# Unsuitability of NOTEARS for Causal Graph Discovery

arXiv: https://arxiv.org/abs/2104.05441 · HTML: https://mlsanity.com/paper/2104.05441/

## Key facts

- Cited by 47 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 21 references that are in the map.
- First posted on arXiv 12 Apr 2021.

## Builds on (most cited first, 11 of 11)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Causality for Machine Learning](https://mlsanity.com/paper/1911.10500/) (2019)
- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [Learning Sparse Nonparametric DAGs](https://mlsanity.com/paper/1909.13189/) (2019)
- [DYNOTEARS: Structure Learning from Time-Series Data](https://mlsanity.com/paper/2002.00498/) (2020)
- [On the Role of Sparsity and DAG Constraints for Learning Linear DAGs](https://mlsanity.com/paper/2006.10201/) (2020)
- [Masked Gradient-Based Causal Structure Learning](https://mlsanity.com/paper/1910.08527/) (2019)
- [High-dimensional learning of linear causal networks via inverse covariance estimation](https://mlsanity.com/paper/1311.3492/) (2013)
- [Differentiable Causal Discovery Under Unmeasured Confounding](https://mlsanity.com/paper/2010.06978/) (2020)
- [CASTLE: Regularization via Auxiliary Causal Graph Discovery](https://mlsanity.com/paper/2009.13180/) (2020)

## Built on by (most cited first, 30 of 47)

- [Causal Reasoning and Large Language Models: Opening a New Frontier for Causality](https://mlsanity.com/paper/2305.00050/) (2023)
- [Deep End-to-end Causal Inference](https://mlsanity.com/paper/2202.02195/) (2022)
- [Identifiability Guarantees for Causal Disentanglement from Soft Interventions](https://mlsanity.com/paper/2307.06250/) (2023)
- [Large-Scale Differentiable Causal Discovery of Factor Graphs](https://mlsanity.com/paper/2206.07824/) (2022)
- [Causal Discovery from Temporal Data: An Overview and New Perspectives](https://mlsanity.com/paper/2303.10112/) (2023)
- [Structure Learning with Continuous Optimization: A Sober Look and Beyond](https://mlsanity.com/paper/2304.02146/) (2023)
- [A Scale-Invariant Sorting Criterion to Find a Causal Order in Additive Noise Models](https://mlsanity.com/paper/2303.18211/) (2023)
- [FedDAG: Federated DAG Structure Learning](https://mlsanity.com/paper/2112.03555/) (2021)
- [Standardizing Structural Causal Models](https://mlsanity.com/paper/2406.11601/) (2024)
- [Simultaneous Missing Value Imputation and Structure Learning with Groups](https://mlsanity.com/paper/2110.08223/) (2021)
- [Adjustment Identification Distance: A gadjid for Causal Structure Learning](https://mlsanity.com/paper/2402.08616/) (2024)
- [A Meta-Reinforcement Learning Algorithm for Causal Discovery](https://mlsanity.com/paper/2207.08457/) (2022)
- [CIPCaD-Bench: Continuous Industrial Process datasets for benchmarking Causal Discovery methods](https://mlsanity.com/paper/2208.01529/) (2022)
- [Constraint-Free Structure Learning with Smooth Acyclic Orientations](https://mlsanity.com/paper/2309.08406/) (2023)
- [Learning DAGs from Data with Few Root Causes](https://mlsanity.com/paper/2305.15936/) (2023)
- [Causal Discovery from Time Series with Hybrids of Constraint-Based and Noise-Based Algorithms](https://mlsanity.com/paper/2306.08765/) (2023)
- [Comprehensive Review and Empirical Evaluation of Causal Discovery Algorithms for Numerical Data](https://mlsanity.com/paper/2407.13054/) (2024)
- [CDANs: Temporal Causal Discovery from Autocorrelated and Non-Stationary Time Series Data](https://mlsanity.com/paper/2302.03246/) (2023)
- [Open problems in causal structure learning: A case study of COVID-19 in the UK](https://mlsanity.com/paper/2305.03859/) (2023)
- [A Survey of Methods, Challenges and Perspectives in Causality](https://mlsanity.com/paper/2302.00293/) (2023)
- [Better Simulations for Validating Causal Discovery with the DAG-Adaptation of the Onion Method](https://mlsanity.com/paper/2405.13100/) (2024)
- [Large-Scale Targeted Cause Discovery via Learning from Simulated Data](https://mlsanity.com/paper/2408.16218/) (2024)
- [Tearing Apart NOTEARS: Controlling the Graph Prediction via Variance Manipulation](https://mlsanity.com/paper/2206.07195/) (2022)
- [Discovering Dynamic Causal Space for DAG Structure Learning](https://mlsanity.com/paper/2306.02822/) (2023)
- [Robustness of Algorithms for Causal Structure Learning to Hyperparameter Choice](https://mlsanity.com/paper/2310.18212/) (2023)
- [CausalMan: A physics-based simulator for large-scale causality](https://mlsanity.com/paper/2502.12707/) (2025)
- [Realizing LLMs' Causal Potential Requires Science-Grounded, Novel Benchmarks](https://mlsanity.com/paper/2510.16530/) (2025)
- [Invariant Structure Learning for Better Generalization and Causal Explainability](https://mlsanity.com/paper/2206.06469/) (2022)
- [dotears: Scalable, consistent DAG estimation using observational and interventional data](https://mlsanity.com/paper/2305.19215/) (2023)
- [Trying to Outrun Causality with Machine Learning: Limitations of Model Explainability Techniques for Identifying Predictive Variables](https://mlsanity.com/paper/2202.09875/) (2022)

## Abstract (arXiv)

Causal Discovery methods aim to identify a DAG structure that represents causal relationships from observational data. In this article, we stress that it is important to test such methods for robustness in practical settings. As our main example, we analyze the NOTEARS method, for which we demonstrate a lack of scale-invariance. We show that NOTEARS is a method that aims to identify a parsimonious DAG from the data that explains the residual variance. We conclude that NOTEARS is not suitable for identifying truly causal relationships from the data.