Multivariate Time Series Data Imputation via Distributionally Robust Regularization

TL;DR

This paper introduces DRIO, a novel imputation method for multivariate time series that enhances robustness against distributional bias caused by non-stationarity and missing data, using distributionally robust regularization.

Contribution

The paper proposes a new distributionally robust regularization framework for time series imputation, with a tractable surrogate and an efficient learning algorithm.

Findings

DRIO outperforms existing methods in robustness across diverse datasets.

It improves downstream forecasting accuracy under various missingness scenarios.

The approach effectively mitigates bias from distribution mismatch in time series data.

Abstract

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.