Are We Overlooking the Dimensions? Learning Latent Hierarchical Channel Structure for High-Dimensional Time Series Forecasting

2025-07-20

AI Summary

High-dimensional time series forecasting (HDTSF) faces significant challenges in modeling complex, hierarchical inter-channel dependencies as the number of channels escalates to thousands. Method: This paper proposes U-Cast—a novel architecture featuring (i) a query-based attention mechanism that adaptively discovers latent hierarchical channel structures; (ii) full-rank regularization to disentangle highly correlated channel representations and enhance discriminability; and (iii) a theoretically grounded cross-channel information fusion mechanism. Contribution/Results: We introduce Time-HD, the first large-scale benchmark dataset for HDTSF, and demonstrate that U-Cast achieves state-of-the-art performance on it—delivering both superior forecasting accuracy and improved computational efficiency. U-Cast establishes a scalable and interpretable modeling paradigm for HDTSF, enabling effective handling of ultra-high-dimensional channel spaces while preserving structural transparency.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

Time series forecasting (TSF) is a central problem in time series analysis. However, as the number of channels in time series datasets scales to the thousands or more, a scenario we define as High-Dimensional Time Series Forecasting (HDTSF), it introduces significant new modeling challenges that are often not the primary focus of traditional TSF research. HDTSF is challenging because the channel correlation often forms complex and hierarchical patterns. Existing TSF models either ignore these interactions or fail to scale as dimensionality grows. To address this issue, we propose U-Cast, a channel-dependent forecasting architecture that learns latent hierarchical channel structures with an innovative query-based attention. To disentangle highly correlated channel representation, U-Cast adds a full-rank regularization during training. We also release Time-HD, a benchmark of large, diverse, high-dimensional datasets. Our theory shows that exploiting cross-channel information lowers forecasting risk, and experiments on Time-HD demonstrate that U-Cast surpasses strong baselines in both accuracy and efficiency. Together, U-Cast and Time-HD provide a solid basis for future HDTSF research.

Problem

• Addresses high-dimensional time series forecasting challenges
• Models complex hierarchical channel correlations effectively
• Improves accuracy and efficiency in HDTSF

Innovation

• Learns latent hierarchical channel structures
• Uses query-based attention mechanism
• Applies full-rank regularization training