Recently directed acyclic graph (DAG) structure learning is formulated as a constrained continuous optimization problem with continuous acyclicity constraints and was solved iteratively through subproblem optimization. To further improve efficiency, we propose a novel learning framework to model and learn the weighted adjacency matrices in the DAG space directly. Specifically, we first show that the set of weighted adjacency matrices of DAGs are equivalent to the set of weighted gradients of graph potential functions, and one may perform structure learning by searching in this equivalent set of DAGs. To instantiate this idea, we propose a new algorithm, DAG-NoCurl, which solves the optimization problem efficiently with a two-step procedure: 1) first we find an initial cyclic solution to the optimization problem, and 2) then we employ the Hodge decomposition of graphs and learn an acyclic graph by projecting the cyclic graph to the gradient of a potential function. Experimental studies on benchmark datasets demonstrate that our method provides comparable accuracy but better efficiency than baseline DAG structure learning methods on both linear and generalized structural equation models, often by more than one order of magnitude.

提出了一种新的有向无环图结构学习算法，通过在等价图势函数梯度集合中搜索来解决优化问题，并使用Hodge分解从一个初始环图中学习无环图，该方法在基准数据集上具有与基线算法相当的准确性和更高的效率。

无环DAG: 一种高效的有向无环图结构学习方法