Collection
Special Issue: Half a Century of Information Geometry, Part 1
- Submission status
- Closed
Submission to this special issue is by invitation only.
Information geometry has a long history. The work of H. Hotteling (1895–1973), who visited R.A. Fisher (1890–1962) in 1929 and proposed the Riemannian structure of probability distribution spaces, did not make it to the journals and was forgotten by the academy.
Independently, in 1945, C.R. Rao, then 24 years old and working in Calcutta (now Kolkata), India, wrote a monumental paper proposing the Riemannian geometry of statistical models. However, it took a long time for its real value to be recognized.
In 1972, N.N. Chentsov (born in Moscow in 1930, died in 1992) published his book Statisticheskie reshai︠u︡shchie pravila i optimalʹnye vyvody (English translation: "Statistical Decision Rules and Optimal Inference", published by AMS in 1982). He showed that the Fisher metric that was proposed by Rao can be uniquely determined under the concept of invariance, and that invariant affine connections can be introduced as one-parameter families. He developed a wonderful theoretical system that introduces a geometric structure based on invariance in the space of probability distributions. Fifty years have passed since then, and starting with this work, we can say that fifty years have passed since the birth of invariant information geometry.
Based on invariant geometry, Shun-ichi Amari studied the structure of connection duality and published its statistical theory in 1982. If we take this duality as the origin, then 40 years have passed since then.
Information geometry has made remarkable progress since that time and has become one of the basic methods in many fields dealing with probability and information. Today it is expanding into many fields, such as physics, mathematics, life sciences, and economics, not only in information science.
The year 2022 marks the 50th anniversary of the publication of Chentsov's book. Inspired by this fact, we decided to invite contributions from leading experts from a relatively wide range, in terms of both disciplines and generations, so as to provide the reader with a view of the great variety and the vitality of information geometry.
Editors
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Hiroshi Matsuzoe
Professor, Nagoya Institute of Technology, Japan Hiroshi Matsuzoe, Co-Editor of the journal Information Geometry worked for this special issue as the Managing Editor. Each submission to this special issue has been handled by a board member of this journal. The name of handling editor for each accepted article is indicated with "Communicated by:" heading in its published version.
Articles (32 in this collection)
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Half a century of information geometry, part 1
Authors
- Hiroshi Matsuzoe
- Content type: Preface
- Published: 21 December 2023
- Pages: 3 - 8
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The Fisher metric as a metric on the cotangent bundle
Authors
- Hiroshi Nagaoka
- Content type: Research Paper
- Open Access
- Published: 21 December 2023
- Pages: 651 - 677
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Estimation with infinite-dimensional exponential family and Fisher divergence
Authors
- Kenji Fukumizu
- Content type: Research Paper
- Open Access
- Published: 13 November 2023
- Pages: 609 - 622
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Legendre duality: from thermodynamics to information geometry
Authors
- Jan Naudts
- Jun Zhang
- Content type: Survey Paper
- Published: 08 November 2023
- Pages: 623 - 649
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G-dual Teleparallel Connections in Information Geometry
Authors (first, second and last of 4)
- F. M. Ciaglia
- F. Di Cosmo
- G. Marmo
- Content type: Research Paper
- Open Access
- Published: 25 August 2023
- Pages: 587 - 608
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Doubly autoparallel structure and curvature integrals
Authors
- Atsumi Ohara
- Hideyuki Ishi
- Takashi Tsuchiya
- Content type: Research Paper
- Open Access
- Published: 27 July 2023
- Pages: 555 - 586
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A certain ODE-system defining the geometric divergence
Authors
- Takashi Kurose
- Content type: Research Paper
- Published: 05 June 2023
- Pages: 541 - 554
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Geometry and convergence of natural policy gradient methods
Authors
- Johannes Müller
- Guido Montúfar
- Content type: Research Paper
- Open Access
- Published: 02 June 2023
- Pages: 485 - 523
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Optimal projection filters with information geometry
Authors
- John Armstrong
- Damiano Brigo
- Bernard Hanzon
- Content type: Survey Paper
- Open Access
- Published: 02 June 2023
- Pages: 525 - 540
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Geometric thermodynamics for the Fokker–Planck equation: stochastic thermodynamic links between information geometry and optimal transport
Authors
- Sosuke Ito
- Content type: Research Paper
- Open Access
- Published: 09 March 2023
- Pages: 441 - 483
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A parameterisation-invariant modification of the score test
Authors
- P. E. Jupp
- Content type: Research Paper
- Open Access
- Published: 07 March 2023
- Pages: 429 - 439
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Projections of SDEs onto submanifolds
Authors
- John Armstrong
- Damiano Brigo
- Emilio Ferrucci
- Content type: Research Paper
- Open Access
- Published: 02 February 2023
- Pages: 397 - 427
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The exponential Orlicz space in quantum information geometry
Authors
- Anna Jenčová
- Content type: Research Paper
- Published: 24 January 2023
- Pages: 377 - 395
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Gram matrices of quantum channels via quantum Fisher information with applications to decoherence and uncertainty
Authors
- Shunlong Luo
- Yuan Sun
- Content type: Research Paper
- Published: 22 January 2023
- Pages: 355 - 376
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Parametric models and information geometry on W*-algebras
Authors (first, second and last of 4)
- F. M. Ciaglia
- F. Di Nocera
- L. Schwachhöfer
- Content type: Research Paper
- Open Access
- Published: 12 January 2023
- Pages: 329 - 354
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Uncertainty and Quantum Variance at the light of Quantum Information Geometry
Authors
- Paolo Gibilisco
- Content type: Perspective
- Published: 14 December 2022
- Pages: 293 - 302
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Conformal mirror descent with logarithmic divergences
Authors
- Amanjit Singh Kainth
- Ting-Kam Leonard Wong
- Frank Rudzicz
- Content type: Research Paper
- Open Access
- Published: 14 December 2022
- Pages: 303 - 327
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Natural differentiable structures on statistical models and the Fisher metric
Authors
- Hông Vân Lê
- Content type: Survey Paper
- Published: 13 December 2022
- Pages: 271 - 291
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Hierarchy of deformations in concavity
Authors
- Kazuhiro Ishige
- Paolo Salani
- Asuka Takatsu
- Content type: Research Paper
- Published: 12 December 2022
- Pages: 251 - 269
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Minimum information divergence of Q-functions for dynamic treatment resumes
Authors
- Shinto Eguchi
- Content type: Research Paper
- Published: 09 December 2022
- Pages: 229 - 249
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Recent advances in algebraic geometry and Bayesian statistics
Authors
- Sumio Watanabe
- Content type: Survey Paper
- Published: 06 December 2022
- Pages: 187 - 209
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A two-parameter family of non-parametric, deformed exponential manifolds
Authors
- Nigel J. Newton
- Content type: Research Paper
- Open Access
- Published: 06 December 2022
- Pages: 171 - 186
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Geometry and applied statistics
Authors
- Paul Marriott
- Content type: Survey Paper
- Published: 06 December 2022
- Pages: 211 - 227
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Generalized estimators, slope, efficiency, and fisher information bounds
Authors
- Paul Vos
- Content type: Research Paper
- Published: 04 December 2022
- Pages: 151 - 170
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Conditional inference of Poisson models and information geometry: an ancillary review
Authors
- Tomonari Sei
- Content type: Survey Paper
- Open Access
- Published: 27 November 2022
- Pages: 131 - 150
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Affine statistical bundle modeled on a Gaussian Orlicz–Sobolev space
Authors
- Giovanni Pistone
- Content type: Survey Paper
- Published: 24 November 2022
- Pages: 109 - 130
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Toward differential geometry of statistical submanifolds
Authors
- Hitoshi Furuhata
- Content type: Perspective
- Published: 22 November 2022
- Pages: 99 - 108
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Hommage to Chentsov’s theorem
Authors
- Akio Fujiwara
- Content type: Survey Paper
- Open Access
- Published: 21 November 2022
- Pages: 79 - 98
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Geometry of EM and related iterative algorithms
Authors
- Hideitsu Hino
- Shotaro Akaho
- Noboru Murata
- Content type: Survey Paper
- Published: 19 November 2022
- Pages: 39 - 77
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Independent component analysis in the light of Information Geometry
Authors
- Jean-François Cardoso
- Content type: Perspective
- Published: 24 October 2022
- Pages: 29 - 38
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On partial likelihood and the construction of factorisable transformations
Authors
- H. S. Battey
- D. R. Cox
- Su Hyeong Lee
- Content type: Research Paper
- Open Access
- Published: 28 June 2022
- Pages: 9 - 28