# Identification of Causal Structure in the Presence of Missing Data with Additive Noise Model

arXiv: https://arxiv.org/abs/2312.12206 · HTML: https://mlsanity.com/paper/2312.12206/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 35 references that are in the map.
- First posted on arXiv 19 Dec 2023.

## Builds on (most cited first, 13 of 13)

- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [Causal Inference and Causal Explanation with Background Knowledge](https://mlsanity.com/paper/1302.4972/) (2013)
- [Graphical Models for Processing Missing Data](https://mlsanity.com/paper/1801.03583/) (2018)
- [Causal Discovery in the Presence of Missing Data](https://mlsanity.com/paper/1807.04010/) (2018)
- [Large-Scale Kernel Methods for Independence Testing](https://mlsanity.com/paper/1606.07892/) (2016)
- [Identifiable Generative Models for Missing Not at Random Data Imputation](https://mlsanity.com/paper/2110.14708/) (2021)
- [Full Law Identification In Graphical Models Of Missing Data: Completeness Results](https://mlsanity.com/paper/2004.04872/) (2020)
- [Fast Causal Inference with Non-Random Missingness by Test-Wise Deletion](https://mlsanity.com/paper/1705.09031/) (2017)
- [MissDAG: Causal Discovery in the Presence of Missing Data with Continuous Additive Noise Models](https://mlsanity.com/paper/2205.13869/) (2022)
- [THP: Topological Hawkes Processes for Learning Causal Structure on Event Sequences](https://mlsanity.com/paper/2105.10884/) (2021)
- [Structural Hawkes Processes for Learning Causal Structure from Discrete-Time Event Sequences](https://mlsanity.com/paper/2305.05986/) (2023)
- [Greedy structure learning from data that contain systematic missing values](https://mlsanity.com/paper/2107.04184/) (2021)
- [Causality on Cross-Sectional Data: Stable Specification Search in Constrained Structural Equation Modeling](https://mlsanity.com/paper/1506.05600/) (2015)

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

- [COKE: Causal Discovery with Chronological Order and Expert Knowledge in High Proportion of Missing Manufacturing Data](https://mlsanity.com/paper/2407.12254/) (2024)
- [Causal Discovery for Irregularly Time Series with Consistency Guarantees](https://mlsanity.com/paper/2507.03310/) (2025)
- [Consistency evaluation of benchmarks used for causal discovery](https://mlsanity.com/paper/2606.01789/) (2026)
- [Generalizing Identifiability Results in Causal Discovery from Complete Data to Missing Data Settings](https://mlsanity.com/paper/2610.19211/) (2026)

## Abstract (arXiv)

Missing data are an unavoidable complication frequently encountered in many causal discovery tasks. When a missing process depends on the missing values themselves (known as self-masking missingness), the recovery of the joint distribution becomes unattainable, and detecting the presence of such self-masking missingness remains a perplexing challenge. Consequently, due to the inability to reconstruct the original distribution and to discern the underlying missingness mechanism, simply applying existing causal discovery methods would lead to wrong conclusions. In this work, we found that the recent advances additive noise model has the potential for learning causal structure under the existence of the self-masking missingness. With this observation, we aim to investigate the identification problem of learning causal structure from missing data under an additive noise model with different missingness mechanisms, where the `no self-masking missingness' assumption can be eliminated appropriately. Specifically, we first elegantly extend the scope of identifiability of causal skeleton to the case with weak self-masking missingness (i.e., no other variable could be the cause of self-masking indicators except itself). We further provide the sufficient and necessary identification conditions of the causal direction under additive noise model and show that the causal structure can be identified up to an IN-equivalent pattern. We finally propose a practical algorithm based on the above theoretical results on learning the causal skeleton and causal direction. Extensive experiments on synthetic and real data demonstrate the efficiency and effectiveness of the proposed algorithms.