D
Demerzel
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Geometry of Statistical Data via Large Deviation Theory and Legendre-Fenchel Duality
A perspective that derives the entropy functions of information theory (Shannon entropy, mutual information, relative and conditional entropy) as large-deviation rate functions via Sanov's theorem, and uses the Legendre-Fenchel transform to expose a dual geometric structure (contractions, lifts, projections) linking information geometry to statistical thermodynamics, introducing empirical 'data' into information geometry through LF-conjugate parametrization of the manifold of empirical means.