Causal Abstraction with Soft Interventions

Riccardo Massidda, Atticus Geiger, Thomas Icard, Davide Bacciu
Proceedings of the Second Conference on Causal Learning and Reasoning, PMLR 213:68-87, 2023.

Abstract

Causal abstraction provides a theory describing how several causal models can represent the same system at different levels of detail. Existing theoretical proposals limit the analysis of abstract models to "hard" interventions fixing causal variables to be constant values. In this work, we extend causal abstraction to "soft" interventions, which assign possibly non-constant functions to variables without adding new causal connections. Specifically, (i) we generalize $\tau$-abstraction from Beckers and Halpern (2019) to soft interventions, (ii) we propose a further definition of soft abstraction to ensure a unique map $\omega$ between soft interventions, and (iii) we prove that our constructive definition of soft abstraction guarantees the intervention map $\omega$ has a specific and necessary explicit form.

Cite this Paper

BibTeX
@InProceedings{pmlr-v213-massidda23a, title = {Causal Abstraction with Soft Interventions}, author = {Massidda, Riccardo and Geiger, Atticus and Icard, Thomas and Bacciu, Davide}, booktitle = {Proceedings of the Second Conference on Causal Learning and Reasoning}, pages = {68--87}, year = {2023}, editor = {van der Schaar, Mihaela and Zhang, Cheng and Janzing, Dominik}, volume = {213}, series = {Proceedings of Machine Learning Research}, month = {11--14 Apr}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v213/massidda23a/massidda23a.pdf}, url = {https://proceedings.mlr.press/v213/massidda23a.html}, abstract = {Causal abstraction provides a theory describing how several causal models can represent the same system at different levels of detail. Existing theoretical proposals limit the analysis of abstract models to "hard" interventions fixing causal variables to be constant values. In this work, we extend causal abstraction to "soft" interventions, which assign possibly non-constant functions to variables without adding new causal connections. Specifically, (i) we generalize $\tau$-abstraction from Beckers and Halpern (2019) to soft interventions, (ii) we propose a further definition of soft abstraction to ensure a unique map $\omega$ between soft interventions, and (iii) we prove that our constructive definition of soft abstraction guarantees the intervention map $\omega$ has a specific and necessary explicit form.} }
Endnote
%0 Conference Paper %T Causal Abstraction with Soft Interventions %A Riccardo Massidda %A Atticus Geiger %A Thomas Icard %A Davide Bacciu %B Proceedings of the Second Conference on Causal Learning and Reasoning %C Proceedings of Machine Learning Research %D 2023 %E Mihaela van der Schaar %E Cheng Zhang %E Dominik Janzing %F pmlr-v213-massidda23a %I PMLR %P 68--87 %U https://proceedings.mlr.press/v213/massidda23a.html %V 213 %X Causal abstraction provides a theory describing how several causal models can represent the same system at different levels of detail. Existing theoretical proposals limit the analysis of abstract models to "hard" interventions fixing causal variables to be constant values. In this work, we extend causal abstraction to "soft" interventions, which assign possibly non-constant functions to variables without adding new causal connections. Specifically, (i) we generalize $\tau$-abstraction from Beckers and Halpern (2019) to soft interventions, (ii) we propose a further definition of soft abstraction to ensure a unique map $\omega$ between soft interventions, and (iii) we prove that our constructive definition of soft abstraction guarantees the intervention map $\omega$ has a specific and necessary explicit form.
APA
Massidda, R., Geiger, A., Icard, T. & Bacciu, D.. (2023). Causal Abstraction with Soft Interventions. Proceedings of the Second Conference on Causal Learning and Reasoning, in Proceedings of Machine Learning Research 213:68-87 Available from https://proceedings.mlr.press/v213/massidda23a.html.

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