We consider the task of learning causal structures from data stored on multiple machines, and propose a novel structure learning method called distributed annealing on regularized likelihood score (DARLS) to solve this problem. We model causal structures by a directed acyclic graph that is parameterized with generalized linear models, so that our method is applicable to various types of data. To obtain a high-scoring causal graph, DARLS simulates an annealing process to search over the space of topological sorts, where the optimal graphical structure compatible with a sort is found by a distributed optimization method. This distributed optimization relies on multiple rounds of communication between local and central machines to estimate the optimal structure. We establish its convergence to a global optimizer of the overall score that is computed on all data across local machines. To the best of our knowledge, DARLS is the first distributed method for learning causal graphs with such theoretical guarantees. Through extensive simulation studies, DARLS has shown competing performance against existing methods on distributed data, and achieved comparable structure learning accuracy and test-data likelihood with competing methods applied to pooled data across all local machines. In a real-world application for modeling protein-DNA binding networks with distributed ChIP-Sequencing data, DARLS also exhibits higher predictive power than other methods, demonstrating a great advantage in estimating causal networks from distributed data.
翻译:我们考虑从多机储存的数据中学习因果结构的任务,并提议一种新结构学习方法,称为在常规概率分数上分发分配的肛门,以解决这一问题。我们用一个带有通用线性模型参数的定向循环图来模拟因果结构,以便我们的方法适用于各种类型的数据。为了获得高分因果图,DARLS模拟一个在地形空间搜索的肛门过程,通过分布式优化方法可以找到与某类相容的最佳图形结构。这种分布式优化取决于地方和中央机器之间的多轮通信,以估计最佳结构。我们将其与一个全球总体分数优化器的趋同,该分数是用通用的线性模型,根据我们的知识,DARLS是第一个在理论保证下学习因果图表的分布方法。通过广泛的模拟研究,DARLS展示了与现有分布式数据方法相竞争的性能,并取得了可比较的结构学习准确性和测试数据的可能性,所有地方机器都应用了相互竞争的方法来估计最佳结构结构结构结构结构结构结构结构。在现实世界中,在模拟、CRimal-Dalimal-assiming silling silling网络中也展示了其他数据优势,在模拟的模型上展示了其他的模型上展示了高蛋白-assilling silling sillingalmaquelationalus