# GLAIM: Learning Global and Local Adaptive Inter-Variable Dependency for Multivariate Time Series Imputation

arXiv: https://arxiv.org/abs/2608.02366 · HTML: https://mlsanity.com/paper/2608.02366/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 50 references that are in the map.
- First posted on arXiv 3 Aug 2026.

## Builds on (most cited first, 29 of 29)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Spectral Temporal Graph Neural Network for Multivariate Time-series Forecasting](https://mlsanity.com/paper/2103.07719/) (2021)
- [Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models](https://mlsanity.com/paper/2208.09399/) (2022)
- [Frequency-domain MLPs are More Effective Learners in Time Series Forecasting](https://mlsanity.com/paper/2311.06184/) (2023)
- [Discrete Graph Structure Learning for Forecasting Multiple Time Series](https://mlsanity.com/paper/2101.06861/) (2021)
- [SAITS: Self-Attention-based Imputation for Time Series](https://mlsanity.com/paper/2202.08516/) (2022)
- [FourierGNN: Rethinking Multivariate Time Series Forecasting from a Pure Graph Perspective](https://mlsanity.com/paper/2311.06190/) (2023)
- [Filling the G_ap_s: Multivariate Time Series Imputation by Graph Neural Networks](https://mlsanity.com/paper/2108.00298/) (2021)
- [PriSTI: A Conditional Diffusion Framework for Spatiotemporal Imputation](https://mlsanity.com/paper/2302.09746/) (2023)
- [Learning to Reconstruct Missing Data from Spatiotemporal Graphs with Sparse Observations](https://mlsanity.com/paper/2205.13479/) (2022)
- [TimeFilter: Patch-Specific Spatial-Temporal Graph Filtration for Time Series Forecasting](https://mlsanity.com/paper/2501.13041/) (2025)
- [Deep Learning for Multivariate Time Series Imputation: A Survey](https://mlsanity.com/paper/2402.04059/) (2024)
- [ImputeFormer: Low Rankness-Induced Transformers for Generalizable Spatiotemporal Imputation](https://mlsanity.com/paper/2312.01728/) (2023)
- [MIRA: Medical Time Series Foundation Model for Real-World Health Data](https://mlsanity.com/paper/2506.07584/) (2025)
- [Time Series Continuous Modeling for Imputation and Forecasting with Implicit Neural Representations](https://mlsanity.com/paper/2306.05880/) (2023)
- [TimeDART: A Diffusion Autoregressive Transformer for Self-Supervised Time Series Representation](https://mlsanity.com/paper/2410.05711/) (2024)
- [WeatherGFM: Learning A Weather Generalist Foundation Model via In-context Learning](https://mlsanity.com/paper/2411.05420/) (2024)
- [Graph Spatiotemporal Process for Multivariate Time Series Anomaly Detection with Missing Values](https://mlsanity.com/paper/2401.05800/) (2024)
- [Higher-order Spatio-temporal Physics-incorporated Graph Neural Network for Multivariate Time Series Imputation](https://mlsanity.com/paper/2405.10995/) (2024)
- [Task-oriented Time Series Imputation Evaluation via Generalized Representers](https://mlsanity.com/paper/2410.06652/) (2024)
- [Mining of Switching Sparse Networks for Missing Value Imputation in Multivariate Time Series](https://mlsanity.com/paper/2409.09930/) (2024)
- [Filling out the missing gaps: Time Series Imputation with Semi-Supervised Learning](https://mlsanity.com/paper/2304.04275/) (2023)

## Abstract (arXiv)

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.