Differential Geometrical Theory of Statistics

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symmetric positive definite matrices; Laplace distribution; expectation-maximization; Bayesian information criterion; texture classification; syntax; principles and parameters; error-correcting codes; asymptotic bound; Kolmogorov complexity; Gilbert–Varshamov bound; Shannon entropy; Lie groups; symplectic geometry; affine tensors; continuum thermodynamics; statistical mechanics; ϕ–divergences; robust estimation; EM algorithm; proximal-point algorithms; mixture models; curve system entropy; curves manifold; curve clustering; probability distribution estimation; air traffic management; Lagrangian formalism; Hamiltonian formalism; symplectic manifolds; Poisson structures; symmetry groups; momentum maps; thermodynamic equilibria; generalized Gibbs states; directional data; circular mean; universal confidence sets; non-asymptotic confidence sets; mass concentration inequalities; Hoeffding’s inequality; convex cone; homogeneous cone; graphical model; Koszul–Vinberg characteristic function; Lie group thermodynamics; moment map; Gibbs density; Gibbs equilibrium; maximum entropy; information geometry; symplectic geometry; Cartan-Poincaré integral invariant; geometric mechanics; Euler-Poincaré equation; Fisher metric; gauge theory; affine group; kernel density estimation; Siegel space; symmetric spaces; radar signals; Rényi divergence; φ-function; φ-divergence; φ-family; statistical manifold; information geometry; extended multinomial models; goodness-of-fit testing; information geometry; sub-Riemannian geometry; geodesics; most probable paths; stochastic development; non-linear data analysis; statistics; KV cohomoloy; functor of Amari; Riemannian foliation; symplectic foliation; entropy flow; moduli space of statistical models; homological statistical models; geometry of Koszul; localization; vanishing theorem; information geometry; mixture models; α-divergences; log-sum-exp bounds; escort distribution; escort expectation; statistical manifold; deformed exponential family; Tsallis statistics; information geometry