# Markov Missing Graph: A Graphical Approach for Missing Data Imputation

arXiv: https://arxiv.org/abs/2509.03410 · HTML: https://mlsanity.com/paper/2509.03410/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 40 references that are in the map.
- First posted on arXiv 3 Sep 2025.

## Builds on (most cited first, 16 of 16)

- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [Prediction-Powered Inference](https://mlsanity.com/paper/2301.09633/) (2023)
- [Handling Missing Data with Graph Representation Learning](https://mlsanity.com/paper/2010.16418/) (2020)
- [Composing graphical models with neural networks for structured representations and fast inference](https://mlsanity.com/paper/1603.06277/) (2016)
- [Graphical Models for Processing Missing Data](https://mlsanity.com/paper/1801.03583/) (2018)
- [Full Law Identification In Graphical Models Of Missing Data: Completeness Results](https://mlsanity.com/paper/2004.04872/) (2020)
- [Identification In Missing Data Models Represented By Directed Acyclic Graphs](https://mlsanity.com/paper/1907.00241/) (2019)
- [Semiparametric Inference for Non-monotone Missing-Not-at-Random Data: the No Self-Censoring Model](https://mlsanity.com/paper/1909.01848/) (2019)
- [Multiple Imputation of Missing Categorical and Continuous Values via Bayesian Mixture Models with Local Dependence](https://mlsanity.com/paper/1410.0438/) (2014)
- [Itemwise conditionally independent nonresponse modeling for incomplete multivariate data](https://mlsanity.com/paper/1609.00656/) (2016)
- [Discrete Choice Models for Nonmonotone Nonignorable Missing Data: Identification and Inference](https://mlsanity.com/paper/1607.02631/) (2016)
- [Pattern graphs: a graphical approach to nonmonotone missing data](https://mlsanity.com/paper/2004.00744/) (2020)
- [A self-censoring model for multivariate nonignorable nonmonotone missing data](https://mlsanity.com/paper/2207.08535/) (2022)
- [Nonparametric Pattern-Mixture Models for Inference with Missing Data](https://mlsanity.com/paper/1904.11085/) (2019)
- [Modeling Missing at Random Neuropsychological Test Scores Using a Mixture of Binomial Product Experts](https://mlsanity.com/paper/2310.09384/) (2023)
- [Recursive Equations For Imputation Of Missing Not At Random Data With Sparse Pattern Support](https://mlsanity.com/paper/2507.16107/) (2025)

## 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.