VLBM: Variational Latent Basis Modeling for OOD Robust Multivariate Time Series Forecasting
2026-06-01 • Machine Learning
Machine LearningArtificial Intelligence
AI summaryⓘ
The authors address the challenge of predicting rare but important unusual events (out of distribution, OOD) in multivariate time series data, which usual forecasting methods often miss because they focus on common patterns. They propose a model called VLBM that separates normal stable behaviors from unusual deviations by learning a shared set of basic underlying patterns and handling deviations separately. Their method improves accuracy and robustness across various real-world datasets, showing better performance on both normal and rare events. The work suggests that structuring predictions around latent stable patterns helps make forecasting more reliable when unusual events occur.
Out of Distribution (OOD)Multivariate Time Series ForecastingVariational Latent Basis Model (VLBM)Latent SpaceLow Rank SubspacePosterior and Prior AlignmentMean Absolute Error (MAE)Mean Squared Error (MSE)Forecasting RobustnessTime Series Decomposition
Authors
Xudong Zhang, Jierui Lei, Jiacheng Li, Lingdong Shen, Jian Cui, Haina Tang
Abstract
Out of distribution (OOD) events in multivariate time series forecasting are rare but often dominate real world risk, making average case forecasting insufficient for reliable deployment. Under standard average risk training on mixed ID/OOD distributions, optimization signals from rare OOD events can be overwhelmed by frequent in distribution (ID) patterns, so strong benchmark accuracy may not translate into reliability under high impact shifts. To address this issue, we propose VLBM (Variational Latent Basis Model), a theory guided latent forecasting framework that separates stable dynamics from OOD induced deviations. VLBM learns a shared latent basis that defines a low rank subspace for stable ID dynamics, explicitly decomposes inputs into basis subspace components and orthogonal residual components, and aligns a future aware posterior with a future blind prior so that test time latent inference depends only on historical input. Across 12 benchmark tasks spanning transportation, weather, power systems, and other real world domains, including newly constructed real world OOD traffic datasets, VLBM achieves state of the art OOD robustness and ID accuracy, with average MAE and MSE gains of 15.08\% and 7.74\% over the strongest baseline. On a synthetic simulation dataset, VLBM also consistently achieves the best performance and better tracks OOD pulse recovery. These results support latent structured forecasting as a principled route to robust prediction under mixed ID and OOD conditions. The code is available at https://github.com/leijieruilq/VLBM_OOD_forecast.