Transport information Hessian distances
Wuchen Li
TL;DR
This paper derives explicit formulas for Hessian distances of information entropies within one-dimensional probability spaces using the L2-Wasserstein metric, facilitating advanced analysis of probability distributions.
Contribution
It introduces closed-form expressions for Hessian distances of information entropies in 1D Wasserstein space, a novel analytical tool.
Findings
Provides explicit formulas for Hessian distances
Enables new analysis of probability distributions
Facilitates future research in information geometry
Abstract
We formulate closed-form Hessian distances of information entropies in one-dimensional probability density space embedded with the L2-Wasserstein metric.
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Taxonomy
TopicsStatistical Mechanics and Entropy · Geometric Analysis and Curvature Flows · Topological and Geometric Data Analysis