We propose a continuous optimization framework for discovering a latent directed acyclic graph (DAG) from observational data. Our approach optimizes over the polytope of permutation vectors, the so-called Permutahedron, to learn a topological ordering. Edges can be optimized jointly, or learned conditional on the ordering via a non-differentiable subroutine. Compared to existing continuous optimization approaches our formulation has a number of advantages including: 1. validity: optimizes over exact DAGs as opposed to other relaxations optimizing approximate DAGs; 2. modularity: accommodates any edge-optimization procedure, edge structural parameterization, and optimization loss; 3. end-to-end: either alternately iterates between node-ordering and edge-optimization, or optimizes them jointly. We demonstrate, on real-world data problems in protein-signaling and transcriptional network discovery, that our approach lies on the Pareto frontier of two key metrics, the SID and SHD.

翻译：我们提出一个持续优化框架,用于从观测数据中发现潜在定向圆形图(DAG),我们的方法优化了变异矢量的多功能范围,即所谓的Permutahedron,以学习一个地形顺序。边缘可以联合优化,也可以通过非区别的子例程法在订购上学习。与现有的连续优化方法相比,我们的配方有若干优点,包括:1.有效性:优化精确的DAG,而不是其他的放松,以优化大致的DAG;2.模块化:适应任何边缘优化程序、边缘结构参数化和优化损失;3.端到端:要么在节点排序和边缘优化之间交替重复,要么联合优化。关于蛋白质发型和转录网络发现中的真实世界数据问题,我们的方法在于两种关键指标(SID和SPHD)的Pareto前沿。