Causal Geometry
Name
entropy-23-00024.pdf
Size
2.06 MB
Format
Adobe PDF
Checksum (MD5)
c199dd5dc0f41d5945f6ad3500e33cbd
Author(s)
Chvykov, Pavel
Hoel, Erik
Date Issued
December 26, 2020
Publisher
Multidisciplinary Digital Publishing Institute
Citation
Entropy 23 (1): 24 (2021)
Version
Final published version
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Physics
Terms of Use
Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.3390/e23010024
