异质缺失数据的重要性加权变分插补

Importance-Weighted Variational Imputation for Heterogeneous Missing Data

摘要: 针对异质表格数据中的缺失值插补问题，本文构建重要性加权变分插补框架H-MIWAE (Heterogeneous Missing-data Importance-Weighted Autoencoder)。该框架在混合离散–连续潜变量结构下引入类型特异观测分布，并结合多样本重要性加权目标与自归一化重要性采样，实现对异质属性的统一建模与条件预测。为区分训练阶段与插补阶段的重要性采样作用，本文分别以$K_{tr}$ 和$L_{imp}$ 表示两个阶段使用的重要性样本数，并研究二者对不同属性类型插补性能的联合影响。在合成数据集和真实异质数据集上的实验表明，H-MIWAE能够对多类异质属性进行统一插补，并在不同数据条件下表现出较强的竞争力。结果表明，多样本训练所带来的插补收益依赖于后续的重要性采样，且这种依赖在不同属性类型上表现并不一致。

Abstract: This paper develops the Heterogeneous Missing-data Importance-Weighted Autoencoder (H-MIWAE), an importance-weighted variational imputation framework for missing-value imputation in heterogeneous tabular data. Under a mixed discrete-continuous latent-variable structure, the framework incorporates type-specific observation distributions and combines a multi-sample importance-weighted objective with self-normalized importance sampling to achieve unified modeling and conditional prediction for heterogeneous attributes. To distinguish the roles of importance sampling in the training and imputation stages, $K_{tr}$ and $L_{imp}$ denote the numbers of importance samples used in the two stages, respectively, and their joint effects on imputation performance across different attribute types are investigated. Experiments on synthetic and real-world heterogeneous data sets show that H-MIWAE can perform unified imputation for multiple types of heterogeneous attributes and achieves competitive performance under different data settings. The results further show that the imputation gains brought by multi-sample training depend on the subsequent importance sampling, and that this dependence varies across attribute types.