# Multivariate Time Series Data Imputation via Distributionally Robust Regularization

arXiv: https://arxiv.org/abs/2602.00844 · HTML: https://mlsanity.com/paper/2602.00844/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 56 references that are in the map.
- First posted on arXiv 31 Jan 2026.

## Builds on (most cited first, 19 of 19)

- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [Certifying Some Distributional Robustness with Principled Adversarial Training](https://mlsanity.com/paper/1710.10571/) (2017)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [Generative Moment Matching Networks](https://mlsanity.com/paper/1502.02761/) (2015)
- [Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models](https://mlsanity.com/paper/2208.09399/) (2022)
- [SAITS: Self-Attention-based Imputation for Time Series](https://mlsanity.com/paper/2202.08516/) (2022)
- [Generative Models and Model Criticism via Optimized Maximum Mean Discrepancy](https://mlsanity.com/paper/1611.04488/) (2016)
- [Missing Data Imputation using Optimal Transport](https://mlsanity.com/paper/2002.03860/) (2020)
- [Learning to Reconstruct Missing Data from Spatiotemporal Graphs with Sparse Observations](https://mlsanity.com/paper/2205.13479/) (2022)
- [not-MIWAE: Deep Generative Modelling with Missing not at Random Data](https://mlsanity.com/paper/2006.12871/) (2020)
- [Sinkhorn Divergences for Unbalanced Optimal Transport](https://mlsanity.com/paper/1910.12958/) (2019)
- [ImputeFormer: Low Rankness-Induced Transformers for Generalizable Spatiotemporal Imputation](https://mlsanity.com/paper/2312.01728/) (2023)
- [Generative Modeling through the Semi-dual Formulation of Unbalanced Optimal Transport](https://mlsanity.com/paper/2305.14777/) (2023)
- [Sinkhorn Distributionally Robust Optimization](https://mlsanity.com/paper/2109.11926/) (2021)
- [The Wasserstein-Fourier Distance for Stationary Time Series](https://mlsanity.com/paper/1912.05509/) (2019)
- [On the Sample Complexity of Graphical Model Selection for Non-Stationary Processes](https://mlsanity.com/paper/1701.04724/) (2017)
- [Temporal Wasserstein Imputation: A Versatile Method for Time Series Imputation](https://mlsanity.com/paper/2411.02811/) (2024)
- [Missing data in non-stationary multivariate time series from digital studies in Psychiatry](https://mlsanity.com/paper/2506.14946/) (2025)

## Abstract (arXiv)

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.