Structural causal models (SCMs) are widely used in various disciplines to represent causal relationships among variables in complex systems. Unfortunately, the underlying causal structure is often unknown, and estimating it from data remains a challenging task. In many situations, however, the end goal is to localize the changes (shifts) in the causal mechanisms between related datasets instead of learning the full causal structure of the individual datasets. Some applications include root cause analysis, analyzing gene regulatory network structure changes between healthy and cancerous individuals, or explaining distribution shifts. This paper focuses on identifying the causal mechanism shifts in two or more related datasets over the same set of variables -- without estimating the entire DAG structure of each SCM. Prior work under this setting assumed linear models with Gaussian noises; instead, in this work we assume that each SCM belongs to the more general class of nonlinear additive noise models (ANMs). A key technical contribution of this work is to show that the Jacobian of the score function for the mixture distribution allows for the identification of shifts under general non-parametric functional mechanisms. Once the shifted variables are identified, we leverage recent work to estimate the structural differences, if any, for the shifted variables. Experiments on synthetic and real-world data are provided to showcase the applicability of this approach. Code implementing the proposed method is open-source and publicly available at https://github.com/kevinsbello/iSCAN.

翻译：结构因果模型（SCM）广泛应用于多个学科领域，以表示复杂系统中变量间的因果关系。然而，底层因果结构通常是未知的，从数据中估计这一结构仍是一项具有挑战性的任务。但在许多情境下，最终目标并非学习单个数据集的完整因果结构，而是定位相关数据集之间因果机制的变化（偏移）。部分应用包括根因分析、分析健康个体与癌症个体之间基因调控网络结构的变化，或解释分布偏移。本文聚焦于在两个或多个共享同一变量集合的相关数据集中识别因果机制变化——无需估计每个SCM的完整有向无环图（DAG）结构。先前在此设定下的研究假设为高斯噪声的线性模型；相反，本文假定每个SCM属于更一般的非线性加性噪声模型（ANM）类别。本工作的一项关键技术贡献在于：证明了混合分布得分函数的雅可比矩阵能够识别一般非参数函数机制下的变量偏移。一旦识别出发生偏移的变量，我们利用近期工作来估计这些偏移变量（如果存在）的结构差异。通过在合成数据与真实数据上的实验，展示了该方法的适用性。实现所提方法的开源代码公开可获取于 https://github.com/kevinsbello/iSCAN。