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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

Traffic forecasting is essential for the traffic construction of smart cities in the new era. However, traffic data's complex spatial and temporal dependencies make traffic forecasting extremely challenging. Most existing traffic…

Machine Learning · Computer Science 2022-10-03 Wei Zhao , Shiqi Zhang , Bing Zhou , Bei Wang

Nonlinear differential equations rarely admit closed-form solutions, thus requiring numerical time-stepping algorithms to approximate solutions. Further, many systems characterized by multiscale physics exhibit dynamics over a vast range of…

Machine Learning · Computer Science 2020-08-26 Yuying Liu , J. Nathan Kutz , Steven L. Brunton

We consider deep multivariate models for heterogeneous collections of random variables. In the context of computer vision, such collections may e.g. consist of images, segmentations, image attributes, and latent variables. When developing…

Machine Learning · Computer Science 2026-02-03 Dmitrij Schlesinger , Boris Flach , Alexander Shekhovtsov

This study introduces a deep learning-based framework for forecasting weather-related traffic crash risk using heterogeneous spatiotemporal data. Given the complex, non-linear relationship between crash occurrence and factors such as road…

Applications · Statistics 2026-03-06 Abimbola Ogungbire , Srinivas Pulugurtha

Deep learning based approaches have been utilized to model and generate graphs subjected to different distributions recently. However, they are typically unsupervised learning based and unconditioned generative models or simply conditioned…

Machine Learning · Computer Science 2023-08-29 Shanchao Yang , Jing Liu , Kai Wu , Mingming Li

Recently, the incorporation of both temporal features and the correlation across time series has become an effective approach in time series prediction. Spatio-Temporal Graph Neural Networks (STGNNs) demonstrate good performance on many…

Machine Learning · Computer Science 2024-07-29 Wenbo Yan , Ying Tan

Spatio-temporal forecasting in various domains, like traffic prediction and weather forecasting, is a challenging endeavor, primarily due to the difficulties in modeling propagation dynamics and capturing high-dimensional interactions among…

Machine Learning · Computer Science 2024-05-29 Xiaobei Zou , Luolin Xiong , Yang Tang , Jürgen Kurths

Generating forecasts for time series with multiple seasonal cycles is an important use-case for many industries nowadays. Accounting for the multi-seasonal patterns becomes necessary to generate more accurate and meaningful forecasts in…

Applications · Statistics 2020-04-28 Kasun Bandara , Christoph Bergmeir , Hansika Hewamalage

Trend change prediction in complex systems with a large number of noisy time series is a problem with many applications for real-world phenomena, with stock markets as a notoriously difficult to predict example of such systems. We approach…

Computational Finance · Quantitative Finance 2018-11-30 Ben Moews , J. Michael Herrmann , Gbenga Ibikunle

Time series forecasting traditionally relies on unimodal numerical inputs, which often struggle to capture high-level semantic patterns due to their dense and unstructured nature. While recent approaches have explored representing time…

Machine Learning · Computer Science 2025-07-02 Sixun Dong , Wei Fan , Teresa Wu , Yanjie Fu

Probabilistic time series forecasting involves estimating the distribution of future based on its history, which is essential for risk management in downstream decision-making. We propose a deep state space model for probabilistic time…

Machine Learning · Computer Science 2021-02-02 Longyuan Li , Junchi Yan , Xiaokang Yang , Yaohui Jin

Hidden Markov Models (HMMs) comprise a powerful generative approach for modeling sequential data and time-series in general. However, the commonly employed assumption of the dependence of the current time frame to a single or multiple…

Machine Learning · Computer Science 2021-09-13 Konstantinos P. Panousis , Sotirios Chatzis , Sergios Theodoridis

Modeling long horizon marked event sequences is a fundamental challenge in many real-world applications, including healthcare, finance, and user behavior modeling. Existing neural temporal point process models are typically autoregressive,…

Machine Learning · Computer Science 2025-08-08 Xiao Shou

Deep neural network models have become ubiquitous in recent years, and have been applied to nearly all areas of science, engineering, and industry. These models are particularly useful for data that have strong dependencies in space (e.g.,…

Machine Learning · Statistics 2022-06-07 Christopher K. Wikle , Andrew Zammit-Mangion

Spatio-temporal prediction plays an important role in many application areas especially in traffic domain. However, due to complicated spatio-temporal dependency and high non-linear dynamics in road networks, traffic prediction task is…

Machine Learning · Computer Science 2019-03-05 Bing Yu , Mengzhang Li , Jiyong Zhang , Zhanxing Zhu

Traffic accident forecasting is a significant problem for transportation management and public safety. However, this problem is challenging due to the spatial heterogeneity of the environment and the sparsity of accidents in space and time.…

Machine Learning · Computer Science 2022-03-08 Bang An , Amin Vahedian , Xun Zhou , W. Nick Street , Yanhua Li

Heterogeneous graph convolutional networks have gained great popularity in tackling various network analytical tasks on heterogeneous network data, ranging from link prediction to node classification. However, most existing works ignore the…

Social and Information Networks · Computer Science 2022-08-15 Pengyang Yu , Chaofan Fu , Yanwei Yu , Chao Huang , Zhongying Zhao , Junyu Dong

Multivariate time series forecasting is essential in domains such as finance, transportation, climate, and energy. However, existing patch-based methods typically adopt fixed-length segmentation, overlooking the heterogeneity of local…

Machine Learning · Computer Science 2026-01-06 Kuiye Ding , Fanda Fan , Chunyi Hou , Zheya Wang , Lei Wang , Zhengxin Yang , Jianfeng Zhan

Producing probabilistic forecasts for large collections of similar and/or dependent time series is a practically relevant and challenging task. Classical time series models fail to capture complex patterns in the data, and multivariate…

Machine Learning · Statistics 2019-05-30 Yuyang Wang , Alex Smola , Danielle C. Maddix , Jan Gasthaus , Dean Foster , Tim Januschowski