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 iteratively transports an initial particle ensemble toward the target distribution. Simulation studies and real-data benchmarks demonstrate that FLOWGEM achieves state-of-the-art performance across a range of settings, including the challenging case of non-monotonic MAR mechanisms. Together, these results position FLOWGEM as a principled and practical alternative to existing imputation methods, and a decisive step towards closing the gap between theoretical rigor and empirical performance.

翻译：数据科学中缺失值的普遍存在对任何进一步分析都构成了重大风险。尽管已有大量研究，但处理一般非单调缺失机制的原则性非参数方法仍然稀缺。相反，人们常采用临时插补方法，而此类方法能否恢复正确的分布尚不明确。本文提出FLOWGEM，这是一种从含随机缺失（MAR）值的数据集中生成完整数据集的原则性迭代方法。受忽略极大似然估计收敛结果的启发，该方法通过最小化不同缺失模式下观测数据分布与生成样本分布之间的期望Kullback-Leibler（KL）散度。为最小化KL散度，我们采用相应Wasserstein梯度流的离散化粒子演化过程，其中速度场通过密度比的局部线性估计来近似。该构造产生一种数据生成方案，可迭代地将初始粒子系综向目标分布输运。仿真研究和真实数据基准测试表明，FLOWGEM在包括非单调MAR机制这一挑战性场景在内的多种设置中均实现了最先进的性能。这些结果共同将FLOWGEM定位为现有插补方法的原则性实用替代方案，并标志着弥合理论严谨性与实证性能之间差距的决定性一步。