2022-06-28-otsuka22a.md

abstract	booktitle	title	year	layout	series	publisher	issn	id	month	tex_title	firstpage	lastpage	page	order	cycles	bibtex_author	author	date	address	container-title	volume	genre	issued	pdf	extras
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 Syn_G of graph $G$ to the category 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. It is shown that when one model is a $\Phi$-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 $\Phi$-abstraction, when transformations are deterministic.	First Conference on Causal Learning and Reasoning	On the Equivalence of Causal Models: A Category-Theoretic Approach	2022	inproceedings	Proceedings of Machine Learning Research	PMLR	2640-3498	otsuka22a	0	On the Equivalence of Causal Models: A Category-Theoretic Approach	634	646	634-646	634	false	Otsuka, Jun and Saigo, Hayato	given family Jun Otsuka given family Hayato Saigo	2022-06-28		Proceedings of the First Conference on Causal Learning and Reasoning	177	inproceedings	date-parts 2022 6 28	https://proceedings.mlr.press/v177/otsuka22a/otsuka22a.pdf