# Pattern graphs: a graphical approach to nonmonotone missing data

arXiv: https://arxiv.org/abs/2004.00744 · HTML: https://mlsanity.com/paper/2004.00744/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Apr 2020.

## Built on by (most cited first, 4 of 4)

- [Evaluation of Active Feature Acquisition Methods for Static Feature Settings](https://mlsanity.com/paper/2312.03619/) (2023)
- [Robust prediction under missingness shifts](https://mlsanity.com/paper/2406.16484/) (2024)
- [Recursive Equations For Imputation Of Missing Not At Random Data With Sparse Pattern Support](https://mlsanity.com/paper/2507.16107/) (2025)
- [Markov Missing Graph: A Graphical Approach for Missing Data Imputation](https://mlsanity.com/paper/2509.03410/) (2025)

## Abstract (arXiv)

We introduce the concept of pattern graphs--directed acyclic graphs representing how response patterns are associated. A pattern graph represents an identifying restriction that is nonparametrically identified/saturated and is often a missing not at random restriction. We introduce a selection model and a pattern mixture model formulations using the pattern graphs and show that they are equivalent. A pattern graph leads to an inverse probability weighting estimator as well as an imputation-based estimator. We also study the semi-parametric efficiency theory and derive a multiply-robust estimator using pattern graphs.