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Modeling the time-varying covariance structures of high-dimensional variables is critical across diverse scientific and industrial applications; however, existing approaches exhibit notable limitations in either modeling flexibility or…

Methodology · Statistics 2026-01-21 Taehee Lee , Jun S. Liu

Spatiotemporal systems are common in the real-world. Forecasting the multi-step future of these spatiotemporal systems based on the past observations, or, Spatiotemporal Sequence Forecasting (STSF), is a significant and challenging problem.…

Machine Learning · Computer Science 2018-08-22 Xingjian Shi , Dit-Yan Yeung

Improving the predictive accuracy of a dynamics model is crucial to obtaining good control performance and safety from Model Predictive Controllers (MPC). One approach involves learning unmodelled (residual) dynamics, in addition to nominal…

Systems and Control · Electrical Eng. & Systems 2025-11-19 Leroy D'Souza , Yash Vardhan Pant , Sebastian Fischmeister

As environments evolve, temporal distribution shifts can degrade time series forecasting performance. A straightforward solution is to adapt to nonstationary changes while preserving stationary dependencies. Hence, some methods disentangle…

Machine Learning · Computer Science 2025-03-11 Zijian Li , Ruichu Cai , Zhenhui Yang , Haiqin Huang , Guangyi Chen , Yifan Shen , Zhengming Chen , Xiangchen Song , Kun Zhang

Space-Time Projection (STP) is introduced as a data-driven forecasting approach for high-dimensional and time-resolved data. The method computes extended space-time proper orthogonal modes from training data spanning a prediction horizon…

Machine Learning · Computer Science 2025-04-01 Oliver T. Schmidt

Multivariate time series long-term prediction, which aims to predict the change of data in a long time, can provide references for decision-making. Although transformer-based models have made progress in this field, they usually do not make…

Machine Learning · Computer Science 2023-08-08 Chengqing Yu , Fei Wang , Zezhi Shao , Tao Sun , Lin Wu , Yongjun Xu

Reliable multi-horizon traffic forecasting is challenging because network conditions are stochastic, incident disruptions are intermittent, and effective spatial dependencies vary across time-of-day patterns. This study is conducted on the…

Machine Learning · Computer Science 2026-03-18 Mayur Patil , Qadeer Ahmed , Shawn Midlam-Mohler , Stephanie Marik , Allen Sheldon , Rajeev Chhajer , Nithin Santhanam

Multi-variate time series (MTS) forecasting is crucial for various applications. Existing methods have shown promising results owing to their strong ability to capture intra- and inter-variate dependencies. However, these methods often…

Machine Learning · Computer Science 2025-09-05 Binqing Wu , Zongjiang Shang , Jianlong Huang , Ling Chen

Time-evolving traffic flow forecasting are playing a vital role in intelligent transportation systems and smart cities. However, the dynamic traffic flow forecasting is a highly nonlinear problem with complex temporal-spatial dependencies.…

Machine Learning · Computer Science 2025-08-05 Zhenan Lin , Yuni Lai , Wai Lun Lo , Richard Tai-Chiu Hsung , Harris Sik-Ho Tsang , Xiaoyu Xue , Kai Zhou , Yulin Zhu

Multivariate time-series data are frequently observed in critical care settings and are typically characterized by sparsity (missing information) and irregular time intervals. Existing approaches for learning representations in this domain…

Machine Learning · Computer Science 2022-02-17 Sindhu Tipirneni , Chandan K. Reddy

In this paper, we find that ubiquitous time series (TS) forecasting models are prone to severe overfitting. To cope with this problem, we embrace a de-redundancy approach to progressively reinstate the intrinsic values of TS for future…

Machine Learning · Computer Science 2024-06-18 Daojun Liang , Haixia Zhang , Dongfeng Yuan , Bingzheng Zhang , Minggao Zhang

Multivariate Time Series (MTS) forecasting plays a vital role in various real-world applications, such as traffic management and predictive maintenance. Existing approaches typically model MTS data in either Euclidean or Riemannian space,…

Machine Learning · Computer Science 2025-12-17 Yong Fang , Na Li , Hangguan Shan , Eryun Liu , Xinyu Li , Wei Ni , Er-Ping Li

As a decisive part in the success of Mobility-as-a-Service (MaaS), spatio-temporal predictive modeling for crowd movements is a challenging task particularly considering scenarios where societal events drive mobility behavior deviated from…

Machine Learning · Computer Science 2021-12-17 Zhaonan Wang , Renhe Jiang , Hao Xue , Flora D. Salim , Xuan Song , Ryosuke Shibasaki

Accurate traffic forecasting is a fundamental problem in intelligent transportation systems and learning long-range traffic representations with key information through spatiotemporal graph neural networks (STGNNs) is a basic assumption of…

Machine Learning · Computer Science 2024-03-26 Qinyao Luo , Silu He , Xing Han , Yuhan Wang , Haifeng Li

The Transformer architecture yields state-of-the-art results in many tasks such as natural language processing (NLP) and computer vision (CV), since the ability to efficiently capture the precise long-range dependency coupling between input…

Machine Learning · Computer Science 2023-01-06 Peiwang Tang , Xianchao Zhang

Traffic forecasting is a complex multivariate time-series regression task of paramount importance for traffic management and planning. However, existing approaches often struggle to model complex multi-range dependencies using local…

Machine Learning · Computer Science 2023-11-07 Dongcheng Zou , Senzhang Wang , Xuefeng Li , Hao Peng , Yuandong Wang , Chunyang Liu , Kehua Sheng , Bo Zhang

The past few years have witnessed the rapid development in multivariate time series forecasting. The key to accurate forecasting results is capturing the long-term dependency between each time step (cross-time dependency) and modeling the…

Machine Learning · Computer Science 2023-06-06 Donghao Luo , Xue Wang

High-dimensional multivariate time series are challenging due to the dependent and high-dimensional nature of the data, but in many applications there is additional structure that can be exploited to reduce computing time along with…

Methodology · Statistics 2020-03-13 Michael Schweinberger , Sergii Babkin , Katherine Ensor

Currently, iTransformer is one of the most popular and effective models for multivariate time series (MTS) forecasting. Thanks to its inverted framework, iTransformer effectively captures multivariate correlation. However, the inverted…

Machine Learning · Computer Science 2025-07-17 Hongming Tan , Ting Chen , Ruochong Jin , Wai Kin Chan

Probabilistic forecasting of high dimensional multivariate time series is a notoriously challenging task, both in terms of computational burden and distribution modeling. Most previous work either makes simple distribution assumptions or…

Machine Learning · Computer Science 2021-01-27 Nam Nguyen , Brian Quanz
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