Weighting-Based Identification and Estimation in Graphical Models of Missing Data

2026-02-11

AI Summary

This study addresses selection bias arising from missing data in graphical models by proposing an intervention-based framework for identification and estimation. Treating missingness indicators as intervenable variables, the authors introduce a novel tree-based identification algorithm to explicitly characterize the propagation pathways of selection bias and leverage do-calculus to assess the identifiability of target functionals. Building on this foundation, they develop a recursive inverse probability weighting approach to construct efficient estimating equations that jointly model the missingness mechanism and parameters of interest. The accompanying R package, flexMissing, enables end-to-end analysis, and both simulation studies and real-data applications demonstrate that the proposed method accurately determines identifiability and yields robust estimates.

Technology Category

• Reasoning under Uncertainty: Graphical Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Knowledge Representation and Reasoning: Diagnosis and Abductive Reasoning

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: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

We propose a constructive algorithm for identifying complete data distributions in graphical models of missing data. The complete data distribution is unrestricted, while the missingness mechanism is assumed to factorize according to a conditional directed acyclic graph. Our approach follows an interventionist perspective in which missingness indicators are treated as variables that can be intervened on. A central challenge in this setting is that sequences of interventions on missingness indicators may induce and propagate selection bias, so that identification can fail even when a propensity score is invariant to available interventions. To address this challenge, we introduce a tree-based identification algorithm that explicitly tracks the creation and propagation of selection bias and determines whether it can be avoided through admissible intervention strategies. The resulting tree provides both a diagnostic and a constructive characterization of identifiability under a given missingness mechanism. Building on these results, we develop recursive inverse probability weighting procedures that mirror the intervention logic of the identification algorithm, yielding valid estimating equations for both the missingness mechanism and functionals of the complete data distribution. Simulation studies and a real-data application illustrate the practical performance of the proposed methods. An accompanying R package, flexMissing, implements all proposed procedures.

Problem

• missing data
• graphical models
• selection bias
• identifiability
• intervention

Innovation

• interventionist perspective
• selection bias propagation
• tree-based identification algorithm
• recursive inverse probability weighting
• graphical models of missing data