mlsanityData to 7 Oct 2026

Markov Missing Graph: A Graphical Approach for Missing Data Imputation

arXiv 2509.03410 ↗First posted 3 Sep 2025stat.ME math.ST stat.MLcited by 0

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Abstract (arXiv)

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.

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References · 16

  1. 2018GAIN: Missing Data Imputation using Generative Adversarial Netscited by 349
  2. 2023Prediction-Powered Inferencecited by 214
  3. 2020Handling Missing Data with Graph Representation Learningcited by 132
  4. 2016Composing graphical models with neural networks for structured representations and fast inferencecited by 113
  5. 2018Graphical Models for Processing Missing Datacited by 57
  6. 2020Full Law Identification In Graphical Models Of Missing Data: Completeness Resultscited by 26
  7. 2019Identification In Missing Data Models Represented By Directed Acyclic Graphscited by 19
  8. 2019Semiparametric Inference for Non-monotone Missing-Not-at-Random Data: the No Self-Censoring Modelcited by 12
  9. 2014Multiple Imputation of Missing Categorical and Continuous Values via Bayesian Mixture Models with Local Dependencecited by 10
  10. 2016Itemwise conditionally independent nonresponse modeling for incomplete multivariate datacited by 6
  11. 2016Discrete Choice Models for Nonmonotone Nonignorable Missing Data: Identification and Inferencecited by 5
  12. 2020Pattern graphs: a graphical approach to nonmonotone missing datacited by 4
4 more
  1. 2022A self-censoring model for multivariate nonignorable nonmonotone missing datacited by 4
  2. 2019Nonparametric Pattern-Mixture Models for Inference with Missing Datacited by 1
  3. 2023Modeling Missing at Random Neuropsychological Test Scores Using a Mixture of Binomial Product Expertscited by 1
  4. 2025Recursive Equations For Imputation Of Missing Not At Random Data With Sparse Pattern Supportcited by 1

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