Title: VLBM: A Variational Latent Basis Approach for Robust Multivariate Time Series Forecasting Against Out-of-Distribution Shifts

Abstract

Out-of-distribution (OOD) occurrences in multivariate time series forecasting, while infrequent, often account for the majority of real-world risk. Consequently, relying solely on average-case forecasting is inadequate for ensuring reliable model deployment. When models are trained under standard average risk objectives on mixed in-distribution (ID) and OOD data, the optimization signals generated by rare OOD events are frequently overshadowed by the abundance of common ID patterns. As a result, high benchmark accuracy does not necessarily guarantee robustness during significant distributional shifts.

To mitigate this challenge, we introduce VLBM (Variational Latent Basis Model), a theory-driven latent forecasting framework designed to distinguish between stable dynamics and deviations caused by OOD events. VLBM constructs a shared latent basis that characterizes a low-rank subspace for stable ID dynamics. The method explicitly decomposes input data into components within this basis subspace and orthogonal residual components. Furthermore, it aligns a future-aware posterior with a future-blind prior, ensuring that latent inference at test time relies exclusively on historical inputs.

Evaluated across 12 benchmark tasks covering transportation, weather, power systems, and other practical domains—including newly developed real-world OOD traffic datasets—VLBM demonstrates state-of-the-art robustness to OOD shifts while maintaining high ID accuracy. Compared to the strongest baseline, VLBM yields average improvements of 15.08% in Mean Absolute Error (MAE) and 7.74% in Mean Squared Error (MSE). Additionally, on a synthetic simulation dataset, VLBM consistently delivers superior performance and more effectively tracks OOD pulse recovery. These findings underscore latent structured forecasting as a principled methodology for achieving robust predictions under conditions where ID and OOD data coexist. The implementation is publicly accessible at https://github.com/leijieruilq/VLBM_OOD_forecast.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC