# Non-negative Weighted DAG Structure Learning

arXiv: https://arxiv.org/abs/2409.07880 · HTML: https://mlsanity.com/paper/2409.07880/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 35 references that are in the map.
- First posted on arXiv 12 Sep 2024.

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

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [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)
- [How to learn a graph from smooth signals](https://mlsanity.com/paper/1601.02513/) (2016)
- [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)
- [Network Topology Inference from Spectral Templates](https://mlsanity.com/paper/1608.03008/) (2016)
- [Signal Processing on Directed Graphs](https://mlsanity.com/paper/2008.00586/) (2020)
- [Learning Graphs from Smooth and Graph-Stationary Signals with Hidden Variables](https://mlsanity.com/paper/2111.05588/) (2021)
- [Online Topology Inference from Streaming Stationary Graph Signals with Partial Connectivity Information](https://mlsanity.com/paper/2007.03653/) (2020)
- [Accelerated Graph Learning from Smooth Signals](https://mlsanity.com/paper/2110.09677/) (2021)
- [Joint Network Topology Inference in the Presence of Hidden Nodes](https://mlsanity.com/paper/2306.17364/) (2023)
- [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)
- [Network Topology Inference with Graphon Spectral Penalties](https://mlsanity.com/paper/2010.07872/) (2020)
- [Enhanced graph-learning schemes driven by similar distributions of motifs](https://mlsanity.com/paper/2207.04747/) (2022)
- [Global Optimality in Bivariate Gradient-based DAG Learning](https://mlsanity.com/paper/2306.17378/) (2023)
- [Convolutional Learning on Directed Acyclic Graphs](https://mlsanity.com/paper/2405.03056/) (2024)

## Built on by (most cited first, 7 of 7)

- [BUILD with Precision: Bottom-Up Inference of Linear DAGs](https://mlsanity.com/paper/2512.16111/) (2025)
- [Exploiting Non-Negativity in DAG Structure Learning](https://mlsanity.com/paper/2605.19947/) (2026)
- [Directed Acyclic Graph Convolutional Networks](https://mlsanity.com/paper/2506.12218/) (2025)
- [Estimating Fair Graphs from Graph-Stationary Data](https://mlsanity.com/paper/2510.07536/) (2025)
- [Non-negative DAG Learning from Time-Series Data](https://mlsanity.com/paper/2512.07267/) (2025)
- [A Framework for Directed Acyclic Hypergraph Learning](https://mlsanity.com/paper/2606.21668/) (2026)
- [Nonnegative DAG Learning via Concomitant Estimation](https://mlsanity.com/paper/2609.34595/) (2026)

## Abstract (arXiv)

We address the problem of learning the topology of directed acyclic graphs (DAGs) from nodal observations, which adhere to a linear structural equation model. Recent advances framed the combinatorial DAG structure learning task as a continuous optimization problem, yet existing methods must contend with the complexities of non-convex optimization. To overcome this limitation, we assume that the latent DAG contains only non-negative edge weights. Leveraging this additional structure, we argue that cycles can be effectively characterized (and prevented) using a convex acyclicity function based on the log-determinant of the adjacency matrix. This convexity allows us to relax the task of learning the non-negative weighted DAG as an abstract convex optimization problem. We propose a DAG recovery algorithm based on the method of multipliers, that is guaranteed to return a global minimizer. Furthermore, we prove that in the infinite sample size regime, the convexity of our approach ensures the recovery of the true DAG structure. We empirically validate the performance of our algorithm in several reproducible synthetic-data test cases, showing that it outperforms state-of-the-art alternatives.