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,
however, 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。