# Discovering Dynamic Causal Space for DAG Structure Learning

arXiv: https://arxiv.org/abs/2306.02822 · HTML: https://mlsanity.com/paper/2306.02822/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 58 references that are in the map.
- First posted on arXiv 5 Jun 2023.

## Builds on (most cited first, 23 of 23)

- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [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)
- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [Causality for Machine Learning](https://mlsanity.com/paper/1911.10500/) (2019)
- [Gradient-Based Neural DAG Learning](https://mlsanity.com/paper/1906.02226/) (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)
- [On the Role of Sparsity and DAG Constraints for Learning Linear DAGs](https://mlsanity.com/paper/2006.10201/) (2020)
- [Causal Inference in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/1302.4983/) (2013)
- [Causal Discovery from Heterogeneous/Nonstationary Data with Independent Changes](https://mlsanity.com/paper/1903.01672/) (2019)
- [Causal Discovery with Reinforcement Learning](https://mlsanity.com/paper/1906.04477/) (2019)
- [High-dimensional learning of linear causal networks via inverse covariance estimation](https://mlsanity.com/paper/1311.3492/) (2013)
- [Efficient Neural Causal Discovery without Acyclicity Constraints](https://mlsanity.com/paper/2107.10483/) (2021)
- [DAGs with No Fears: A Closer Look at Continuous Optimization for Learning Bayesian Networks](https://mlsanity.com/paper/2010.09133/) (2020)
- [Differentiable Causal Discovery Under Unmeasured Confounding](https://mlsanity.com/paper/2010.06978/) (2020)
- [A Graph Autoencoder Approach to Causal Structure Learning](https://mlsanity.com/paper/1911.07420/) (2019)
- [DAGs with No Curl: An Efficient DAG Structure Learning Approach](https://mlsanity.com/paper/2106.07197/) (2021)
- [Unsuitability of NOTEARS for Causal Graph Discovery](https://mlsanity.com/paper/2104.05441/) (2021)
- [CASTLE: Regularization via Auxiliary Causal Graph Discovery](https://mlsanity.com/paper/2009.13180/) (2020)
- [Addendum on the scoring of Gaussian directed acyclic graphical models](https://mlsanity.com/paper/1402.6863/) (2014)
- [Learning DAGs without imposing acyclicity](https://mlsanity.com/paper/2006.03005/) (2020)
- [Identifiability of Gaussian Structural Equation Models with Dependent Errors Having Equal Variances](https://mlsanity.com/paper/1806.08156/) (2018)

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

- [Modeling Time-evolving Causality over Data Streams](https://mlsanity.com/paper/2502.08963/) (2025)
- [The Robustness of Differentiable Causal Discovery in Misspecified Scenarios](https://mlsanity.com/paper/2510.12503/) (2025)
- [Brain Effective Connectivity Estimation via Fourier Spatiotemporal Attention](https://mlsanity.com/paper/2503.11283/) (2025)
- [Scaling Causal Mediation for Complex Systems: A Framework for Root Cause Analysis](https://mlsanity.com/paper/2512.14764/) (2025)

## Abstract (arXiv)

Discovering causal structure from purely observational data (i.e., causal discovery), aiming to identify causal relationships among variables, is a fundamental task in machine learning. The recent invention of differentiable score-based DAG learners is a crucial enabler, which reframes the combinatorial optimization problem into a differentiable optimization with a DAG constraint over directed graph space. Despite their great success, these cutting-edge DAG learners incorporate DAG-ness independent score functions to evaluate the directed graph candidates, lacking in considering graph structure. As a result, measuring the data fitness alone regardless of DAG-ness inevitably leads to discovering suboptimal DAGs and model vulnerabilities. Towards this end, we propose a dynamic causal space for DAG structure learning, coined CASPER, that integrates the graph structure into the score function as a new measure in the causal space to faithfully reflect the causal distance between estimated and ground truth DAG. CASPER revises the learning process as well as enhances the DAG structure learning via adaptive attention to DAG-ness. Grounded by empirical visualization, CASPER, as a space, satisfies a series of desired properties, such as structure awareness and noise robustness. Extensive experiments on both synthetic and real-world datasets clearly validate the superiority of our CASPER over the state-of-the-art causal discovery methods in terms of accuracy and robustness.