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arXiv · 1903.11190

Information Geometric Complexity of Entropic Motion on Curved Statistical Manifolds under Different Metrizations of Probability Spaces

Steven Gassner·Carlo Cafaro
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Abstract

We investigate the effect of different metrizations of probability spaces on the information geometric complexity of entropic motion on curved statistical manifolds. Specifically, we provide a comparative analysis based upon Riemannian geometric properties and entropic dynamical features of a Gaussian probability space where the two distinct dissimilarity measures between probability distributions are the Fisher-Rao information metric and the alpha-order entropy metric. In the former case, we observe an asymptotic linear temporal growth of the information geometric entropy (IGE) together with a fast convergence to the final state of the system. In the latter case, instead, we note an asymptotic logarithmic temporal growth of the IGE together with a slow convergence to the final state of the system. Finally, motivated by our findings, we provide some insights on a tradeoff between complexity and speed of convergence to the final state in our information geometric approach to problems of entropic inference.

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Steven Gassner, Carlo Cafaro. 2019-03-26. Information Geometric Complexity of Entropic Motion on Curved Statistical Manifolds under Different Metrizations of Probability Spaces. https://doi.org/10.1142/s0219887819500828

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