[2604.04567] Generative Modeling under Non-Monotonic MAR Missingness via Approximate Wasserstein Gradient Flows

Statistics > Machine Learning arXiv:2604.04567 (stat) [Submitted on 6 Apr 2026] Title:Generative Modeling under Non-Monotonic MAR Missingness via Approximate Wasserstein Gradient Flows Authors:Gitte Kremling, Jeffrey Näf, Johannes Lederer View a PDF of the paper titled Generative Modeling under Non-Monotonic MAR Missingness via Approximate Wasserstein Gradient Flows, by Gitte Kremling and 2 other authors View PDF HTML (experimental) Abstract:The prevalence of missing values in data science poses a substantial risk to any further analyses. Despite a wealth of research, principled nonparametric methods to deal with general non-monotone missingness are still scarce. Instead, ad-hoc imputation methods are often used, for which it remains unclear whether the correct distribution can be recovered. In this paper, we propose FLOWGEM, a principled iterative method for generating a complete dataset from a dataset with values Missing at Random (MAR). Motivated by convergence results of the ignoring maximum likelihood estimator, our approach minimizes the expected Kullback-Leibler (KL) divergence between the observed data distribution and the distribution of the generated sample over different missingness patterns. To minimize the KL divergence, we employ a discretized particle evolution of the corresponding Wasserstein Gradient Flow, where the velocity field is approximated using a local linear estimator of the density ratio. This construction yields a data generation scheme that ite...