论文标题
关于因果模型的等效性：类别理论方法
On the Equivalence of Causal Models: A Category-Theoretic Approach
论文作者
论文摘要
我们开发了一个类别理论标准，用于确定在离散变量上具有不同但同构的无环图的因果模型的等效性。遵循Jacobs等。 （2019年），我们将因果模型定义为一种因果弦图的概率解释，即``语法'''类别$ \ textsf {syn} _g $ g $ of cate $ \ textsf $ \ textsf {stochsf {stoch} $的函数。然后根据两个这样的函数之间的自然变换或同构定义因果模型的等效性，我们将其称为$φ$ -ABSTRACTION和$φ$ - 等价性。结果表明，当一种模型是另一个模型的$φ$ -ABSTRACTION时，可以将前者的干预计算始终转换为后者的干预计算。我们还确定了当变换是确定性时，模型可容纳$φ$ -ABSTRACTION的条件。
We develop a category-theoretic criterion for determining the equivalence of causal models having different but homomorphic directed acyclic graphs over discrete variables. Following Jacobs et al. (2019), we define a causal model as a probabilistic interpretation of a causal string diagram, i.e., a functor from the ``syntactic'' category $\textsf{Syn}_G$ of graph $G$ to the category $\textsf{Stoch}$ of finite sets and stochastic matrices. The equivalence of causal models is then defined in terms of a natural transformation or isomorphism between two such functors, which we call a $Φ$-abstraction and $Φ$-equivalence, respectively. It is shown that when one model is a $Φ$-abstraction of another, the intervention calculus of the former can be consistently translated into that of the latter. We also identify the condition under which a model accommodates a $Φ$-abstraction, when transformations are deterministic.
