The ubiquity of missing values in real-world datasets poses a challenge for statistical inference and can prevent similar datasets from being analyzed in the same study, precluding many existing datasets from being used for new analyses. While an extensive collection of packages and algorithms have been developed for data imputation, the overwhelming majority perform poorly if there are many missing values and low sample sizes, which are unfortunately common characteristics in empirical data. Such low-accuracy estimations adversely affect the performance of downstream statistical models. We develop a statistical inference framework for regression and classification in the presence of missing data without imputation. Our framework, RIFLE (Robust InFerence via Low-order moment Estimations), estimates low-order moments of the underlying data distribution with corresponding confidence intervals to learn a distributionally robust model. We specialize our framework to linear regression and normal discriminant analysis, and we provide convergence and performance guarantees. This framework can also be adapted to impute missing data. In numerical experiments, we compare RIFLE to several state-of-the-art approaches (including MICE, Amelia, MissForest, KNN-imputer, MIDA, and Mean Imputer) for imputation and inference in the presence of missing values. Our experiments demonstrate that RIFLE outperforms other benchmark algorithms when the percentage of missing values is high and/or when the number of data points is relatively small. RIFLE is publicly available at https://github.com/optimization-for-data-driven-science/RIFLE.

翻译：现实数据集中缺失值的普遍存在给统计推断带来了挑战，并可能阻碍相似数据集在同一研究中的分析，导致许多现有数据集无法用于新分析。尽管已有大量用于数据插补的软件包和算法被开发出来，但绝大多数方法在面对高缺失率和低样本量时表现不佳——而这两者在实证数据中往往是常见特征。这种低精度估计会严重削弱下游统计模型的性能。本文针对存在缺失数据的情况，提出了一种无需插补的回归与分类统计推断框架。该框架名为RIFLE（基于低阶矩估计的稳健推断），通过估计底层数据分布的低阶矩及其置信区间，学习一个分布鲁棒模型。我们将该框架具体应用于线性回归和正态判别分析，并提供了收敛性与性能保障。该框架还可适用于缺失数据的插补任务。在数值实验中，我们将RIFLE与多种前沿方法（包括MICE、Amelia、MissForest、KNN插补器、MIDA和均值插补器）在缺失值环境下的插补与推断性能进行了比较。实验结果表明，当缺失值比例较高或数据样本量较小时，RIFLE优于其他基准算法。RIFLE的公开代码见 https://github.com/optimization-for-data-driven-science/RIFLE。