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 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.

翻译：在结构学习任务中，基于评分的方法因其可扩展性而蓬勃发展。连续松弛化是这一进展的关键原因。尽管取得了令人鼓舞的成果，但大多数此类方法仍难以通过最小化定义评分来确保从潜在空间生成的图是无环的。另一趋势是基于排列的方法，其关注有向无环图中变量的拓扑排序搜索，以限制图的搜索空间。在本研究中，我们提出一种替代方法，通过整合拓扑排序的知识来严格约束图的非循环性。我们的方法能够降低推理复杂度，同时确保所生成图的结构为无环。通过模拟数据和真实数据的实证实验表明，我们的方法可以优于相关的贝叶斯评分方法。