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Special Issue: Half a Century of Information Geometry

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.

Articles (1 in this collection)