GLAIM: Learning Global and Local Adaptive Inter-Variable Dependency for Multivariate Time Series Imputation
2026-08-03 • Machine Learning
Machine LearningArtificial Intelligence
AI summaryⓘ
The authors focus on filling in missing data in multivariate time series, which is important for analyzing such data correctly. They point out that current methods either look at overall patterns across all data or focus on details for each individual sample, but each approach has weaknesses. To fix this, they propose GLAIM, which combines a stable global view of relationships between variables with a flexible local adjustment tailored to each sample. Their tests on real datasets show that GLAIM performs better and is more reliable, especially when data is missing randomly or in blocks.
multivariate time seriesdata imputationinter-variable dependenciesglobal dependencieslocal dependenciestemporal non-stationaritymissing datatime series analysismachine learning models
Authors
Mingyang Wang, Rongwen Li, Xiao Wang, Changjian Chen
Abstract
Multivariate time series imputation is fundamental to downstream analysis, yet modeling inter-variable dependencies with incomplete observations remains challenging. Existing methods learn global dependencies across samples or dynamic local dependencies per sample. Global dependencies are stable but adapt poorly to sample variations and temporal non-stationarity, whereas local dependencies are adaptive yet unreliable when observations are insufficient, causing erroneous information propagation. To address these limitations, we propose GLAIM, a Global-Local Adaptive Inter-variable Dependency Modeling framework for multivariate time series imputation. GLAIM comprises two complementary components. The Stable Global Dependency Constructor derives robust global inter-variable dependencies from complementary temporal representations, providing a stable backbone less affected by sample-specific missingness and noise. The Sample-Conditioned Dependency Refiner adapts this backbone to each sample and time step using its temporal state and available observations, enabling reliable local refinement under incomplete observations. Extensive experiments on nine real-world datasets demonstrate that GLAIM achieves state-of-the-art performance under random and block missingness, remains robust to missing-rate shifts, and benefits from its complementary global and local components. Code is available at https://github.com/LuRenjias/GLAIM.