We study the problem of causal structure learning with no assumptions on the functional relationships and noise. We develop DAG-FOCI, a computationally fast algorithm for this setting that is based on the FOCI variable selection algorithm in \cite{azadkia2019simple}. DAG-FOCI requires no tuning parameter and outputs the parents and the Markov boundary of a response variable of interest. We provide high-dimensional guarantees of our procedure when the underlying graph is a polytree. Furthermore, we demonstrate the applicability of DAG-FOCI on real data from computational biology \cite{sachs2005causal} and illustrate the robustness of our methods to violations of assumptions.

翻译：我们研究因果结构学习的问题,没有关于功能关系和噪音的假设。我们开发了DAG-FoCI,这是基于在\cite{azadkia2019simple}中的FOCI变量选择算法的这一设置的计算快速算法。DAG-FoCI不需要调整参数和输出,父母和响应变量的Markov边界。当基本图表是多树时,我们为我们的程序提供了高维的保障。此外,我们展示了DAG-FoCI对计算生物学中真实数据的适用性,并说明了我们的方法对违反假设的力度。