Code, notebooks and resources on the problem of abstraction of structural causal models.
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notebooks: collection of notebooks providing introduction, tutorial and reproductions of work in the literature.
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src: up-to-date source code for implementing and working with abstractions between SCMs.
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tutorials: notebooks illustrating how to use the source code for custom problems.
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papers: resources related to specific publications.
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legacy: legacy code required to run some notebooks.
This is a work in progress: code and notebooks are executable, but in continuous development. TODO sections are sprinkled across the notebooks and the code.
Feedbacks are welcome: mistakes are in all likelihood due to my misunderstandings and suggestions/corrections are very welcome! :)
References: content often refers to ideas from causality and category theory. Useful references for causality are [Pearl2009,Peters2017], while for category theory are [Spivak2014,Fong2018].
[Rubenstein2017] Paul K Rubenstein, Sebastian Weichwald, Stephan Bongers, Joris M Mooij, Dominik Janzing, Moritz Grosse-Wentrup, and Bernhard Scholkopf. "Causal consistency of structural equation models." Uncertainty in Artificial Intelligence (UAI). 2017.
[Rischel2020] Rischel, Eigil Fjeldgren. "The Category Theory of Causal Models." (2020).
[Rischel2021] Rischel, Eigil F., and Sebastian Weichwald. "Compositional abstraction error and a category of causal models." Uncertainty in Artificial Intelligence. PMLR, 2021.
[Pearl2009] Pearl, Judea. Causality. Cambridge university press, 2009.
[Peters2017] Peters, Jonas, Dominik Janzing, and Bernhard Schölkopf. Elements of causal inference: foundations and learning algorithms. The MIT Press, 2017.
[Spivak2014] Spivak, David I. Category theory for the sciences. MIT Press, 2014.
[Fong2018] Fong, Brendan, and David I. Spivak. "Seven sketches in compositionality: An invitation to applied category theory." arXiv preprint arXiv:1803.05316 (2018).
[Otsuka2022] Otsuka, Jun, and Hayato Saigo. "On the Equivalence of Causal Models: A Category-Theoretic Approach." arXiv preprint arXiv:2201.06981 (2022).
[Beckers2019] Beckers, Sander, and Joseph Y. Halpern. "Abstracting causal models." Proceedings of the AAAI conference on artificial intelligence. Vol. 33. No. 01. 2019.
[Beckers2020] Beckers, Sander, Frederick Eberhardt, and Joseph Y. Halpern. "Approximate causal abstractions." Uncertainty in Artificial Intelligence. PMLR, 2020.
[Chalupka2015] Chalupka, Krzysztof, Pietro Perona, and Frederick Eberhardt. "Visual causal feature learning." Proceedings of the Thirty-First Conference on Uncertainty in Artificial Intelligence. 2015.
[Chalupka2017] Chalupka, Krzysztof, Frederick Eberhardt, and Pietro Perona. "Causal feature learning: an overview." Behaviormetrika 44.1 (2017): 137-164.
[Hoel2013] Hoel, Erik P., Larissa Albantakis, and Giulio Tononi. "Quantifying causal emergence shows that macro can beat micro." Proceedings of the National Academy of Sciences 110.49 (2013): 19790-19795.
[Hoel2017] Hoel, Erik P. "When the map is better than the territory." Entropy 19.5 (2017): 188.
[Zennaro2022a] Zennaro, Fabio Massimo, Paolo Turrini, and Theodoros Damoulas. "Towards Computing an Optimal Abstraction for Structural Causal Models." UAI 2022 Workshop on Causal Representation Learning.
[Zennaro2022b] Zennaro, Fabio Massimo. "Abstraction between Structural Causal Models: A Review of Definitions and Properties." UAI 2022 Workshop on Causal Representation Learning.
[Zennaro2023a] Zennaro, Fabio Massimo, Máté Drávucz, Geanina Apachitei, W. Dhammika Widanage, Theodoros Damoulas. "Jointly Learning Consistent Causal Abstractions Over Multiple Interventional Distributions." CleaR 2023.
[Zennaro2023b] Zennaro, Fabio Massimo, Paolo Turrini, and Theodoros Damoulas. "Quantifying Consistency and Information Loss for Causal Abstraction Learning." IJCAI 2023.