# Learning DAGs from Data with Few Root Causes

arXiv: https://arxiv.org/abs/2305.15936 · HTML: https://mlsanity.com/paper/2305.15936/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 50 references that are in the map.
- First posted on arXiv 25 May 2023.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [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)
- [CAM: Causal additive models, high-dimensional order search and penalized regression](https://mlsanity.com/paper/1310.1533/) (2013)
- [Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game](https://mlsanity.com/paper/2102.13647/) (2021)
- [DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterization](https://mlsanity.com/paper/2209.08037/) (2022)
- [High-dimensional learning of linear causal networks via inverse covariance estimation](https://mlsanity.com/paper/1311.3492/) (2013)
- [DAGs with No Curl: An Efficient DAG Structure Learning Approach](https://mlsanity.com/paper/2106.07197/) (2021)
- [Causal Discovery Toolbox: Uncover causal relationships in Python](https://mlsanity.com/paper/1903.02278/) (2019)
- [Unsuitability of NOTEARS for Causal Graph Discovery](https://mlsanity.com/paper/2104.05441/) (2021)
- [Differentiable DAG Sampling](https://mlsanity.com/paper/2203.08509/) (2022)
- [Scaling structural learning with NO-BEARS to infer causal transcriptome networks](https://mlsanity.com/paper/1911.00081/) (2019)
- [On the folded normal distribution](https://mlsanity.com/paper/1402.3559/) (2014)
- [CausalBench: A Large-scale Benchmark for Network Inference from Single-cell Perturbation Data](https://mlsanity.com/paper/2210.17283/) (2022)
- [Concave Penalized Estimation of Sparse Gaussian Bayesian Networks](https://mlsanity.com/paper/1401.0852/) (2014)
- [Learning Identifiable Gaussian Bayesian Networks in Polynomial Time and Sample Complexity](https://mlsanity.com/paper/1703.01196/) (2017)
- [Causal Fourier Analysis on Directed Acyclic Graphs and Posets](https://mlsanity.com/paper/2209.07970/) (2022)
- [DAG Learning on the Permutahedron](https://mlsanity.com/paper/2301.11898/) (2023)

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

- [A Survey of AIOps in the Era of Large Language Models](https://mlsanity.com/paper/2507.12472/) (2025)
- [The CausalBench challenge: A machine learning contest for gene network inference from single-cell perturbation data](https://mlsanity.com/paper/2308.15395/) (2023)
- [Identifying General Mechanism Shifts in Linear Causal Representations](https://mlsanity.com/paper/2410.24059/) (2024)
- [LOCAL: Learning with Orientation Matrix to Infer Causal Structure from Time Series Data](https://mlsanity.com/paper/2410.19464/) (2024)
- [SpinSVAR: Estimating Structural Vector Autoregression Assuming Sparse Input](https://mlsanity.com/paper/2501.03130/) (2025)
- [From topology learning to graph generation: A unifying perspective](https://mlsanity.com/paper/2609.02286/) (2026)
- [Nonnegative DAG Learning via Concomitant Estimation](https://mlsanity.com/paper/2609.34595/) (2026)
- [Signal Processing over Product DAGs: Causal Shifts and Filters](https://mlsanity.com/paper/2609.40275/) (2026)

## Abstract (arXiv)

We present a novel perspective and algorithm for learning directed acyclic graphs (DAGs) from data generated by a linear structural equation model (SEM). First, we show that a linear SEM can be viewed as a linear transform that, in prior work, computes the data from a dense input vector of random valued root causes (as we will call them) associated with the nodes. Instead, we consider the case of (approximately) few root causes and also introduce noise in the measurement of the data. Intuitively, this means that the DAG data is produced by few data-generating events whose effect percolates through the DAG. We prove identifiability in this new setting and show that the true DAG is the global minimizer of the L0-norm of the vector of root causes. For data with few root causes, with and without noise, we show superior performance compared to prior DAG learning methods.