This paper presents a novel approach to causal discovery through a divide-and-conquer framework. By decomposing the problem into smaller subproblems defined on Markov blankets, the proposed DCDILP method first explores in parallel the local causal graphs of these subproblems. However, this local discovery phase encounters systematic challenges due to the presence of hidden confounders (variables within each Markov blanket may be influenced by external variables). Moreover, aggregating these local causal graphs in a consistent global graph defines a large size combinatorial optimization problem. DCDILP addresses these challenges by: i) restricting the local subgraphs to causal links only related with the central variable of the Markov blanket; ii) formulating the reconciliation of local causal graphs as an integer linear programming method. The merits of the approach, in both terms of causal discovery accuracy and scalability in the size of the problem, are showcased by experiments and comparisons with the state of the art.

翻译：本文提出了一种通过分治框架进行因果发现的新方法。通过将问题分解为基于马尔可夫毯定义的更小子问题，所提出的DCDILP方法首先并行探索这些子问题的局部因果图。然而，由于存在隐藏混杂因素（每个马尔可夫毯内的变量可能受到外部变量的影响），这一局部发现阶段面临系统性挑战。此外，将这些局部因果图聚合为一个一致的全局图，定义了一个大规模组合优化问题。DCDILP通过以下方式应对这些挑战：i) 将局部子图限制为仅与马尔可夫毯中心变量相关的因果链接；ii) 将局部因果图的协调问题形式化为整数线性规划方法。实验及与现有先进方法的比较，展示了该方法在因果发现准确性和问题规模可扩展性两方面的优势。