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.

本文研究如何在不确定模型图结构的情况下，通过识别函数机制变化来比较两个或多个相关结构因果模型。我们提出使用非线性加性噪声模型对各模型进行建模，并证明了使用混合分布的分数函数的雅可比矩阵可以用于识别非参数函数机制中的变化。在确认变化的因素后，我们进一步使用其他方法来估计变化的结构差异，以此来帮助理解在不同环境下各个变量的差异。