Causal discovery in multi-rate time series encounters greater challenges compared to regular time series. This stems from a potential problem that has not been noticed and explored in existing studies:information granularity heterogeneity, which refers to the natural difference in information granularity between fast sampling rate data (high information granularity) and slow sampling rate data (low information granularity). Such an imbalance in information granularity can hinder forecasting relationships modeling and induce biased causal learning. Therefore, we propose aMutual Information-iNspired causalDiscovery framework (MIND), aiming to derive rate-agnostic features with consistent information granularity to alleviate information granularity heterogeneity problem. Technically, MIND comprises Stage 1 (pre-training) and Stage 2 (fine-tuning and causal discovery). In Stage 1, empowered by pseudo-slow sampling rate data (generated through the interleaved down sampling strategy) and mutual information, we can eliminate the influence of sampling rates and drive rate-aware encoders (RAEs) to sense key information (i.e., rate-agnostic) that remains unchanged across varying sampling rates. In Stage 2, the well-trained RAEs can extract rate-agnostic features from real multi-rate time series, thus facilitating effective forecasting relationships modeling and yield accurate causal discovery. Empirically, MIND realizes superior performance on various multi-rate scenarios, including four simulation datasets and one real-world dataset.

Cross-time spatial dependence (i.e., the interaction between different variables at different time points) is indispensable for detecting anomalies in multivariate time series, as certain anomalies may have time delays in their propagation from one variable to another. However, accurately capturing cross-time spatial dependence remains a challenge. Specifically, real-world time series usually exhibits complex and incomprehensible evolutions that may be compounded by multiple temporal states (i.e., temporal patterns, such as rising, fluctuating, and peak). These temporal states mix and overlap with each other and exhibit dynamic and heterogeneous evolution laws in different time series, making the cross-time spatial dependence extremely intricate and mutable. Therefore, a cross-time spatial graph network with fuzzy embedding is proposed to disentangle latent and mixing temporal states and exploit it to meticulously learn cross-time spatial dependence. First, considering that temporal states are diversiform and their mixing modes are unknown, we introduce a fuzzy state set to uniformly characterize potential temporal states and adaptively generate corresponding membership degrees to depict how these states mix. Further, we propose a cross-time spatial graph, quantifying similarities among fuzzy states and sensing their dynamic evolutions, to flexibly learn mutable cross-time spatial dependence. Finally, we design state diversity and temporal proximity constraints to ensure the differences among fuzzy states and the evolution continuity of fuzzy states. Experiments on real-world datasets show that the proposed model outperforms the state-of-the-art models.

Causal discovery under Granger causality framework has yielded widespread concerns in time series analysis task. Nevertheless, most previous methods are unaware of the underlying causality disappearing problem, that is, certain weak causalities are less focusable and may be lost during the modeling process, thus leading to biased causal conclusions. Therefore, we propose to introduce joint causal influences (i.e., causal influences from the union of multiple variables) as additional causal indication information to help identify weak causalities. Further, to break the limitation of existing methods that implicitly and coarsely model joint causal influences, we propose a novel hidden variable-driven causal hypergraph neural network to meticulously explore the locality and diversity of joint causal influences, and realize its explicit and fine-grained modeling. Specifically, we introduce hidden variables to construct a causal hypergraph for explicitly characterizing various fine-grained joint causal influences. Then, we customize a dual causal information transfer mechanism (encompassing a multi-level causal path and an information aggregation path) to realize the free diffusion and meticulous aggregation of joint causal influences and facilitate its adaptive learning. Finally, we design a multi-view collaborative optimization constraint to guarantee the characterization diversity of causal hypergraph and capture remarkable forecasting relationships (i.e., causalities). Experiments are conducted to demonstrate the superiority of the proposed model.

Accurately capturing the spatial correlations of traffic network significantly benefits short-term traffic forecasting. Some existing works represent spatial correlations in a simple one-dimensional space, but they cannot represent the real spatial correlations among sensors comprehensively. The other existing works represent the spatial correlations through grid-based method, but the local correlation of constructed spatial map is too superficial to extract deep spatial features effectively. Therefore, a novel deep learning model is proposed, which aims to represent the spatial correlations more effectively through a new correlation matrix structure. In the proposed model, the correlations among sensors are calculated from multiple perspectives to construct the speed, volume, and occupancy correlation matrices respectively. Then, considering that highly correlated sensors are close in the spatial dimension, an enhanced heuristic optimization algorithm is proposed to evolve these three correlation matrices into optimal ones by reorganizing the highly correlated sensors into each others neighborhood. Finally, the three optimal correlation matrices are combined to form a three-dimensional multivariate correlation matrix characterized by locally high correlation, which is beneficial to exploit the deep spatial features of traffic network. The experiments show that the proposed model has better accuracy and stability than other commonly used baseline models.