Large deviation entropy defines the geometry of empirical data manifolds, breaking spherical geometry for pairwise statistics, and equates information projections from information geometry with those in Kolmogorov probability theory under i.i.d. and Markov assumptions.
Statistical analysis of random motion and energetic behavior of counting: Gibbs’ theory revisited
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The Geometry of Statistical Data and Information: A Large Deviation Perspective
Large deviation entropy defines the geometry of empirical data manifolds, breaking spherical geometry for pairwise statistics, and equates information projections from information geometry with those in Kolmogorov probability theory under i.i.d. and Markov assumptions.