Temporal causal discovery aims to uncover causal relations in time series data. Current deep learning-based methods usually analyze the parameters of some components of the trained models, which is an incomplete mapping process from the model parameters to the causality and fails to investigate the other components. To address this, this paper presents an interpretable transformer-based causal discovery model termed CausalFormer, which consists of: 1) the causality-aware transformer which learns the causal representation with the multi-kernel causal convolution under the temporal priority constraint, and 2) the decomposition-based causality detector which identifies causality by interpreting the global structure of the trained transformer with the regression relevance propagation.

Accurate spatial-temporal (ST) traffic prediction plays an essential role in intelligent transportation systems. Existing advanced traffic prediction methods typically utilize spatial-temporal graph neural networks (STGNNs) to capture the ST correlations and achieve excellent prediction performance. However, our experimental investigation reveals that existing static and dynamic graph-based STGNNs still incur excessive noise and redundancy, and fail to discover robust and reliable ST correlations in traffic networks. Moreover, most methods cannot explain the underlying reasons behind the ST correlations. To solve these problems, we propose a novel S patial- T emporal G raph M odeling framework via A daptive contrastive learning (ST-GMA). Firstly, we design a robust augmentation learning module to generate high-level and robust data augmentations via a self-supervised task for modeling reliable correlations. Then, we develop an adaptive contrastive learning module to update correlation graphs by effectively selecting positive and negative augmentations, reducing redundant calculations, and providing insights into the correlation changes. Finally, ST-GMA integrates the generated correlation graphs with ST convolution blocks to conduct traffic prediction tasks. Experimental results on five real-world datasets demonstrate that ST-GMA not only achieves significant prediction performance compared with state-of-the-art methods but also exhibits a new perspective on the interpretability of correlation changes.

Temporal causal discovery is a crucial task aimed at uncovering the causal relations within time series data. The latest temporal causal discovery methods usually train deep learning models on prediction tasks to uncover the causality between time series. They capture causal relations by analyzing the parameters of some components of the trained models, e.g., attention weights and convolution weights. However, this is an incomplete mapping process from the model parameters to the causality and fails to investigate the other components, e.g., fully connected layers and activation functions, that are also significant for causal discovery. To facilitate the utilization of the whole deep learning models in temporal causal discovery, we proposed an interpretable transformer-based causal discovery model termed CausalFormer, which consists of the causality-aware transformer and the decomposition-based causality detector. The causality-aware transformer learns the causal representation of time series data using a prediction task with the designed multi-kernel causal convolution which aggregates each input time series along the temporal dimension under the temporal priority constraint. Then, the decomposition-based causality detector interprets the global structure of the trained causality-aware transformer with the proposed regression relevance propagation to identify potential causal relations and finally construct the causal graph. Experiments on synthetic, simulated, and real datasets demonstrate the state-of-the-art performance of CausalFormer on discovering temporal causality.