The abundance of fine-grained spatio-temporal data, such as traffic sensor networks, offers vast opportunities for scientific discovery. However, inferring causal relationships from such observational data remains challenging, particularly due to unobserved confounders that are specific to units (e.g., geographical locations) yet influence outcomes over time. Most existing methods for spatio-temporal causal inference assume that all confounders are observed, an assumption that is often violated in practice. In this paper, we introduce Spatio-Temporal Hierarchical Causal Models (ST-HCMs), a novel graphical framework that extends hierarchical causal modeling to the spatio-temporal domain. At the core of our approach is the Spatio-Temporal Collapse Theorem, which shows that a complex ST-HCM converges to a simpler flat causal model as the amount of subunit data increases. This theoretical result enables a general procedure for causal identification, allowing ST-HCMs to recover causal effects even in the presence of unobserved, time-invariant unit-level confounders, a scenario where standard non-hierarchical models fail. We validate the effectiveness of our framework on both synthetic and real-world datasets, demonstrating its potential for robust causal inference in complex dynamic systems.

Spatio-temporal tasks often encounter incomplete data arising from missing or inaccessible sensors, making spatio-temporal kriging crucial for inferring the completely missing temporal information. However, current models struggle with ensuring the validity and generalizability of inferred spatio-temporal patterns, especially in capturing dynamic spatial dependencies and temporal shifts, and optimizing the generalizability of unknown sensors. To overcome these limitations, we propose Spatio-Temporal Aware Graph Adversarial Neural Network (STA-GANN), a novel GNN-based kriging framework that improves spatio-temporal pattern validity and generalization. STA-GANN integrates (i) Decoupled Phase Module that senses and adjusts for timestamp shifts. (ii) Dynamic Data-Driven Metadata Graph Modeling to update spatial relationships using temporal data and metadata; (iii) An adversarial transfer learning strategy to ensure generalizability. Extensive validation across nine datasets from four fields and theoretical evidence both demonstrate the superior performance of STA-GANN.

Spatio-temporal graphs are powerful tools for modeling complex dependencies in traffic time series. However, the distributed nature of real-world traffic data across multiple stakeholders poses significant challenges in modeling and reconstructing inter-client spatial dependencies while adhering to data locality constraints. Existing methods primarily address static dependencies, overlooking their dynamic nature and resulting in suboptimal performance. In response, we propose Federated Spatio-Temporal Graph with Dynamic Inter-Client Dependencies (FedSTGD), a framework designed to model and reconstruct dynamic inter-client spatial dependencies in federated learning. FedSTGD incorporates a federated nonlinear computation decomposition module to approximate complex graph operations. This is complemented by a graph node embedding augmentation module, which alleviates performance degradation arising from the decomposition. These modules are coordinated through a client-server collective learning protocol, which decomposes dynamic inter-client spatial dependency learning tasks into lightweight, parallelizable subtasks. Extensive experiments on four real-world datasets demonstrate that FedSTGD achieves superior performance over state-of-the-art baselines in terms of RMSE, MAE, and MAPE, approaching that of centralized baselines. Ablation studies confirm the contribution of each module in addressing dynamic inter-client spatial dependencies, while sensitivity analysis highlights the robustness of FedSTGD to variations in hyperparameters.

Spatial-temporal causal time series (STC-TS) involve region-specific temporal observations driven by causally relevant covariates and interconnected across geographic or network-based spaces. Existing methods often model spatial and temporal dynamics independently and overlook causality-driven probabilistic forecasting, limiting their predictive power. To address this, we propose STOAT (Spatial-Temporal Probabilistic Causal Inference Network), a novel framework for probabilistic forecasting in STC-TS. The proposed method extends a causal inference approach by incorporating a spatial relation matrix that encodes interregional dependencies (e.g. proximity or connectivity), enabling spatially informed causal effect estimation. The resulting latent series are processed by deep probabilistic models to estimate the parameters of the distributions, enabling calibrated uncertainty modeling. We further explore multiple output distributions (e.g., Gaussian, Student's-$t$, Laplace) to capture region-specific variability. Experiments on COVID-19 data across six countries demonstrate that STOAT outperforms state-of-the-art probabilistic forecasting models (DeepAR, DeepVAR, Deep State Space Model, etc.) in key metrics, particularly in regions with strong spatial dependencies. By bridging causal inference and geospatial probabilistic forecasting, STOAT offers a generalizable framework for complex spatial-temporal tasks, such as epidemic management.

Accurate and robust weather forecasting remains a fundamental challenge due to the inherent spatio-temporal complexity of atmospheric systems. In this paper, we propose a novel self-supervised learning framework that leverages spatio-temporal structures to improve multi-variable weather prediction. The model integrates a graph neural network (GNN) for spatial reasoning, a self-supervised pretraining scheme for representation learning, and a spatio-temporal adaptation mechanism to enhance generalization across varying forecasting horizons. Extensive experiments on both ERA5 and MERRA-2 reanalysis datasets demonstrate that our approach achieves superior performance compared to traditional numerical weather prediction (NWP) models and recent deep learning methods. Quantitative evaluations and visual analyses in Beijing and Shanghai confirm the model's capability to capture fine-grained meteorological patterns. The proposed framework provides a scalable and label-efficient solution for future data-driven weather forecasting systems.

Traffic forecasting represents a crucial problem within intelligent transportation systems. In recent research, Large Language Models (LLMs) have emerged as a promising method, but their intrinsic design, tailored primarily for sequential token processing, introduces notable challenges in effectively capturing spatial dependencies. Specifically, the inherent limitations of LLMs in modeling spatial relationships and their architectural incompatibility with graph-structured spatial data remain largely unaddressed. To overcome these limitations, we introduce ST-LINK, a novel framework that enhances the capability of Large Language Models to capture spatio-temporal dependencies. Its key components are Spatially-Enhanced Attention (SE-Attention) and the Memory Retrieval Feed-Forward Network (MRFFN). SE-Attention extends rotary position embeddings to integrate spatial correlations as direct rotational transformations within the attention mechanism. This approach maximizes spatial learning while preserving the LLM's inherent sequential processing structure. Meanwhile, MRFFN dynamically retrieves and utilizes key historical patterns to capture complex temporal dependencies and improve the stability of long-term forecasting. Comprehensive experiments on benchmark datasets demonstrate that ST-LINK surpasses conventional deep learning and LLM approaches, and effectively captures both regular traffic patterns and abrupt changes.

--As digital data transmission continues to scale, concerns about privacy grow increasingly urgent --yet privacy remains a socially constructed and ambiguously defined concept, lacking a universally accepted quantitative measure. This work examines information leakage in image data, a domain where information-theoretic guarantees are still underexplored. At the intersection of deep learning, information theory, and cryptography, we investigate the use of mutual information (MI) estimators -- in particular, the empirical estimator and the MINE framework -- to detect leakage from selectively encrypted images. Motivated by the intuition that a robust estimator would require a probabilistic frameworks that can capture spatial dependencies and residual structures -- even within encrypted representations - our work represent a promising direction for image information leakage estimation. Images are among the most common forms of data shared online, and with the widespread use of cloud storage, users frequently upload images to the web. Regardless of content sensitivity, image privacy remains a critical concern.

Due to the extensive retention of building operation data, data-driven building load prediction methods have demonstrated powerful capabilities in forecasting building energy loads. Buildings with similar operating conditions, physical characteristics, and types often exhibit similar energy usage patterns, which are reflected in their operation data showing similar trends and spatial dependencies. However, conventional building load prediction methods have significant limitations in extracting these spatial dependencies. To address this challenge, this paper proposes a multi-building load prediction method based on spatio-temporal graph neural networks, which is divided into three main steps: graph representation, graph learning, and method interpretation. First, a graph representation method is developed that identifies building correlations based on intrinsic characteristics and environmental factors. Next, a multi-level spatiotemporal graph convolu-tional architecture with an attention mechanism is designed to predict energy loads for multiple buildings. Finally, a model interpretation method based on the optimal graph structure obtained from the training process is devel-Corresponding author Email address: ychen@eitech.edu.cn Experiments on the Building Data Genome Project 2 dataset validate that the proposed method outperforms commonly used baseline models like XGBoost, SVR, FCNN, GRU, and Na ıve in terms of prediction accuracy. Additionally, the model demonstrates strong robustness and generalization, performing reliably under uncertainty and unseen data. Visualization of the building similarity matrix confirms the model's interpretability, revealing its ability to group similar buildings and establish meaningful spatial dependencies, proving that the proposed Att-GCN method for learning spatial dependencies between buildings with similar energy usage patterns is both reasonable and interpretable. Introduction With urbanization increasing, building energy consumption and carbon emissions are growing. Construction and operation of buildings account for 34% of global energy use, with 30% from operations.