# Full Law Identification In Graphical Models Of Missing Data: Completeness Results

arXiv: https://arxiv.org/abs/2004.04872 · HTML: https://mlsanity.com/paper/2004.04872/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Apr 2020.

## Built on by (most cited first, 26 of 26)

- [MIRACLE: Causally-Aware Imputation via Learning Missing Data Mechanisms](https://mlsanity.com/paper/2111.03187/) (2021)
- [MissDAG: Causal Discovery in the Presence of Missing Data with Continuous Additive Noise Models](https://mlsanity.com/paper/2205.13869/) (2022)
- [Conditional Generation of Medical Time Series for Extrapolation to Underrepresented Populations](https://mlsanity.com/paper/2201.08186/) (2022)
- [Copula-Based Deep Survival Models for Dependent Censoring](https://mlsanity.com/paper/2306.11912/) (2023)
- [Evaluation of Active Feature Acquisition Methods for Time-varying Feature Settings](https://mlsanity.com/paper/2312.01530/) (2023)
- [Optimal Transport for Structure Learning Under Missing Data](https://mlsanity.com/paper/2402.15255/) (2024)
- [Learning-To-Measure: In-Context Active Feature Acquisition](https://mlsanity.com/paper/2510.12624/) (2025)
- [Variational Gibbs Inference for Statistical Model Estimation from Incomplete Data](https://mlsanity.com/paper/2111.13180/) (2021)
- [On Testability and Goodness of Fit Tests in Missing Data Models](https://mlsanity.com/paper/2203.00132/) (2022)
- [Sufficient Identification Conditions and Semiparametric Estimation under Missing Not at Random Mechanisms](https://mlsanity.com/paper/2306.06443/) (2023)
- [Evaluation of Active Feature Acquisition Methods for Static Feature Settings](https://mlsanity.com/paper/2312.03619/) (2023)
- [Identification of Causal Structure in the Presence of Missing Data with Additive Noise Model](https://mlsanity.com/paper/2312.12206/) (2023)
- [Leveraging Structured Biological Knowledge for Counterfactual Inference: a Case Study of Viral Pathogenesis](https://mlsanity.com/paper/2101.05136/) (2021)
- [Correcting for Selection Bias and Missing Response in Regression using Privileged Information](https://mlsanity.com/paper/2303.16800/) (2023)
- [Learning High-dimensional Gaussians from Censored Data](https://mlsanity.com/paper/2504.19446/) (2025)
- [Identification and Estimation for Nonignorable Missing Data: A Data Fusion Approach](https://mlsanity.com/paper/2311.09015/) (2023)
- [MissNODAG: Differentiable Cyclic Causal Graph Learning from Incomplete Data](https://mlsanity.com/paper/2410.18918/) (2024)
- [Recursive Equations For Imputation Of Missing Not At Random Data With Sparse Pattern Support](https://mlsanity.com/paper/2507.16107/) (2025)
- [Zero Inflation as a Missing Data Problem: a Proxy-based Approach](https://mlsanity.com/paper/2406.00549/) (2024)
- [Multi-armed Bandits with Missing Outcome](https://mlsanity.com/paper/2411.05661/) (2024)
- [Domain Adaptation Under MNAR Missingness](https://mlsanity.com/paper/2504.00322/) (2025)
- [Markov Missing Graph: A Graphical Approach for Missing Data Imputation](https://mlsanity.com/paper/2509.03410/) (2025)
- [Response to Discussions of "Causal and Counterfactual Views of Missing Data Models"](https://mlsanity.com/paper/2510.14694/) (2025)
- [Identifiable Deep Latent Variable Models for MNAR Data](https://mlsanity.com/paper/2603.24771/) (2026)
- [Missingness-MDPs: Bridging the Theory of Missing Data and POMDPs](https://mlsanity.com/paper/2605.12262/) (2026)
- [Counterfactual Evaluation of Temporal Observation Protocols](https://mlsanity.com/paper/2608.22221/) (2026)

## Abstract (arXiv)

Missing data has the potential to affect analyses conducted in all fields of scientific study, including healthcare, economics, and the social sciences. Several approaches to unbiased inference in the presence of non-ignorable missingness rely on the specification of the target distribution and its missingness process as a probability distribution that factorizes with respect to a directed acyclic graph. In this paper, we address the longstanding question of the characterization of models that are identifiable within this class of missing data distributions. We provide the first completeness result in this field of study -- necessary and sufficient graphical conditions under which, the full data distribution can be recovered from the observed data distribution. We then simultaneously address issues that may arise due to the presence of both missing data and unmeasured confounding, by extending these graphical conditions and proofs of completeness, to settings where some variables are not just missing, but completely unobserved.