线性设定下基于约束的差异图发现
Constraint-based difference graph discovery in a linear setting
AI总结：
针对两个环境间的因果差异图推断问题，提出基于回归系数相等性检验的线性结构因果模型发现方法，引入diff-separation准则和LDiffPC算法。
摘要：
在许多科学领域中，比较不同群体间的因果关系至关重要。本文研究了推断两个环境间差异图的问题，并提出了一种基于回归系数相等性检验的线性结构因果模型因果发现方法。我们表明，回归系数的不变性受超越标准d-separation的图形条件支配。因此，我们引入了diff-separation，这是一种图形准则，用于刻画当条件集阻断所有能够引起跨环境回归系数差异的路径时的情形。基于这一准则，我们引入了相应的diff-faithfulness假设，将图形diff-separation陈述与回归系数的等式约束联系起来。最后，我们提出了LDiffPC，一种PC风格的算法，该算法利用回归系数的相等性检验从多环境数据中恢复差异。
英文摘要：
Comparing causal relationships across populations is essential in many scientific domains. This paper studies the problem of inferring a difference graph between two environments and proposes a causal discovery method for linear structural causal models based on equality tests of regression coefficients. We show that invariance of regression coefficients is governed by graphical conditions that go beyond standard d-separation. Therefore, we introduce diff-separation, a graphical criterion that characterizes when a conditioning set blocks all paths capable of inducing differences in regression coefficients across environments. Building on this criterion, we introduce a corresponding diff-faithfulness assumption, linking graphical diff-separation statements to equality constraints on regression coefficients. Finally, we propose LDiffPC, a PC-style algorithm that uses equality tests of regression coefficients to recover the differences from multi-environment data.
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