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Tensor time series (TTS) data, a generalization of one-dimensional time series on a high-dimensional space, is ubiquitous in real-world scenarios, especially in monitoring systems involving multi-source spatio-temporal data (e.g.,…

Machine Learning · Computer Science 2023-06-08 Jiewen Deng , Jinliang Deng , Renhe Jiang , Xuan Song

Quantifying predictive uncertainty is essential for real world machine learning applications, especially in scenarios requiring reliable and interpretable predictions. Many common parametric approaches rely on neural networks to estimate…

Machine Learning · Statistics 2026-03-31 Yang Yang , Chunlin Ji , Haoyang Li , Ke Deng

Traffic forecasting is a challenging spatio-temporal modeling task and a critical component of urban transportation management. Current studies mainly focus on deterministic predictions, with limited considerations on the uncertainty and…

Machine Learning · Computer Science 2026-04-20 Weijiang Xiong , Robert Fonod , Nikolas Geroliminis

We propose an Gaussian Mixture Model (GMM) learning algorithm, based on our previous work of GMM expansion idea. The new algorithm brings more robustness and simplicity than classic Expectation Maximization (EM) algorithm. It also improves…

Machine Learning · Computer Science 2023-09-07 Weiguo Lu , Xuan Wu , Deng Ding , Gangnan Yuan

The non-stationary nature of real-world Multivariate Time Series (MTS) data presents forecasting models with a formidable challenge of the time-variant distribution of time series, referred to as distribution shift. Existing studies on the…

Machine Learning · Computer Science 2024-07-19 Hui He , Qi Zhang , Kun Yi , Xiaojun Xue , Shoujin Wang , Liang Hu , Longbing Cao

Forecasting on sparse multivariate time series (MTS) aims to model the predictors of future values of time series given their incomplete past, which is important for many emerging applications. However, most existing methods process MTS's…

Machine Learning · Computer Science 2021-03-04 Yinjun Wu , Jingchao Ni , Wei Cheng , Bo Zong , Dongjin Song , Zhengzhang Chen , Yanchi Liu , Xuchao Zhang , Haifeng Chen , Susan Davidson

The standard regression tree method applied to observations within clusters poses both methodological and implementation challenges. Effectively leveraging these data requires methods that account for both individual-level and sample-level…

Methodology · Statistics 2025-03-05 Jeremiah Allis , Xin Jin , Riddhi Ghosh

Forecasting models that are trained across sets of many time series, known as Global Forecasting Models (GFM), have shown recently promising results in forecasting competitions and real-world applications, outperforming many…

Machine Learning · Computer Science 2020-08-07 Kasun Bandara , Hansika Hewamalage , Yuan-Hao Liu , Yanfei Kang , Christoph Bergmeir

Effectively modeling non-stationary dynamics in probabilistic multivariate time series(MTS) forecasting requires balancing expressiveness with robustness. Existing parametric approaches benefit from strong inductive biases but lack…

Machine Learning · Computer Science 2026-05-25 Jinglin Li , Jun Tan , QI Fang , Ning Gui

Multivariate time series analysis is becoming an integral part of data analysis pipelines. Understanding the individual time point connections between covariates as well as how these connections change in time is non-trivial. To this aim,…

Machine Learning · Statistics 2021-02-04 Federico Ciech , Veronica Tozzo

Generative probabilistic forecasting produces future time series samples according to the conditional probability distribution given past time series observations. Such techniques are essential in risk-based decision-making and planning…

Machine Learning · Computer Science 2024-02-22 Xinyi Wang , Lang Tong , Qing Zhao

Existing generative models for time series forecasting often transform simple priors (typically Gaussian) into complex data distributions. However, their sampling initialization, independent of historical data, hinders the capture of…

Machine Learning · Computer Science 2025-08-12 Huibo Xu , Runlong Yu , Likang Wu , Xianquan Wang , Qi Liu

Generating high-quality synthetic time series is a fundamental yet challenging task across domains such as forecasting and anomaly detection, where real data can be scarce, noisy, or costly to collect. Unlike static data generation,…

Machine Learning · Computer Science 2025-09-25 MohammadReza EskandariNasab , Shah Muhammad Hamdi , Soukaina Filali Boubrahimi

To obtain a probabilistic model for a dependent variable based on some set of explanatory variables, a distributional approach is often adopted where the parameters of the distribution are linked to regressors. In many classical models this…

Methodology · Statistics 2020-01-14 Lisa Schlosser , Torsten Hothorn , Reto Stauffer , Achim Zeileis

With large quantities of data typically available nowadays, forecasting models that are trained across sets of time series, known as Global Forecasting Models (GFM), are regularly outperforming traditional univariate forecasting models that…

Machine Learning · Computer Science 2021-09-22 Rakshitha Godahewa , Kasun Bandara , Geoffrey I. Webb , Slawek Smyl , Christoph Bergmeir

Many methods for machine learning rely on approximate inference from intractable probability distributions. Variational inference approximates such distributions by tractable models that can be subsequently used for approximate inference.…

Machine Learning · Computer Science 2020-10-08 Oleg Arenz , Mingjun Zhong , Gerhard Neumann

Time series forecasting is crucial for many fields, such as disaster warning, weather prediction, and energy consumption. The Transformer-based models are considered to have revolutionized the field of sequence modeling. However, the…

Machine Learning · Computer Science 2022-11-01 Junlong Tong , Liping Xie , Wankou Yang , Kanjian Zhang

In settings ranging from weather forecasts to political prognostications to financial projections, probability estimates of future binary outcomes often evolve over time. For example, the estimated likelihood of rain on a specific day…

Machine Learning · Computer Science 2021-11-05 Zhiyuan Jerry Lin , Hao Sheng , Sharad Goel

Diffusion models have shown promise in forecasting future data from multivariate time series. However, few existing methods account for recurring structures, or patterns, that appear within the data. We present Pattern-Guided Diffusion…

Machine Learning · Computer Science 2025-12-17 Vivian Lin , Kuk Jin Jang , Wenwen Si , Insup Lee

Probabilistic forecasting of multivariate time series is essential for various downstream tasks. Most existing approaches rely on the sequences being uniformly spaced and aligned across all variables. However, real-world multivariate time…

Machine Learning · Computer Science 2025-02-18 Yijun Li , Cheuk Hang Leung , Qi Wu
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