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2022

On the Equivalence of Causal Models: A Category-Theoretic Approach

Otsuka, Jun, Saigo, Hayato

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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 $\Phi$-abstraction and $\Phi$-equivalence, respectively.

On the Equivalence of Causal Models: A Category-Theoretic Approach · Around

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Category Theory
Steve Awodey · 2010
Earlier work this paper cites.
Visual causal feature learning
Krzysztof Chalupka, Pietro Perona, and Frederick Eberhardt · 2014
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Multi-Level Cause-Effect systems
Krzysztof Chalupka, Frederick Eberhardt, and Pietro Perona · 2016
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