Fast Causal Orientation Learning in Directed Acyclic Graphs

Ramin Safaeian, Saber Salehkaleybar, M. Tabandeh
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Abstract

Causal relationships among a set of variables are commonly represented by a directed acyclic graph. The orientations of some edges in the causal DAG can be discovered from observational/interventional data. Further edges can be oriented by iteratively applying so-called Meek rules. Inferring edges’ orientations from some previously oriented edges, which we call Causal Orientation Learning (COL), is a common problem in various causal discovery tasks. In these tasks, it is often required to solve multiple COL problems and therefore applying Meek rules could be time consuming. Motivated by Meek rules, we introduce Meek functions that can be utilized in solving COL problems. In particular, we show that these functions have some desirable properties, enabling us to speed up the process of applying Meek rules. In particular, we propose a dynamic programming (DP) based method to apply Meek functions. Moreover, based on the proposed DP method, we present a lower bound on the number of edges that can be oriented as a result of intervention. We also propose a method to check whether some oriented edges belong to a causal DAG. Experimental results show that the proposed methods can outperform previous work in several causal discovery tasks in terms of running-time.
有向无环图的快速因果定向学习
一组变量之间的因果关系通常用有向无环图来表示。因果DAG中某些边的方向可以从观测/干预数据中发现。进一步的边缘可以通过迭代地应用所谓的Meek规则来定位。从一些先前定向的边缘推断边缘的方向,我们称之为因果取向学习(COL),是各种因果发现任务中的常见问题。在这些任务中,通常需要解决多个COL问题,因此应用Meek规则可能非常耗时。在Meek规则的激励下,我们引入了可用于解决COL问题的Meek函数。特别是,我们展示了这些函数具有一些理想的属性,使我们能够加快应用Meek规则的过程。我们特别提出了一种基于动态规划(DP)的方法来应用Meek函数。此外,基于所提出的DP方法,我们给出了由于干预而可以定向的边的数量的下界。我们还提出了一种检验一些有向边是否属于因果DAG的方法。实验结果表明,本文提出的方法在运行时间上优于已有的因果发现方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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