Emputation: Identification-Guided Neural Imputation Framework

2026-07-06

AI Summary

This work addresses the challenge of accurately modeling the extrapolation distribution of missing variables under non-ignorable missingness. The authors propose Emputation, a novel framework that explicitly incorporates identifiability assumptions into the training objective of deep generative models. By employing an energy score–based risk function, Emputation directly models the conditional distribution of missing variables and supports both multiple imputation and conditional sampling. The method is designed to accommodate a variety of non-ignorable missing data mechanisms. In simulation studies, it significantly outperforms baseline approaches in both point estimation and distributional metrics. Its practical efficacy is further demonstrated on a real-world Alzheimer’s disease dataset, confirming its applicability to complex biomedical data with non-random missingness.

Abstract

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.

Problem

• missing data
• imputation
• identification
• extrapolation distribution
• missing-not-at-random

Innovation

• neural imputation
• identification-guided learning
• extrapolation distribution
• missing-not-at-random
• energy-score-based risk