Score-based approaches in the structure learning task are thriving because of
their scalability. Continuous relaxation has been the key reason for this
advancement. Despite achieving promising outcomes, most of these methods are
still struggling to ensure that the graphs generated from the latent space are
acyclic by minimizing a defined score. There has also been another trend of
permutation-based approaches, which concern the search for the topological
ordering of the variables in the directed acyclic graph (DAG) in order to limit
the search space of the graph. In this study, we propose an alternative
approach for strictly constraining the acyclicty of the graphs with an
integration of the knowledge from the topological orderings. Our approach can
reduce inference complexity while ensuring the structures of the generated
graphs to be acyclic. Our empirical experiments with simulated and real-world
data show that our approach can outperform related Bayesian score-based
approaches.

通过结合拓扑排序的知识，我们提出了一种用于限制生成图的无环性的替代方法，该方法可以降低推理复杂度，同时确保生成的图的结构是无环的，并在模拟和真实数据的实证实验中表现优于相关的基于贝叶斯评分的方法。