  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.
