Information geometric complexity of a trivariate Gaussian statistical model

Abstract

We evaluate the information geometric complexity of entropic motion on low-dimensional Gaussian statistical manifolds in order to quantify how difficult is making macroscopic predictions about a systems in the presence of limited information. Specifically, we observe that the complexity of such entropic inferences not only depends on the amount of available pieces of information but also on the manner in which such pieces are correlated. Finally, we uncover that for certain correlational structures, the impossibility of reaching the most favorable configuration from an entropic inference viewpoint, seems to lead to an information geometric analog of the well-known frustration effect that occurs in statistical physics.

arXiv comment16 pages, 1 figure

References in corpus (10)

• Maximum Entropy and Bayesian Data Analysis: Entropic Priors
• Entropic Dynamics
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• Noiseless Collective Motion out of Noisy Chaos
• Works on an information geometrodynamical approach to chaos
• Networks in Motion
• The Effect Of Microscopic Correlations On The Information Geometric Complexity Of Gaussian Statistical Models
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Cited by in corpus (5)

• Information geometric methods for complexity
• Application of the Maximum relative Entropy method to the physics of ferromagnetic materials
• Theoretical investigations of an information geometric approach to complexity
• Approximation and bounding techniques for the Fisher-Rao distances between parametric statistical models
• An information geometric perspective on the complexity of macroscopic predictions arising from incomplete information