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.

本文解决了从节点观测中学习有向无环图（DAG）拓扑结构的问题，现有方法在非凸优化中面临挑战。我们提出了一种基于对数行列式的凸无环性函数的新方法，能够有效地规范边权为非负，从而保证全局最优解，并在无穷样本条件下恢复真实DAG结构。实验结果显示该算法在多个合成数据测试中性能优于现有最先进的方法。

非负加权有向无环图结构学习