Imputation via Domain Adaptation: Rethinking Variable Subset Forecasting from Knowledge Transfer

Multivariate time series forecasting in practical deployment faces a critical challenge termed Variable Subset Forecasting (VSF), where certain variables accessible during training are entirely missing during inference. This creates a stark discrepancy between the training (source domain with full variables) and inference (target domain with partial variables) environments, disrupting cross-variable dependencies and fragmenting global temporal patterns. Existing imputation methods, limited to transferring local knowledge (e.g., temporal neighbors or pairwise correlations), fail to capture essential global dynamics, leading to severe performance degradation under distribution shifts. To address these challenges, we redefine VSF as a cross-domain knowledge transfer problem and propose VIDA, a framework that systematically transfers Variable Invariant knowledge from complete to partial observations through Domain Adaptation. Key to our approach is (1) Global time-frequency joint representation learning, which encodes temporal dynamics via dilated convolutions and captures low-frequency spectral consistency using Fourier neural operators, and (2) Sinkhorn-regularized distribution alignment to bridge non-overlapping feature supports across domains via optimal transport. Unlike imputation-first methods, VIDA enforces task-driven consistency by jointly optimizing predictions on reconstructed and original data, ensuring the transferred knowledge directly enhances forecasting robustness. Extensive experiments across four real-world datasets show that VIDA outperforms state-of-the-art imputation methods by 25% on average with partially observed variables. This work establishes a new paradigm for variable-missing scenarios by unifying imputation and forecasting through principled knowledge transfer.