Multivariate Time Series Data Imputation via Distributionally Robust Regularization
For practitioners dealing with incomplete multivariate time series, this work offers a robust imputation method that handles distribution shifts, though it is an incremental improvement over existing distributionally robust approaches.
The paper addresses the bias in multivariate time series imputation caused by distribution mismatch due to non-stationarity and systematic missingness. The proposed DRIO method achieves robust imputation and improved downstream forecasting across diverse real-world datasets.
Multivariate time series imputation is often compromised by mismatch between the observed and true data distributions, a bias induced by the combined effects of time-series non-stationarity and systematic missingness. Standard methods that encourage point-wise reconstruction or direct distributional alignment may overfit these biased observations. We propose the Distributionally Robust Regularized Imputer Objective (DRIO), which jointly minimizes reconstruction error and the worst-case divergence between the imputer distribution and data distributions within a Wasserstein ambiguity set. We derive a tractable upper-bound surrogate that reduces infinite-dimensional optimization over measures to adversarial search over sample trajectories, and develop an alternating learning algorithm compatible with modern deep learning backbones. Comprehensive experiments on diverse real-world datasets show that DRIO consistently provides robust imputation and suggests improved downstream forecasting under various missingness scenarios.