Multivariate Time Series Data Imputation via Distributionally Robust Regularization

2026-01-31

AI Summary

This work addresses the challenges of distributional shift, bias, and overfitting in multivariate time series imputation caused by non-stationarity and systematic missingness. To this end, we propose the Distributionally Robust Imputation Objective (DRIO), which introduces distributionally robust optimization into time series imputation for the first time. DRIO models the uncertainty between the observed and true data distributions using a Wasserstein ambiguity set and jointly minimizes the reconstruction error and the worst-case distributional divergence. Leveraging duality theory, the infinite-dimensional measure optimization is transformed into an adversarial search over observed sample trajectories, enabling the design of an adversarial learning algorithm compatible with deep neural networks. Extensive experiments on real-world datasets demonstrate that DRIO consistently achieves significant performance gains under both missing-at-random and non-random missing scenarios, attaining a Pareto-optimal trade-off between reconstruction accuracy and distributional consistency.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Multivariate time series (MTS) imputation is often compromised by mismatch between observed and true data distributions -- a bias exacerbated by non-stationarity and systematic missingness. Standard methods that minimize reconstruction error or encourage distributional alignment risk overfitting these biased observations. We propose the Distributionally Robust Regularized Imputer Objective (DRIO), which jointly minimizes reconstruction error and the divergence between the imputer and a worst-case distribution within a Wasserstein ambiguity set. We derive a tractable dual formulation that reduces infinite-dimensional optimization over measures to adversarial search over sample trajectories, and propose an adversarial learning algorithm compatible with flexible deep learning backbones. Comprehensive experiments on diverse real-world datasets show DRIO consistently improves imputation under both missing-completely-at-random and missing-not-at-random settings, reaching Pareto-optimal trade-offs between reconstruction accuracy and distributional alignment.

Problem

• Multivariate Time Series
• Data Imputation
• Distributional Mismatch
• Non-stationarity
• Systematic Missingness

Innovation

• Distributionally Robust Optimization
• Time Series Imputation
• Wasserstein Ambiguity Set
• Adversarial Learning
• Multivariate Time Series