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Information Geometry and Its Applications

On the Occasion of Shun-ichi Amari's 80th Birthday, IGAIA IV Liblice, Czech Republic, June 2016

  • Nihat Ay
  • Paolo Gibilisco
  • František  Matúš
Conference proceedings IGAIA IV 2016

Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 252)

Table of contents

  1. Front Matter
    Pages i-x
    PDF

  2. Applications of Information Geometry

    1. Front Matter
      Pages 1-1
      PDF
    2. Geometry of Information Integration
      Shun-ichi Amari, Naotsugu Tsuchiya, Masafumi Oizumi
      Pages 3-17
    3. Information Geometry and Game Theory
      Jürgen Jost, Nils Bertschinger, Eckehard Olbrich, David Wolpert
      Pages 19-46
    4. Higher Order Equivalence of Bayes Cross Validation and WAIC
      Sumio Watanabe
      Pages 47-73
    5. Restricted Boltzmann Machines: Introduction and Review
      Guido Montúfar
      Pages 75-115

  3. Infinite-Dimensional Information Geometry

    1. Front Matter
      Pages 117-117
      PDF
    2. Information Geometry of the Gaussian Space
      Giovanni Pistone
      Pages 119-155
    3. Congruent Families and Invariant Tensors
      Lorenz Schwachhöfer, Nihat Ay, Jürgen Jost, Hông Vân Lê
      Pages 157-187
    4. Nonlinear Filtering and Information Geometry: A Hilbert Manifold Approach
      Nigel J. Newton
      Pages 189-208
    5. Infinite-Dimensional Log-Determinant Divergences III: Log-Euclidean and Log-Hilbert–Schmidt Divergences
      Hà Quang Minh
      Pages 209-243

  4. Theoretical Aspects of Information Geometry

    1. Front Matter
      Pages 245-245
      PDF
    2. Entropy on Spin Factors
      Peter Harremoës
      Pages 247-278
    3. Information Geometry Associated with Generalized Means
      Shinto Eguchi, Osamu Komori, Atsumi Ohara
      Pages 279-295
    4. Information Geometry with (Para-)Kähler Structures
      Jun Zhang, Teng Fei
      Pages 297-321
    5. Doubly Autoparallel Structure on the Probability Simplex
      Atsumi Ohara, Hideyuki Ishi
      Pages 323-334
    6. Complementing Chentsov’s Characterization
      Akio Fujiwara
      Pages 335-347
    7. Constant Curvature Connections On Statistical Models
      Alexander Rylov
      Pages 349-361
    8. Relation Between the Kantorovich–Wasserstein Metric and the Kullback–Leibler Divergence
      Roman V. Belavkin
      Pages 363-373

  5. Quantum Information Geometry

    1. Front Matter
      Pages 375-375
      PDF
    2. Some Inequalities for Wigner–Yanase Skew Information
      Shunlong Luo, Yuan Sun
      Pages 377-398
    3. Information Geometry of Quantum Resources
      Davide Girolami
      Pages 399-410
    4. Characterising Two-Sided Quantum Correlations Beyond Entanglement via Metric-Adjusted f–Correlations
      Marco Cianciaruso, Irénée Frérot, Tommaso Tufarelli, Gerardo Adesso
      Pages 411-430
    5. The Effects of Random Qubit-Qubit Quantum Channels to Entropy Gain, Fidelity and Trace Distance
      Attila Andai
      Pages 431-443
    6. Robertson-Type Uncertainty Principles and Generalized Symmetric and Antisymmetric Covariances
      Attila Lovas
      Pages 445-456

About these proceedings

Introduction

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.

Keywords

60A10, 62B05, 62B10, 62G05, 53B21 53B05, 46B20, 94A15, 94A17, 94B27 Geometric theory differentiable manifold information science machine learning statistical inference computation geometry

Editors and affiliations

  • Nihat Ay
    • 1
  • Paolo Gibilisco
    • 2
  • František  Matúš
    • 3
  1. 1.Information Theory of Cognitive SystemsMPI for Mathematics in the SciencesLeipzigGermany
  2. 2.Department of Economics and FinanceUniversity of Rome “Tor Vergata”RomeItaly
  3. 3.Institute of Information Theory and AutomationAcademy of Sciences of the Czech RepublicPragueCzech Republic

Bibliographic information