DAGs with No Curl: An Efficient DAG Structure Learning Approach
Abstract
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, DAGNoCurl, which solves the optimization problem efficiently with a twostep 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.
 Publication:

arXiv eprints
 Pub Date:
 June 2021
 DOI:
 10.48550/arXiv.2106.07197
 arXiv:
 arXiv:2106.07197
 Bibcode:
 2021arXiv210607197Y
 Keywords:

 Computer Science  Machine Learning;
 Computer Science  Artificial Intelligence;
 Statistics  Machine Learning
 EPrint:
 ICML2021, Code is available at https://github.com/fishmoon1234/DAGNoCurl