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Article

Causal Geometry

by 1,* and 2
1
Physics of Living Systems, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
2
Allen Discovery Center, Tufts University, Medford, MA 02155, USA
*
Author to whom correspondence should be addressed.
Entropy 2021, 23(1), 24; https://doi.org/10.3390/e23010024
Received: 15 October 2020 / Revised: 4 December 2020 / Accepted: 21 December 2020 / Published: 26 December 2020
(This article belongs to the Collection Feature Papers in Information Theory)
Information geometry has offered a way to formally study the efficacy of scientific models by quantifying the impact of model parameters on the predicted effects. However, there has been little formal investigation of causation in this framework, despite causal models being a fundamental part of science and explanation. Here, we introduce causal geometry, which formalizes not only how outcomes are impacted by parameters, but also how the parameters of a model can be intervened upon. Therefore, we introduce a geometric version of “effective information”—a known measure of the informativeness of a causal relationship. We show that it is given by the matching between the space of effects and the space of interventions, in the form of their geometric congruence. Therefore, given a fixed intervention capability, an effective causal model is one that is well matched to those interventions. This is a consequence of “causal emergence,” wherein macroscopic causal relationships may carry more information than “fundamental” microscopic ones. We thus argue that a coarse-grained model may, paradoxically, be more informative than the microscopic one, especially when it better matches the scale of accessible interventions—as we illustrate on toy examples. View Full-Text
Keywords: model selection; causality; sloppy models; information geometry; effective information model selection; causality; sloppy models; information geometry; effective information
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MDPI and ACS Style

Chvykov, P.; Hoel, E. Causal Geometry. Entropy 2021, 23, 24. https://doi.org/10.3390/e23010024

AMA Style

Chvykov P, Hoel E. Causal Geometry. Entropy. 2021; 23(1):24. https://doi.org/10.3390/e23010024

Chicago/Turabian Style

Chvykov, Pavel, and Erik Hoel. 2021. "Causal Geometry" Entropy 23, no. 1: 24. https://doi.org/10.3390/e23010024

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