Structural causal models (SCMs) are widely used in various disciplines to represent causal relationships among variables in complex systems. Unfortunately, the true underlying directed acyclic graph (DAG) structure is often unknown, and determining it from observational or interventional data remains a challenging task. However, in many situations, the end goal is to identify changes (shifts) in causal mechanisms between related SCMs rather than recovering the entire underlying DAG structure. Examples include analyzing gene regulatory network structure changes between healthy and cancerous individuals or understanding variations in biological pathways under different cellular contexts. This paper focuses on identifying $\textit{functional}$ mechanism shifts in two or more related SCMs over the same set of variables -- $\textit{without estimating the entire DAG structure of each SCM}$. 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 contribution of this work is to show that the Jacobian of the score function for the $\textit{mixture distribution}$ allows for identification of shifts in 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.

翻译：结构因果模型（SCMs）广泛应用于多个学科，用于表示复杂系统中变量间的因果关系。然而，真实的有向无环图（DAG）结构通常是未知的，从观测数据或干预数据中推断该结构仍具挑战性。在许多场景中，最终目标并非恢复完整的底层DAG结构，而是识别相关SCM之间因果机制的差异（变化）。例如，分析健康个体与癌症个体之间基因调控网络结构的变化，或理解不同细胞背景下生物通路的变异。本文聚焦于识别两个或多个相关SCM中同一变量集合上的$\textit{功能}$机制变化——且$\textit{无需估计每个SCM的完整DAG结构}$。先前在此框架下的研究假设线性模型和高斯噪声；而本文假设每个SCM属于更一般的非线性加性噪声模型（ANM）类别。本研究的关键贡献在于证明：$\textit{混合分布}$的得分函数的雅可比矩阵能够识别非参数功能机制的变化。在识别出变化变量后，我们利用最新研究成果估计这些变量可能存在的结构差异。通过合成数据与真实数据的实验验证了该方法的适用性。