Directed acyclic graphical models, or DAG models, are widely used to represent complex causal systems. Since the basic task of learning such a model from data is NP-hard, a standard approach is greedy search over the space of directed acyclic graphs or Markov equivalence classes of directed acyclic graphs. As the space of directed acyclic graphs on $p$ nodes and the associated space of Markov equivalence classes are both much larger than the space of permutations, it is desirable to consider permutation-based greedy searches. Here, we provide the first consistency guarantees, both uniform and high-dimensional, of a greedy permutation-based search. This search corresponds to a simplex-like algorithm operating over the edge-graph of a sub-polytope of the permutohedron, called a DAG associahedron. Every vertex in this polytope is associated with a directed acyclic graph, and hence with a collection of permutations that are consistent with the directed acyclic graph ordering. A walk is performed on the edges of the polytope maximizing the sparsity of the associated directed acyclic graphs. We show via simulated and real data that this permutation search is competitive with current approaches.

翻译：由于从数据中学习这种模型的基本任务为NP-硬度,一种标准的方法是贪婪地搜索定向环状图或定向环状图的Markov等效等级的空间。由于美元节点上的定向环状图的空间以及Markov等同等级的相关空间都大大大于调整空间,因此最好考虑基于调和的贪婪搜索。在这里,我们提供了从数据中学习这种模型的基本任务,即NP-硬度和高度的首次一致性保证。这种搜索相当于在正对流线子粒子粒子谱的边缘图上运行的简单X式算法,称为DAG 相形相形色色色。这个多线形图中的每个脊椎都与定向环形图相联系,因此也应考虑与定向单状图相一致的调。在贪婪基于贪婪的搜索基础上进行的第一次统一和高维度的搜索。在多线形图边缘上行走,这种简单化的算法相当于当前正态的模拟方法,我们以最优化的方式展示了当前正态的模拟方法。