Multiple imputation (MI) has been widely applied to missing value problems in biomedical, social and econometric research, in order to avoid improper inference in the downstream data analysis. In the presence of high-dimensional data, imputation models that include feature selection, especially $\ell_1$ regularized regression (such as Lasso, adaptive Lasso, and Elastic Net), are common choices to prevent the model from underdetermination. However, conducting MI with feature selection is difficult: existing methods are often computationally inefficient and poor in performance. We propose MISNN, a novel and efficient algorithm that incorporates feature selection for MI. Leveraging the approximation power of neural networks, MISNN is a general and flexible framework, compatible with any feature selection method, any neural network architecture, high/low-dimensional data and general missing patterns. Through empirical experiments, MISNN has demonstrated great advantages over state-of-the-art imputation methods (e.g. Bayesian Lasso and matrix completion), in terms of imputation accuracy, statistical consistency and computation speed.

本文提出了一个新的算法 MISNN，用于处理高维缺失数据的多重插补问题，该算法借助于神经网络的逼近能力，将特征选择嵌入 MI 模型中，经过实验证明在插补准确度、统计一致性和计算速度等方面优于现有的 Bayesian Lasso 和矩阵补全等最新算法。

MISNN: 半参数神经网络多元插补