Published: Springer, 2019
Description:
1 online resource (xix, 770 pages) : illustrations (some color).
Contents:
“…Part II: Extreme values.- Part 8: Computational Information Geometry.- Topological methods for unsupervised learning.- Geometry and fixed-rate quantization in Riemannian metric spaces induced by separable Bregman divergences.- The statistical Minkowski distances: Closed-form formula for Gaussian Mixture Models.- Parameter estimation with generalized empirical localization.- Properties of the cross entropy of ARMA processes.- Part 9: Statistical Manifold & Hessian Information Geometry.- Inequalities for Statistical Submanifolds in Hessian Manifolds of Constant Hessian curvature.- Inequalities for statistical submanifolds in sasakian statistical manifolds.- Generalized Wintgen Inequality for Legendrian Submanifolds in Sasakian statistical manifolds.- Logarithmic divergence: geometry and interpretation of curvature.- Hessian Curvature and Optimal Transport.- Part 10: Non-parametric Information Geometry.- Divergence functions in Information Geometry.- Sobolev Statistical Manifolds and Exponential Models.- Minimization of the Kullback-Leibler divergence over a log-normal exponential arc.- Riemannian distance and diameter of the space of probability measures and the parametrix.- Part 11: Statistics on non-linear data.- A unified formulation for the Bures-Wasserstein and Log-Euclidean/Log-Hilbert-Schmidt distances between positive definite
operators.- Exploration of Balanced Metrics on Symmetric Positive Definite Matrices.- Affine-invariant midrange statistics.- Is affine-invariance well
defined on SPD matrices? …”
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