Learning the structure of a causal graphical model using both observational and interventional data is a fundamental problem in many scientific fields. A promising direction is continuous optimization for score-based methods, which efficiently learn the causal graph in a data-driven manner. However, to date, those methods require constrained optimization to enforce acyclicity or lack convergence guarantees. In this paper, we present ENCO, an efficient structure learning method for directed, acyclic causal graphs leveraging observational and interventional data. ENCO formulates the graph search as an optimization of independent edge likelihoods, with the edge orientation being modeled as a separate parameter. Consequently, we can provide convergence guarantees of ENCO under mild conditions without constraining the score function with respect to acyclicity. In experiments, we show that ENCO can efficiently recover graphs with hundreds of nodes, an order of magnitude larger than what was previously possible, while handling deterministic variables and latent confounders.

本文提出了一种新的有向无环因果图结构学习方法ENCO，可以将因果图搜索表述为独立边似然的优化，并在不需要强制保持无环的情况下提供收敛保证。在实验中，作者展示ENCO可以高效地恢复拥有数百个节点的图，并处理确定性变量和潜在混淆因子。

无需利用无环约束的高效神经因果关系发现