# Evaluation of Induced Expert Knowledge in Causal Structure Learning by NOTEARS

arXiv: https://arxiv.org/abs/2301.01817 · HTML: https://mlsanity.com/paper/2301.01817/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 42 references that are in the map.
- First posted on arXiv 4 Jan 2023.

## Builds on (most cited first, 19 of 19)

- [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)
- [Gradient-Based Neural DAG Learning](https://mlsanity.com/paper/1906.02226/) (2019)
- [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)
- [Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game](https://mlsanity.com/paper/2102.13647/) (2021)
- [Domain Adaptation by Using Causal Inference to Predict Invariant Conditional Distributions](https://mlsanity.com/paper/1707.06422/) (2017)
- [DoWhy: An End-to-End Library for Causal Inference](https://mlsanity.com/paper/2011.04216/) (2020)
- [Masked Gradient-Based Causal Structure Learning](https://mlsanity.com/paper/1910.08527/) (2019)
- [DAGs with No Fears: A Closer Look at Continuous Optimization for Learning Bayesian Networks](https://mlsanity.com/paper/2010.09133/) (2020)
- [gCastle: A Python Toolbox for Causal Discovery](https://mlsanity.com/paper/2111.15155/) (2021)
- [How Far are We from Effective Context Modeling? An Exploratory Study on Semantic Parsing in Context](https://mlsanity.com/paper/2002.00652/) (2020)
- [On the Convergence of Continuous Constrained Optimization for Structure Learning](https://mlsanity.com/paper/2011.11150/) (2020)
- [Guided Generation of Cause and Effect](https://mlsanity.com/paper/2107.09846/) (2021)
- [On Low Rank Directed Acyclic Graphs and Causal Structure Learning](https://mlsanity.com/paper/2006.05691/) (2020)
- [Accelerating Human-in-the-loop Machine Learning: Challenges and Opportunities](https://mlsanity.com/paper/1804.05892/) (2018)
- [Causal Identification under Markov Equivalence](https://mlsanity.com/paper/1812.06209/) (2018)
- [Causal Modeling of Twitter Activity During COVID-19](https://mlsanity.com/paper/2005.07952/) (2020)
- [Combining Experts' Causal Judgments](https://mlsanity.com/paper/2005.10180/) (2020)

## Built on by (most cited first, 8 of 8)

- [Integrating Large Language Models in Causal Discovery: A Statistical Causal Approach](https://mlsanity.com/paper/2402.01454/) (2024)
- [Dataflow graphs as complete causal graphs](https://mlsanity.com/paper/2303.09552/) (2023)
- [Optimizing Data-driven Causal Discovery Using Knowledge-guided Search](https://mlsanity.com/paper/2304.05493/) (2023)
- [Weakly-supervised causal discovery based on fuzzy knowledge and complex data complementarity](https://mlsanity.com/paper/2405.08699/) (2024)
- [Cluster-Dags as Powerful Background Knowledge For Causal Discovery](https://mlsanity.com/paper/2512.10032/) (2025)
- [CGLearn: Consistent Gradient-Based Learning for Out-of-Distribution Generalization](https://mlsanity.com/paper/2411.06040/) (2024)
- [Regularized Multi-LLMs Collaboration for Enhanced Score-based Causal Discovery](https://mlsanity.com/paper/2411.17989/) (2024)
- [Quality-Controlled Active Learning via Gaussian Processes for Robust Structure-Property Learning in Autonomous Microscopy](https://mlsanity.com/paper/2603.29135/) (2026)

## Abstract (arXiv)

Causal modeling provides us with powerful counterfactual reasoning and interventional mechanism to generate predictions and reason under various what-if scenarios. However, causal discovery using observation data remains a nontrivial task due to unobserved confounding factors, finite sampling, and changes in the data distribution. These can lead to spurious cause-effect relationships. To mitigate these challenges in practice, researchers augment causal learning with known causal relations. The goal of the paper is to study the impact of expert knowledge on causal relations in the form of additional constraints used in the formulation of the nonparametric NOTEARS. We provide a comprehensive set of comparative analyses of biasing the model using different types of knowledge. We found that (i) knowledge that corrects the mistakes of the NOTEARS model can lead to statistically significant improvements, (ii) constraints on active edges have a larger positive impact on causal discovery than inactive edges, and surprisingly, (iii) the induced knowledge does not correct on average more incorrect active and/or inactive edges than expected. We also demonstrate the behavior of the model and the effectiveness of domain knowledge on a real-world dataset.