通过半正定核密度估计实现分布忠实插补
Distributionally Faithful Imputation via Positive Semi-Definite Kernel Density Estimation
AI总结：
研究针对缺失值问题，提出通过半正定核密度估计进行分布忠实插补的方法，将插补重述为密度估计，利用PSD核密度得到凸经验风险问题并求解，实验表明该方法在分布准确性上有竞争力，优于流行基线。
摘要：
缺失值会破坏统计推断和机器学习流程，然而大多数插补方法依赖启发式或严格的参数假设，忽略了联合数据分布。我们将完全随机缺失（MCAR）情况下的插补重新表述为从掩码观测值进行密度估计：估计一个其观测边际与数据中的边际完全匹配的分布。利用半正定（PSD）核密度，我们得到一个具有封闭形式边际的凸经验风险问题，可通过牛顿内点法求解。所得的PSD插补模型从相同的拟合密度产生单值和多值插补，对于非常规则的概率具有统计一致性，快速自适应超额风险优于维度诅咒。在一个合成数据集和十一个真实世界数据集上的初步实验表明，与流行的插补基线相比，其分布准确性具有竞争力，具有很强的实际应用前景。
英文摘要：
Missing values undermine statistical inference and machine learning pipelines, yet most imputation methods rely on heuristics or restrictive parametric assumptions that ignore the joint data distribution. We recast imputation under missing completely at random (MCAR) as density estimation from masked observations: estimate a distribution whose observed marginals exactly match those in the data. Leveraging positive semi definite (PSD) kernel densities we obtain a convex empirical risk problem with closed form marginals, solvable by a Newton interior point method. The resulting PSD Impute model yields both single and multiple imputations from the same fitted density, enjoys statistical consistency with fast adaptive excess risk beating the curse of dimensionality for very regular probabilities. Preliminary experiments on one synthetic and eleven real world datasets already indicate competitive distributional accuracy compared with popular imputation baselines, suggesting strong practical promise.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
