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，是机器学习中的基础任务。近期提出的可微分的基于分数的有向无环图（DAG）学习器是关键推动技术，它将组合优化问题重新表述为在带DAG约束的有向图空间上的可微优化。尽管这些前沿的DAG学习器取得了巨大成功，但它们采用与DAG无关的评分函数来评估有向图候选解，缺乏对图结构的考量。因此，仅衡量数据拟合度而忽略DAG特性，不可避免地会导致发现次优的DAG并引发模型脆弱性。为此，我们提出了一种用于DAG结构学习的动态因果空间，称为CASPER，该空间将图结构整合到评分函数中，作为因果空间中的新度量，以真实反映估计DAG与真实DAG之间的因果距离。CASPER通过自适应关注DAG特性来修正学习过程并增强DAG结构学习。基于实证可视化的理论支撑，CASPER作为一种空间，满足一系列理想性质，如结构感知性和噪声鲁棒性。在合成数据集和真实数据集上的大量实验清晰验证了我们的CASPER在准确性和鲁棒性上均优于当前最先进的因果发现方法。