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.

翻译：跨群体间因果关系的比较在许多科学领域至关重要。本文研究了推断两个环境之间差异图的问题，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。我们证明了回归系数的不变性受超越标准d-分离的图形条件支配。因此，我们引入了diff-分离（一种图形化准则），该准则刻画了何时条件集能阻断所有可能引起跨环境回归系数差异的路径。基于该准则，我们提出了相应的diff-忠实性假设，将图形化的diff-分离陈述与回归系数的等式约束联系起来。最后，我们提出了LDiffPC算法——一种PC风格算法，通过检验回归系数相等性从多环境数据中恢复差异。