arXiv:2607.28698cs.LG2026-07

让流匹配模型处理缺失数据,理论证明无偏差且最优完成数为1。

Flow Matching with Missing Data

论文配图:Flow Matching with Missing Data
图 1 · 摘自论文原文
  • 将缺失坐标视为隐变量,平均化损失函数以修正偏差
  • 单次补全即可达到完整数据的估计方差,无需多次采样
  • 理论揭示真实补全分布的偏差可被条件Wasserstein距离控制

流匹配通常假设训练数据完全可观测,但现实应用中常存在缺失。本文提出缺失数据流匹配方法,将缺失坐标视为隐变量,对可能取值平均流匹配损失。我们首先证明该修正为精确而非近似;在完全随机缺失且使用真实补全条件下,不完整数据目标函数等于完整数据目标函数,因此缺失不影响学习内容,困难全部转移至补全模型。有限样本分析回答了算法留下的设计问题,结果与直觉不符:缺失仅转移估计方差而非新增,每样本一次补全已达完整数据方差,固定评估预算下一次补全最优。学习的补全模型引入单一不可约偏差,其上界由其期望条件Wasserstein距离于真实补全分布决定。实验验证理论预测,表明确定性而非冻结插补会坍塌生成分布,并在真实表格数据上优于经典及深度插补基线。

原文摘要 · Abstract (English)

Flow matching assumes fully observed training data, which many real-world applications rarely provide. We propose Missing-Data Flow Matching, which treats the missing coordinates of training samples as latent variables and averages the flow matching loss over the values they could take. We first prove the correction is exact rather than approximate. Under missing completely at random with true completions, the incomplete-data objective equals the complete-data objective, so missingness changes nothing about what flow matching learns and the entire difficulty relocates to the completion model. Our finite-sample analysis then answers design questions that the algorithm leaves open, and the answers are not the ones intuition suggests. Missingness transfers estimator variance rather than adding it, one completion per example already matches complete-data variance exactly, and under a fixed evaluation budget one completion is optimal. A learned completion model contributes a single irreducible bias, which we bound by its expected conditional Wasserstein distance to the true completion law. Experiments numerically validate the theoretical predictions, show that deterministic rather than frozen imputation is what collapses the generated distribution, and place our method alongside strong classical and deep imputation baselines on real tabular data.

流匹配缺失数据理论分析插补

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