On The Complexity Of Statistical Models Admitting Correlations

TL;DR

This paper analyzes how correlations in Gaussian statistical models influence the asymptotic behavior of their dynamical complexity, revealing a power law decay and macro-correlations leading to information geometric compression.

Contribution

It introduces an algorithmic approach to compute the asymptotic complexity of correlated Gaussian models and highlights the impact of correlations on complexity decay.

Findings

Complexity decays as a power law with rate depending on correlation coefficient.

Macro-correlations cause asymptotic information geometric compression.

Diagonalization simplifies the analysis of correlated Gaussian models.

Abstract

We compute the asymptotic temporal behavior of the dynamical complexity associated with the maximum probability trajectories on Gaussian statistical manifolds in presence of correlations between the variables labeling the macrostates of the system. The algorithmic structure of our asymptotic computations is presented and special focus is devoted to the diagonalization procedure that allows to simplify the problem in a remarkable way. We observe a power law decay of the information geometric complexity at a rate determined by the correlation coefficient. We conclude that macro-correlations lead to the emergence of an asymptotic information geometric compression of the statistical macrostates explored on the configuration manifold of the model in its evolution between the initial and final macrostates.