Information Geometry and Its Applications

The book gathers contributions from the fourth conference on Information Geometry and its Applications, which was held on June 12-17, 2016, at Liblice Castle, Czech Republic on the occasion of Shun-ichi Amari's 80th birthday and was organized by the Czech Academy of Sciences' Institute of Information Theory and Automation. The conference received valuable financial support from the Max Planck Institute for Mathematics in the Sciences (Information Theory of Cognitive Systems Group), Czech Academy of Sciences' Institute of Information Theory and Automation, and Università degli Studi di Roma Tor Vergata. The aim of the conference was to highlight recent advances in the field of information geometry and to identify new research directions. To this end, the event brought together leading experts in the field who, in invited talks and poster sessions, discussed both theoretical work and achievements in the many fields of application in which information geometry plays an essential role.

Contenu

Part: 1, introduction.- Part 2: Applications of Information Geometry, Shunichi Amari, Naotsugu Tsuchiya, Masafumi Oizumi, Geometry of Information Integration.- Nils Bertschinger, Juergen Jost, Eckehard Olbrich and David Wolpert, Information geometry and game theory.- Sumio Watanabe, Higher order equivalence of Bayes cross validation and WAIC.- Guido Montufar, Restricted Boltzmann Machines: Introduction and Review.- Part 3: Innite-dimensional Information Geometry, Giovanni Pistone, Information Geometry of the Gaussian Space.- Lorenz Schwachhofer, Nihat Ay, Jurgen Jost and Hong Van Le, Congruent families and invariant tensors.- Nigel Newton, Nonlinear Filtering and Information Geometry: a Hilbert Manifold Approach.- Minh Ha Quang, Innite-dimensional Log-Determinant divergences III: Log-Euclidean and Log-Hilbert-Schmidt divergences.- Part 4: Theoretical Aspects of Information Geometry, Peter Harremoes, Entropy on Spin Factors.- Shinto Eguchi, Osamu Komori and Atsumi Ohara, Information geometry associated with generalized means.- Jun Zhang, Codazzi-(Para-)Kahler Geometry.- Atsumi Ohara, Doubly autoparallel structures on the probability simplex.- Akio Fujiwara, Amari-Chentsov's paradox.- Alexander Rylov, Constant curvature connections on statistical models.- Roman Belavkin, Relation between the Kantorovich-Wasserstein metric and the Kullback-Leibler divergence.- Part 5: Quantum Information Geometry, Shunlong Luo and Yuan Sun, Some Inequalities for Wigner-Yanase Skew Information.- Davide Girolami, Information Geometry of Quantum Resources.- Marco Cianciaruso, Irene Frerot, Tommaso Tufarelli, Gerardo Adesso, Maximum local quantum covariances as quantiers of two-sided quantum correlations beyond entanglement.- Attila Andai, The eects of random qubit-qubit quantum channels to entropy gain, delity and trace distance.- Attila Lovas, Robertson-type Uncertainty Principles and Generalized Symmetric and Antisymmetric Covariances.