VLBM: Variational Latent Basis Modeling for OOD Robust Multivariate Time Series Forecasting

2026-06-01

AI Summary

This work addresses the degradation of model reliability in multivariate time series forecasting under out-of-distribution (OOD) events. Existing methods, when trained on mixed in-distribution (ID) and OOD data, are often dominated by prevalent ID patterns and struggle with high-impact distribution shifts. To overcome this, the paper proposes the Variational Latent Basis Model (VLBM), which introduces a theory-guided latent structural modeling approach: it constructs a low-rank subspace via shared latent bases to capture stable ID dynamics, explicitly decomposes inputs into subspace components and orthogonal residuals, and incorporates a future-blind prior to ensure latent variables are inferred solely from historical information at test time. Evaluated on 12 real-world benchmarks, this end-to-end framework achieves state-of-the-art performance, improving average MAE and MSE by 15.08% and 7.74%, respectively, and more accurately tracks OOD impulse recovery in synthetic data.

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.

Problem

• out-of-distribution
• multivariate time series forecasting
• distribution shift
• forecasting robustness
• rare events

Innovation

• Variational Latent Basis Modeling
• OOD Robustness
• Multivariate Time Series Forecasting
• Latent Subspace Decomposition
• Future-Blind Prior