The aim in many sciences is to understand the mechanisms that underlie the observed distribution of variables, starting from a set of initial hypotheses. Causal discovery allows us to infer mechanisms as sets of cause and effect relationships in a generalized way -- without necessarily tailoring to a specific domain. Causal discovery algorithms search over a structured hypothesis space, defined by the set of directed acyclic graphs, to find the graph that best explains the data. For high-dimensional problems, however, this search becomes intractable and scalable algorithms for causal discovery are needed to bridge the gap. In this paper, we define a novel causal graph partition that allows for divide-and-conquer causal discovery with theoretical guarantees. We leverage the idea of a superstructure -- a set of learned or existing candidate hypotheses -- to partition the search space. We prove under certain assumptions that learning with a causal graph partition always yields the Markov Equivalence Class of the true causal graph. We show our algorithm achieves comparable accuracy and a faster time to solution for biologically-tuned synthetic networks and networks up to ${10^4}$ variables. This makes our method applicable to gene regulatory network inference and other domains with high-dimensional structured hypothesis spaces.

我们定义了一种新颖的因果图分区方法，利用超结构的概念对搜索空间进行划分，证明了使用因果图分区进行学习总是得到真实因果图的马尔可夫等价类，我们的算法在生物调节网络推断和其他高维结构假设空间中实现了可比较的准确性和更快的解决时间。

在高维结构假设空间上的因果发现与因果图分区