Information Geometry and Its Applications: On the Occasion of Shun-ichi Amari's 80th Birthday, IGAIA IV Liblice, Czech Republic, June 2016

Description

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. Front Matter ....Pages i-x Front Matter ....Pages 1-1 Geometry of Information Integration (Shun-ichi Amari, Naotsugu Tsuchiya, Masafumi Oizumi)....Pages 3-17 Information Geometry and Game Theory (Jürgen Jost, Nils Bertschinger, Eckehard Olbrich, David Wolpert)....Pages 19-46 Higher Order Equivalence of Bayes Cross Validation and WAIC (Sumio Watanabe)....Pages 47-73 Restricted Boltzmann Machines: Introduction and Review (Guido Montúfar)....Pages 75-115 Front Matter ....Pages 117-117 Information Geometry of the Gaussian Space (Giovanni Pistone)....Pages 119-155 Congruent Families and Invariant Tensors (Lorenz Schwachhöfer, Nihat Ay, Jürgen Jost, Hông Vân Lê)....Pages 157-187 Nonlinear Filtering and Information Geometry: A Hilbert Manifold Approach (Nigel J. Newton)....Pages 189-208 Infinite-Dimensional Log-Determinant Divergences III: Log-Euclidean and Log-Hilbert–Schmidt Divergences (Hà Quang Minh)....Pages 209-243 Front Matter ....Pages 245-245 Entropy on Spin Factors (Peter Harremoës)....Pages 247-278 Information Geometry Associated with Generalized Means (Shinto Eguchi, Osamu Komori, Atsumi Ohara)....Pages 279-295 Information Geometry with (Para-)Kähler Structures (Jun Zhang, Teng Fei)....Pages 297-321 Doubly Autoparallel Structure on the Probability Simplex (Atsumi Ohara, Hideyuki Ishi)....Pages 323-334 Complementing Chentsov’s Characterization (Akio Fujiwara)....Pages 335-347 Constant Curvature Connections On Statistical Models (Alexander Rylov)....Pages 349-361 Relation Between the Kantorovich–Wasserstein Metric and the Kullback–Leibler Divergence (Roman V. Belavkin)....Pages 363-373 Front Matter ....Pages 375-375 Some Inequalities for Wigner–Yanase Skew Information (Shunlong Luo, Yuan Sun)....Pages 377-398 Information Geometry of Quantum Resources (Davide Girolami)....Pages 399-410 Characterising Two-Sided Quantum Correlations Beyond Entanglement via Metric-Adjusted f–Correlations (Marco Cianciaruso, Irénée Frérot, Tommaso Tufarelli, Gerardo Adesso)....Pages 411-430 The Effects of Random Qubit-Qubit Quantum Channels to Entropy Gain, Fidelity and Trace Distance (Attila Andai)....Pages 431-443 Robertson-Type Uncertainty Principles and Generalized Symmetric and Antisymmetric Covariances (Attila Lovas)....Pages 445-456