dramatically reducing the computational burden.

本文提出了一种可扩展的体系结构，利用随机循环神经网络将输入时序的历史数据嵌入到高维状态表示中，并利用不同幂次的图相邻矩阵沿空间维传播以生成节点嵌入，从而实现多尺度的时空特征表示，我们的方法在保证结果竞争力的同时，大大降低了计算负担。