Exclusivity Graph Approach to Instrumental Inequalities

Davide Poderini, Rafael Chaves, Iris Agresti, Gonzalo Carvacho, Fabio Sciarrino
Proceedings of The 35th Uncertainty in Artificial Intelligence Conference, PMLR 115:1274-1283, 2020.

Abstract

Instrumental variables allow the estimation of cause and effect relations even in presence of unobserved latent factors, thus providing a powerful tool for any science wherein causal inference plays an important role. More recently, the instrumental scenario has also attracted increasing attention in quantum physics, since it is related to the seminal Bell’s theorem and in fact allows the detection of even stronger quantum effects, thus enhancing our current capabilities to process information and becoming a valuable tool in quantum cryptography. In this work, we further explore this bridge between causality and quantum theory and apply a technique, originally developed in the field of quantum foundations, to express the constraints implied by causal relations in the language of graph theory. This new approach can be applied to any causal model containing a latent variable. Here, by focusing on the instrumental scenario, it allows us to easily reproduce known results as well as obtain new ones and gain new insights on the connections and differences between the instrumental and the Bell scenarios.

Cite this Paper

BibTeX
@InProceedings{pmlr-v115-poderini20a, title = {Exclusivity Graph Approach to Instrumental Inequalities}, author = {Poderini, Davide and Chaves, Rafael and Agresti, Iris and Carvacho, Gonzalo and Sciarrino, Fabio}, booktitle = {Proceedings of The 35th Uncertainty in Artificial Intelligence Conference}, pages = {1274--1283}, year = {2020}, editor = {Adams, Ryan P. and Gogate, Vibhav}, volume = {115}, series = {Proceedings of Machine Learning Research}, month = {22--25 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v115/poderini20a/poderini20a.pdf}, url = {https://proceedings.mlr.press/v115/poderini20a.html}, abstract = {Instrumental variables allow the estimation of cause and effect relations even in presence of unobserved latent factors, thus providing a powerful tool for any science wherein causal inference plays an important role. More recently, the instrumental scenario has also attracted increasing attention in quantum physics, since it is related to the seminal Bell’s theorem and in fact allows the detection of even stronger quantum effects, thus enhancing our current capabilities to process information and becoming a valuable tool in quantum cryptography. In this work, we further explore this bridge between causality and quantum theory and apply a technique, originally developed in the field of quantum foundations, to express the constraints implied by causal relations in the language of graph theory. This new approach can be applied to any causal model containing a latent variable. Here, by focusing on the instrumental scenario, it allows us to easily reproduce known results as well as obtain new ones and gain new insights on the connections and differences between the instrumental and the Bell scenarios. } }
Endnote
%0 Conference Paper %T Exclusivity Graph Approach to Instrumental Inequalities %A Davide Poderini %A Rafael Chaves %A Iris Agresti %A Gonzalo Carvacho %A Fabio Sciarrino %B Proceedings of The 35th Uncertainty in Artificial Intelligence Conference %C Proceedings of Machine Learning Research %D 2020 %E Ryan P. Adams %E Vibhav Gogate %F pmlr-v115-poderini20a %I PMLR %P 1274--1283 %U https://proceedings.mlr.press/v115/poderini20a.html %V 115 %X Instrumental variables allow the estimation of cause and effect relations even in presence of unobserved latent factors, thus providing a powerful tool for any science wherein causal inference plays an important role. More recently, the instrumental scenario has also attracted increasing attention in quantum physics, since it is related to the seminal Bell’s theorem and in fact allows the detection of even stronger quantum effects, thus enhancing our current capabilities to process information and becoming a valuable tool in quantum cryptography. In this work, we further explore this bridge between causality and quantum theory and apply a technique, originally developed in the field of quantum foundations, to express the constraints implied by causal relations in the language of graph theory. This new approach can be applied to any causal model containing a latent variable. Here, by focusing on the instrumental scenario, it allows us to easily reproduce known results as well as obtain new ones and gain new insights on the connections and differences between the instrumental and the Bell scenarios.
APA
Poderini, D., Chaves, R., Agresti, I., Carvacho, G. & Sciarrino, F.. (2020). Exclusivity Graph Approach to Instrumental Inequalities. Proceedings of The 35th Uncertainty in Artificial Intelligence Conference, in Proceedings of Machine Learning Research 115:1274-1283 Available from https://proceedings.mlr.press/v115/poderini20a.html.

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