From Geometry to Causality- Ricci Curvature and the Reliability of Causal Inference on Networks

Amirhossein Farzam, Allen Tannenbaum, Guillermo Sapiro
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:13086-13108, 2024.

Abstract

Causal inference on networks faces challenges posed in part by violations of standard identification assumptions due to dependencies between treatment units. Although graph geometry fundamentally influences such dependencies, the potential of geometric tools for causal inference on networked treatment units is yet to be unlocked. Moreover, despite significant progress utilizing graph neural networks (GNNs) for causal inference on networks, methods for evaluating their achievable reliability without ground truth are lacking. In this work we establish for the first time a theoretical link between network geometry, the graph Ricci curvature in particular, and causal inference, formalizing the intrinsic challenges that negative curvature poses to estimating causal parameters. The Ricci curvature can then be used to assess the reliability of causal estimates in structured data, as we empirically demonstrate. Informed by this finding, we propose a method using the geometric Ricci flow to reduce causal effect estimation error in networked data, showcasing how this newfound connection between graph geometry and causal inference could improve GNN-based causal inference. Bridging graph geometry and causal inference, this paper opens the door to geometric techniques for improving causal estimation on networks.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-farzam24a, title = {From Geometry to Causality- Ricci Curvature and the Reliability of Causal Inference on Networks}, author = {Farzam, Amirhossein and Tannenbaum, Allen and Sapiro, Guillermo}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {13086--13108}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/farzam24a/farzam24a.pdf}, url = {https://proceedings.mlr.press/v235/farzam24a.html}, abstract = {Causal inference on networks faces challenges posed in part by violations of standard identification assumptions due to dependencies between treatment units. Although graph geometry fundamentally influences such dependencies, the potential of geometric tools for causal inference on networked treatment units is yet to be unlocked. Moreover, despite significant progress utilizing graph neural networks (GNNs) for causal inference on networks, methods for evaluating their achievable reliability without ground truth are lacking. In this work we establish for the first time a theoretical link between network geometry, the graph Ricci curvature in particular, and causal inference, formalizing the intrinsic challenges that negative curvature poses to estimating causal parameters. The Ricci curvature can then be used to assess the reliability of causal estimates in structured data, as we empirically demonstrate. Informed by this finding, we propose a method using the geometric Ricci flow to reduce causal effect estimation error in networked data, showcasing how this newfound connection between graph geometry and causal inference could improve GNN-based causal inference. Bridging graph geometry and causal inference, this paper opens the door to geometric techniques for improving causal estimation on networks.} }
Endnote
%0 Conference Paper %T From Geometry to Causality- Ricci Curvature and the Reliability of Causal Inference on Networks %A Amirhossein Farzam %A Allen Tannenbaum %A Guillermo Sapiro %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-farzam24a %I PMLR %P 13086--13108 %U https://proceedings.mlr.press/v235/farzam24a.html %V 235 %X Causal inference on networks faces challenges posed in part by violations of standard identification assumptions due to dependencies between treatment units. Although graph geometry fundamentally influences such dependencies, the potential of geometric tools for causal inference on networked treatment units is yet to be unlocked. Moreover, despite significant progress utilizing graph neural networks (GNNs) for causal inference on networks, methods for evaluating their achievable reliability without ground truth are lacking. In this work we establish for the first time a theoretical link between network geometry, the graph Ricci curvature in particular, and causal inference, formalizing the intrinsic challenges that negative curvature poses to estimating causal parameters. The Ricci curvature can then be used to assess the reliability of causal estimates in structured data, as we empirically demonstrate. Informed by this finding, we propose a method using the geometric Ricci flow to reduce causal effect estimation error in networked data, showcasing how this newfound connection between graph geometry and causal inference could improve GNN-based causal inference. Bridging graph geometry and causal inference, this paper opens the door to geometric techniques for improving causal estimation on networks.
APA
Farzam, A., Tannenbaum, A. & Sapiro, G.. (2024). From Geometry to Causality- Ricci Curvature and the Reliability of Causal Inference on Networks. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:13086-13108 Available from https://proceedings.mlr.press/v235/farzam24a.html.

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