Discovering causal structure from purely observational data (i.e., causal discovery), aiming to identify causal relationships among variables, is a fundamental task in machine learning. The recent invention of differentiable score-based DAG learners is a crucial enabler, which reframes the combinatorial optimization problem into a differentiable optimization with a DAG constraint over directed graph space. Despite their great success, these cutting-edge DAG learners incorporate DAG-ness independent score functions to evaluate the directed graph candidates, lacking in considering graph structure. As a result, measuring the data fitness alone regardless of DAG-ness inevitably leads to discovering suboptimal DAGs and model vulnerabilities. Towards this end, we propose a dynamic causal space for DAG structure learning, coined CASPER, that integrates the graph structure into the score function as a new measure in the causal space to faithfully reflect the causal distance between estimated and ground truth DAG. CASPER revises the learning process as well as enhances the DAG structure learning via adaptive attention to DAG-ness. Grounded by empirical visualization, CASPER, as a space, satisfies a series of desired properties, such as structure awareness and noise robustness. Extensive experiments on both synthetic and real-world datasets clearly validate the superiority of our CASPER over the state-of-the-art causal discovery methods in terms of accuracy and robustness.

翻译：从纯观测数据中发现因果结构（即因果发现），旨在识别变量间的因果关系，是机器学习中的一项基础任务。近期提出的可微分基于评分的DAG学习器是关键推动技术，它将组合优化问题重新构建为在带DAG约束的有向图空间上的可微分优化问题。尽管这些前沿DAG学习器取得了巨大成功，但它们采用与DAG性无关的评分函数来评估有向图候选结构，缺乏对图结构的考量。因此，仅仅衡量数据拟合度而不考虑DAG性，必然导致发现次优DAG及模型脆弱性。为此，我们提出一种用于DAG结构学习的动态因果空间，命名为CASPER，它将图结构整合进评分函数，作为因果空间中的新度量，以忠实反映估计DAG与真实DAG之间的因果距离。CASPER通过自适应关注DAG性来修正学习过程并增强DAG结构学习。基于经验可视化，CASPER作为空间满足结构感知、噪声鲁棒性等一系列期望性质。在合成数据集和真实数据集上的大量实验清晰表明，我们的CASPER在准确性和鲁棒性方面全面超越现有最先进的因果发现方法。