Modeling Multivariate Missingness with Tree Graphs and Conjugate Odds

2026-02-18

AI Summary

This study addresses the challenge of modeling multivariate missingness patterns under missing not at random (MNAR) mechanisms by proposing a novel approach based on tree-structured graphical models and conjugate prior families. The method preserves closure within the full-data distribution family while providing a conjugate model for the observed data and enabling a concise, efficient imputation mechanism for missing entries. By integrating parametric selection bias modeling, graph structure learning, and sensitivity analysis, the framework flexibly captures complex missingness mechanisms and supports robust inference. Extensive simulations and real-data analyses demonstrate that the proposed method substantially outperforms existing approaches in terms of missing mechanism modeling accuracy, imputation precision, and overall statistical inference performance.

Technology Category

• Reasoning under Uncertainty: Graphical Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Data Mining & Knowledge Management: Mining of Visual, Multimedia & Multimodal Data

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

In this paper, we analyze a specific class of missing not at random (MNAR) assumptions called tree graphs, extending upon the work of pattern graphs. We build off previous work by introducing the idea of a conjugate odds family in which certain parametric models on the selection odds can preserve the data distribution family across all missing data patterns. Under a conjugate odds family and a tree graph assumption, we are able to model the full data distribution elegantly in the sense that for the observed data, we obtain a model that is conjugate from the complete-data, and for the missing entries, we create a simple imputation model. In addition, we investigate the problem of graph selection, sensitivity analysis, and statistical inference. Using both simulations and real data, we illustrate the applicability of our method.

Problem

• missing not at random
• tree graphs
• multivariate missingness
• conjugate odds
• data distribution

Innovation

• conjugate odds family
• tree graphs
• missing not at random
• multivariate missingness
• imputation model