Causal Models with Constraints

Sander Beckers, Joseph Halpern, Christopher Hitchcock
Proceedings of the Second Conference on Causal Learning and Reasoning, PMLR 213:866-879, 2023.

Abstract

Causal models have proven extremely useful in offering formal representations of causal relationships between a set of variables. Yet in many situations, there are non-causal relationships among variables. For example, we may want variables $LDL$, $HDL$, and $TOT$ that represent the level of low-density lipoprotein cholesterol, the level of high-density lipoprotein cholesterol, and total cholesterol level, with the relation $LDL+HDL = TOT$. This cannot be done in standard causal models, because we can intervene simultaneously on all three variables. The goal of this paper is to extend standard causal models to allow for constraints on settings of variables. Although the extension is relatively straightforward, to make it useful we have to define a new intervention operation that disconnects a variable from a causal equation. We give examples showing the usefulness of this extension, and provide a sound and complete axiomatization for causal models with constraints.

Cite this Paper

BibTeX
@InProceedings{pmlr-v213-beckers23a, title = {Causal Models with Constraints}, author = {Beckers, Sander and Halpern, Joseph and Hitchcock, Christopher}, booktitle = {Proceedings of the Second Conference on Causal Learning and Reasoning}, pages = {866--879}, 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/beckers23a/beckers23a.pdf}, url = {https://proceedings.mlr.press/v213/beckers23a.html}, abstract = {Causal models have proven extremely useful in offering formal representations of causal relationships between a set of variables. Yet in many situations, there are non-causal relationships among variables. For example, we may want variables $LDL$, $HDL$, and $TOT$ that represent the level of low-density lipoprotein cholesterol, the level of high-density lipoprotein cholesterol, and total cholesterol level, with the relation $LDL+HDL = TOT$. This cannot be done in standard causal models, because we can intervene simultaneously on all three variables. The goal of this paper is to extend standard causal models to allow for constraints on settings of variables. Although the extension is relatively straightforward, to make it useful we have to define a new intervention operation that disconnects a variable from a causal equation. We give examples showing the usefulness of this extension, and provide a sound and complete axiomatization for causal models with constraints.} }
Endnote
%0 Conference Paper %T Causal Models with Constraints %A Sander Beckers %A Joseph Halpern %A Christopher Hitchcock %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-beckers23a %I PMLR %P 866--879 %U https://proceedings.mlr.press/v213/beckers23a.html %V 213 %X Causal models have proven extremely useful in offering formal representations of causal relationships between a set of variables. Yet in many situations, there are non-causal relationships among variables. For example, we may want variables $LDL$, $HDL$, and $TOT$ that represent the level of low-density lipoprotein cholesterol, the level of high-density lipoprotein cholesterol, and total cholesterol level, with the relation $LDL+HDL = TOT$. This cannot be done in standard causal models, because we can intervene simultaneously on all three variables. The goal of this paper is to extend standard causal models to allow for constraints on settings of variables. Although the extension is relatively straightforward, to make it useful we have to define a new intervention operation that disconnects a variable from a causal equation. We give examples showing the usefulness of this extension, and provide a sound and complete axiomatization for causal models with constraints.
APA
Beckers, S., Halpern, J. & Hitchcock, C.. (2023). Causal Models with Constraints. Proceedings of the Second Conference on Causal Learning and Reasoning, in Proceedings of Machine Learning Research 213:866-879 Available from https://proceedings.mlr.press/v213/beckers23a.html.

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