Emputation: Identification-Guided Neural Imputation Framework

We propose Emputation, a deep generative framework for learning imputation models. Emputation targets the extrapolation distribution of missing variables given observed variables, and training is guided by specific missingness assumptions that guarantee identification of the target distribution. The training objective, called the emputation risk, is an energy-score-based risk in which the identification assumption determines how observed entries are masked and which observations contribute to training. The resulting framework enables direct conditional sampling for multiple imputation. We show that the population minimizer of the emputation risk recovers the target extrapolation distribution under a broad class of identification assumptions, including several missing-not-at-random assumptions. Simulations show strong performance under both pointwise and distributional evaluation metrics, and an application to an Alzheimer's disease dataset demonstrates its practical value.

Masking criteria for selecting an imputation model

The masking-one-out (MOO) procedure, masking an observed entry and comparing it versus its imputed values, is a very common procedure for comparing imputation models. We study the optimum of this procedure and generalize it to a missing data assumption and establish the corresponding semi-parametric efficiency theory. However, MOO is a measure of prediction accuracy, which is not ideal for evaluating an imputation model. To address this issue, we introduce three modified MOO criteria, based on rank transformation, energy distance, and likelihood principle, that allow us to select an imputation model that properly account for the stochastic nature of data. The likelihood approach further enables an elegant framework of learning an imputation model from the data and we derive its statistical and computational learning theories as well as consistency of BIC model selection. We also show how MOO is related to the missing-at-random assumption. Finally, we introduce the prediction-imputation diagram, a two-dimensional diagram visually comparing both the prediction and imputation utilities for various imputation models.

Markov Missing Graph: A Graphical Approach for Missing Data Imputation

We introduce the Markov missing graph (MMG), a novel framework that imputes missing data based on undirected graphs. MMG leverages conditional independence relationships to locally decompose the imputation model. To establish the identification, we introduce the Principle of Available Information (PAI), which guides the use of all relevant observed data. We then propose a flexible statistical learning paradigm, MMG Imputation Risk Minimization under PAI, that frames the imputation task as an empirical risk minimization problem. This framework is adaptable to various modeling choices. We develop theories of MMG, including the connection between MMG and Little's complete-case missing value assumption, recovery under missing completely at random, efficiency theory, and graph-related properties. We show the validity of our method with simulation studies and illustrate its application with a real-world Alzheimer's data set.