Progress in Information Geometry

This book focuses on information-geometric manifolds of structured data and models and related applied mathematics. It features new and fruitful interactions between several branches of science: Advanced Signal/Image/Video Processing, Complex Data Modeling and Analysis, Statistics on Manifolds, Topology/Machine/Deep Learning and Artificial Intelligence. The selection of applications makes the book a substantial information source, not only for academic scientist but it is also highly relevant for industry.

The book project was initiated following discussions at the international conference GSI'2019 - Geometric Science of Information that was held at ENAC, Toulouse (France).

Information Geometry of smooth densities on the Gaussian space: Poincare inequalities. - On Normalization Functions and -families of Probability Distributions. - Affine Connections with Torsion in (para-)complexified Structures. - Contact Hamiltonian systems for probability distribution functions and expectation variables: A study based on a class of master equations. - Invariant Koszul Form of Homogeneous Bounded Domains and Information Geometry Structures. - Gauge freedom of entropies on q-Gaussian measures. - On geodesic triangles with right angles in a dually flat space. - Chain Rule Optimal Transport. - Towards the Shape of Cosmological Observables and the String Theory Landscape with Topological Data Analysis. - A review of two decades of correlations, hierarchies, networks and clustering in financial markets.