Collection
2024_Special Issue: Half a Century of Information Geometry, Part 2
- Submission status
- Closed
Submission to this special issue is by invitation only.
Part 1 of this special issue has been published as Volume 7 Volume 7, Supplement Issue 1. --> https://springerlink.bibliotecabuap.elogim.com/journal/41884/volumes-and-issues/7-1/supplement
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 will be handled by a board member of this journal. The name of handling editor for each accepted article will be indicated with "Communicated by:" heading in its published version.
Articles (5 in this collection)
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Feature learning and generalization error analysis of two-layer linear neural networks for high-dimensional inputs
Authors
- Hayato Nishimori
- Taiji Suzuki
- Content type: Research Paper
- Open Access
- Published: 28 July 2024
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Robust estimation for kernel exponential families with smoothed total variation distances
Authors
- Takafumi Kanamori
- Kodai Yokoyama
- Takayuki Kawashima
- Content type: Research Paper
- Open Access
- Published: 27 July 2024
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Infinite-dimensional distances and divergences between positive definite operators, Gaussian measures, and Gaussian processes
Authors
- Hà Quang Minh
- Content type: Survey Paper
- Published: 21 May 2024
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A harmonic property of right invariant priors
Authors
- Tomonari Sei
- Fumiyasu Komaki
- Content type: Research Paper
- Open Access
- Published: 30 April 2024