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。

可微贝叶斯结构学习中的拓扑排序与保证无环约束

Topological Ordering in Differentiable Bayesian Structure Learning with  Guaranteed Acyclicity Constraint

This paper proves that non-convex quadratically constrained quadratic
programs can be solved in polynomial time when their underlying graph is
acyclic, provided the constraints satisfy a certain technical condition. When
this condition is not satisfied, we propose a heuristic to obtain a feasible
point. We demonstrate this approach on optimal power flow problems over radial
networks.

本文研究表明，当非凸性的二次约束二次规划的基础图为无环图且其约束满足一定的技术条件时，可以在多项式时间内解决；当这个条件不满足时，我们提出了一种启发式方法来获取可行点，并在放射网络的最优功率流问题上展示了此方法的应用。