标题： 因果图的表征与学习来自硬干预 显示英文标题

标题： Characterization and Learning of Causal Graphs from Hard Interventions

摘要： 在实证科学中，一个基本的挑战是通过观察和实验来揭示因果结构。 因果发现涉及通过d-分离将观测数据中的条件独立性不变性与相应的图形约束联系起来。 在本文中，我们考虑一个一般性场景，即我们能够获得来自硬干预的多个实验分布的数据，以及可能来自观测分布的数据。 通过比较不同的干预分布，我们提出了一组与硬干预框架下Pearl的do演算基本相关的图形约束。 这些图形约束将每个图形结构与一组与do演算规则一致的干预分布相关联。 我们表征了带有潜在变量的因果图的干预等价类，并引入了一种图形表示，可用于确定两个因果图是否具有干预等价性，即它们是否与同一组硬干预分布相关联，在该组中，使用do演算的不变性无法区分其元素。 我们还提出了一种学习算法，用于整合来自硬干预的多个数据集，并引入了新的定向规则。 学习目标是一个增强图的元组，它包含一组因果图。 我们还证明了所提出的算法的合理性。 显示英文摘要

摘要： A fundamental challenge in the empirical sciences involves uncovering causal structure through observation and experimentation. Causal discovery entails linking the conditional independence (CI) invariances in observational data to their corresponding graphical constraints via d-separation. In this paper, we consider a general setting where we have access to data from multiple experimental distributions resulting from hard interventions, as well as potentially from an observational distribution. By comparing different interventional distributions, we propose a set of graphical constraints that are fundamentally linked to Pearl's do-calculus within the framework of hard interventions. These graphical constraints associate each graphical structure with a set of interventional distributions that are consistent with the rules of do-calculus. We characterize the interventional equivalence class of causal graphs with latent variables and introduce a graphical representation that can be used to determine whether two causal graphs are interventionally equivalent, i.e., whether they are associated with the same family of hard interventional distributions, where the elements of the family are indistinguishable using the invariances from do-calculus. We also propose a learning algorithm to integrate multiple datasets from hard interventions, introducing new orientation rules. The learning objective is a tuple of augmented graphs which entails a set of causal graphs. We also prove the soundness of the proposed algorithm.