通过降低数据与缺失模式间互信息，提升缺失值填补精度。
Missing Data Imputation by Reducing Mutual Information with Rectified Flows
- 迭代优化使数据与缺失掩码的互信息逐步下降
- 理论证明最优填补可通过求解特定常微分方程实现
- 兼容多种现有方法，适合高维真实数据填补
本文提出一种新型迭代缺失数据填补方法，通过逐步减少数据与缺失掩码之间的互信息来实现。受基于GAN的方法启发，该方法显式地最小化当前迭代中数据与缺失掩码联合分布与边缘分布乘积间的KL散度。理论上，最优填补可通过求解一个速度场最小化修正流训练目标的常微分方程（ODE）实现。我们进一步证明，部分已有填补技术可视为本互信息减少框架的近似特例。在合成数据和真实世界数据集上的广泛实验验证了所提方法的有效性，展现了更优的填补性能。代码已开源：https://github.com/yujhml/MIRI-Imputation。
原文摘要 · Abstract (English)
This paper introduces a novel iterative method for missing data imputation that sequentially reduces the mutual information between data and the corresponding missingness mask. Inspired by GAN-based approaches that train generators to decrease the predictability of missingness patterns, our method explicitly targets this reduction in mutual information. Specifically, our algorithm iteratively minimizes the KL divergence between the joint distribution of the imputed data and missingness mask, and the product of their marginals from the previous iteration. We show that the optimal imputation under this framework can be achieved by solving an ODE whose velocity field minimizes a rectified flow training objective. We further illustrate that some existing imputation techniques can be interpreted as approximate special cases of our mutual-information-reducing framework. Comprehensive experiments on synthetic and real-world datasets validate the efficacy of our proposed approach, demonstrating its superior imputation performance. Our implementation is available at https://github.com/yujhml/MIRI-Imputation.
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