An Overview on Regularized Regression for Multiple Imputation in High‐Dimensional Data: Concepts, Methods, and Practical Guidance

High‐dimensional datasets with missing values present substantial challenges for statistical modeling and inference because conventional multiple imputation (MI) methods may become unstable or nonidentifiable under severe dimensional imbalance. Regularized regression techniques, including lasso, ridge, and related Bayesian formulations, offer a promising way to improve feasibility by enabling variable selection and stabilizing estimation in high‐dimensional settings. This overview provides a structured synthesis of regularized regression‐based MI methods, organized into direct and indirect integration strategies, Bayesian sparsity‐inducing approaches, optimization‐based and sequential penalization methods, and post‐imputation resampling or adjustment techniques. For each category, we summarize the underlying methodological logic, review empirical findings from simulation studies, and highlight practical considerations for implementation. Particular attention is given to methods developed for missing not at random (MNAR) and to the inferential challenges that arise after variable selection. Overall, this overview aims to help researchers choose regularized imputation strategies that are methodologically appropriate, practically feasible, and aligned with the analytical goals of high‐dimensional incomplete‐data studies. This article is categorized under: Technologies > Machine Learning Algorithmic Development > Statistics