# Exploiting Non-Negativity in DAG Structure Learning

arXiv: https://arxiv.org/abs/2605.19947 · HTML: https://mlsanity.com/paper/2605.19947/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 29 references that are in the map.
- First posted on arXiv 19 May 2026.

## Builds on (most cited first, 17 of 17)

- [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)
- [A Survey on Causal Inference](https://mlsanity.com/paper/2002.02770/) (2020)
- [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)
- [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)
- [Connecting the Dots: Identifying Network Structure via Graph Signal Processing](https://mlsanity.com/paper/1810.13066/) (2018)
- [High-dimensional learning of linear causal networks via inverse covariance estimation](https://mlsanity.com/paper/1311.3492/) (2013)
- [DAGs with No Fears: A Closer Look at Continuous Optimization for Learning Bayesian Networks](https://mlsanity.com/paper/2010.09133/) (2020)
- [Signal Processing on Directed Graphs](https://mlsanity.com/paper/2008.00586/) (2020)
- [Optimal estimation of Gaussian DAG models](https://mlsanity.com/paper/2201.10548/) (2022)
- [CoLiDE: Concomitant Linear DAG Estimation](https://mlsanity.com/paper/2310.02895/) (2023)
- [Causal Fourier Analysis on Directed Acyclic Graphs and Posets](https://mlsanity.com/paper/2209.07970/) (2022)
- [Non-negative Weighted DAG Structure Learning](https://mlsanity.com/paper/2409.07880/) (2024)
- [BUILD with Precision: Bottom-Up Inference of Linear DAGs](https://mlsanity.com/paper/2512.16111/) (2025)
- [Directed Acyclic Graph Convolutional Networks](https://mlsanity.com/paper/2506.12218/) (2025)

## Built on by (most cited first, 3 of 3)

- [Concomitant DAG Learning: On the Roles of Noise Adaptivity, Sparsity, and Non-negativity](https://mlsanity.com/paper/2605.23537/) (2026)
- [Support Selection Beyond Smooth DAG Exactness: Completion Geometry,Score Margins, and Selective Certificates](https://mlsanity.com/paper/2608.08103/) (2026)
- [Nonnegative DAG Learning via Concomitant Estimation](https://mlsanity.com/paper/2609.34595/) (2026)

## Abstract (arXiv)

This work addresses the problem of learning directed acyclic graphs (DAGs) from nodal observations adhering to a linear structural equation model. DAG structure learning is a central task in signal processing, machine learning, and causal inference, but it remains challenging because acyclicity is a global combinatorial property and the search space grows superexponentially in the number of nodes. Continuous acyclicity characterizations have led to important algorithmic advances by replacing the discrete DAG restriction with smooth equality constraints on the candidate adjacency matrix. However, existing formulations still involve difficult non-convex optimization landscapes and may suffer from degenerate first-order optimality conditions. Here, we restrict attention to DAGs with non-negative edge weights and exploit this additional structure to obtain a simpler acyclicity characterization devoid of Hadamard products. We propose a new non-negative constrained DAG estimator and develop a tractable, locally convergent algorithm based on the method of multipliers. We further analyze the benign optimization landscape induced by the non-negativity constraints. In the large-sample regime, we show that the true DAG is the unique global minimizer of the population augmented Lagrangian. Moreover, the landscape contains no spurious interior stationary points, and the true DAG is the only acyclic Karush--Kuhn--Tucker (KKT) point. Critically, this allows us to guarantee local convergence to the true DAG given infinite samples. Comprehensive numerical experiments show that the proposed structure identification method improves over state-of-the-art continuous DAG-learning baselines.