Prediction with Missing Data: Target Probabilities and Missingness Mechanisms

2026-03-18

AI Summary

This work addresses the lack of a unified theoretical framework for handling missing data, particularly under missing-not-at-random (MNAR) mechanisms where existing methods often fail to ensure consistent prediction. The authors propose a novel framework that explicitly distinguishes between two prediction objectives—depending on whether the observation indicators of variables are utilized—and introduces a fine-grained classification of missingness mechanisms accordingly. Building on this distinction, they establish conditions weaker than missing-at-random (MAR) under which consistent prediction remains achievable. By integrating probabilistic modeling, pattern-wise submodeling, and unconditional imputation, the framework supports a comprehensive prediction theory spanning model development, validation, and deployment. Empirical evaluations on both synthetic data and a real-world emergency trauma prediction task demonstrate that the proposed approach consistently achieves optimal predictive performance across diverse missingness mechanisms, thereby overcoming the limitations of conventional methods reliant on the MAR assumption.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Conditions ensuring optimal parameter estimation in the presence of missing data are well established in inference, typically relying on the Missing-at-Random (MAR) assumption. In prediction, similar principles are often assumed to apply. However, methods considered biased in inference, such as pattern sub-modelling or unconditional imputation, have been shown to achieve optimal predictive performance under any missingness mechanism, including non-MAR (MNAR). To explain this apparent contradiction, we introduce a new formal framework for describing missingness in prediction. Central to this framework is a distinction between two prediction targets, defined according to whether or not the indicator of observation of the predictors is exploited to predict the outcome. This distinction leads to a classification of the missingness mechanisms describing the conditions under which these targets are equal, and when consistent prediction of each is achievable. A key result is that both targets may be consistently predicted under conditions weaker than MAR. We discuss the implications of this paradigm for handling missing data in prediction, distinguishing between missingness at development, validation and deployment of a forecaster. The findings are illustrated using simulated data and a real-world application with the prediction of significant injury after trauma upon arrival at the emergency department.

Problem

• missing data
• prediction
• missingness mechanism
• non-MAR
• target probability

Innovation

• missing data
• prediction target
• missingness mechanism
• non-MAR
• consistent prediction