# MissNODAG: Differentiable Cyclic Causal Graph Learning from Incomplete Data

arXiv: https://arxiv.org/abs/2410.18918 · HTML: https://mlsanity.com/paper/2410.18918/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 84 references that are in the map.
- First posted on arXiv 24 Oct 2024.

## Builds on (most cited first, 30 of 39)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Invertible Residual Networks](https://mlsanity.com/paper/1811.00995/) (2018)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Residual Flows for Invertible Generative Modeling](https://mlsanity.com/paper/1906.02735/) (2019)
- [Differentiable Causal Discovery from Interventional Data](https://mlsanity.com/paper/2007.01754/) (2020)
- [Learning Sparse Nonparametric DAGs](https://mlsanity.com/paper/1909.13189/) (2019)
- [On the Role of Sparsity and DAG Constraints for Learning Linear DAGs](https://mlsanity.com/paper/2006.10201/) (2020)
- [Invariant Causal Prediction for Nonlinear Models](https://mlsanity.com/paper/1706.08576/) (2017)
- [Foundations of Structural Causal Models with Cycles and Latent Variables](https://mlsanity.com/paper/1611.06221/) (2016)
- [Causal-learn: Causal Discovery in Python](https://mlsanity.com/paper/2307.16405/) (2023)
- [Missing Data Imputation using Optimal Transport](https://mlsanity.com/paper/2002.03860/) (2020)
- [Masked Gradient-Based Causal Structure Learning](https://mlsanity.com/paper/1910.08527/) (2019)
- [Efficient Neural Causal Discovery without Acyclicity Constraints](https://mlsanity.com/paper/2107.10483/) (2021)
- [Permutation-based Causal Inference Algorithms with Interventions](https://mlsanity.com/paper/1705.10220/) (2017)
- [Graphical Models for Processing Missing Data](https://mlsanity.com/paper/1801.03583/) (2018)
- [Differentiable Causal Discovery Under Unmeasured Confounding](https://mlsanity.com/paper/2010.06978/) (2020)
- [MIRACLE: Causally-Aware Imputation via Learning Missing Data Mechanisms](https://mlsanity.com/paper/2111.03187/) (2021)
- [Constraint-based Causal Discovery from Multiple Interventions over Overlapping Variable Sets](https://mlsanity.com/paper/1403.2150/) (2014)
- [Causal Discovery in the Presence of Missing Data](https://mlsanity.com/paper/1807.04010/) (2018)
- [Large-Scale Differentiable Causal Discovery of Factor Graphs](https://mlsanity.com/paper/2206.07824/) (2022)
- [Scaling structural learning with NO-BEARS to infer causal transcriptome networks](https://mlsanity.com/paper/1911.00081/) (2019)
- [A Discovery Algorithm for Directed Cyclic Graphs](https://mlsanity.com/paper/1302.3599/) (2013)
- [Markov Properties for Graphical Models with Cycles and Latent Variables](https://mlsanity.com/paper/1710.08775/) (2017)
- [The Bayesian Structural EM Algorithm](https://mlsanity.com/paper/1301.7373/) (2013)
- [Causal Discovery from Incomplete Data: A Deep Learning Approach](https://mlsanity.com/paper/2001.05343/) (2020)
- [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)

## Built on by (most cited first, 1 of 1)

- [RECLAIM: Cyclic Causal Discovery Amid Measurement Noise](https://mlsanity.com/paper/2603.20585/) (2026)

## Abstract (arXiv)

Causal discovery in real-world systems, such as biological networks, is often complicated by feedback loops and incomplete data. Standard algorithms, which assume acyclic structures or fully observed data, struggle with these challenges. To address this gap, we propose MissNODAG, a differentiable framework for learning both the underlying cyclic causal graph and the missingness mechanism from partially observed data, including data missing not at random. Our framework integrates an additive noise model with an expectation-maximization procedure, alternating between imputing missing values and optimizing the observed data likelihood, to uncover both the cyclic structures and the missingness mechanism. We establish consistency guarantees under exact maximization of the score function in the large sample setting. Finally, we demonstrate the effectiveness of MissNODAG through synthetic experiments and an application to real-world gene perturbation data.