Entropy

Journal Browser

► Journal Browser

SUURI of Information Geometry: Dedicated to SUURI Engineer Professor Shun’ichi Amari on the Occasion of His 90th Birthday

Share This Special Issue

Special Issue Editors

Special Issue Information

Dear Colleagues,

After the work of Rao, who first proposed the Fisher matrix as a Riemannian metric, the modern development of Information Geometry theory is largely due to SUURI engineer Professor Shun'ichi Amari, whose work has had an outstanding global impact among the mathematician and statistician communities. Information Geometry is a powerful formalism that applies concepts from differential geometry to the study of probability distributions and the understanding of curved statistical models. The framework of α-geometry helps us understand different statistical problems like Bayesian inference and optimization methods. It does this by introducing the ideas of α-divergence and dual connections, which are now important tools in statistical physics, machine learning, and optimization.

He has also been a key figure in the development of neural networks between the 1970s and 1980s, helping to establish a mathematical framework for analyzing artificial and biological neural networks. Today, with about 400 peer-reviewed articles, the ideas of SUURI engineer Professor Shun'ichi Amari remain fundamental in understanding the mathematical structures underlying data, learning, and intelligence. SUURI is a Japanese word consisting of two Kanji characters: SUU (numbers, or mathematical objects) and RI (reason, theory, or laws). Although this Japanese word is usually translated as “mathematics” or “applied physics”, it is more fairly related to the method of using mathematics to understand phenomena and problems.

In honor of SUURI engineer Professor Shun'ichi Amari’s 90th birthday, it is a pleasure to present this Special Issue, which aims to gather original research papers and high-quality reviews in Information Geometry and related fields. Works focusing on the successes and future challenges that Information Geometry aims to obtain through its mathematical formalism, theoretical foundations, and applications, especially in machine learning and information theory, are welcome. Contributions that seek to synthesize the potential applications of Information Geometry to statistical physics, as well as present novel results and prospects for its applications, are also encouraged.

Dr. Antonio M. Scarfone
Dr. Tatsuaki Wada
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Benefits of Publishing in a Special Issue

Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.

Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.

Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.

External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.

Reprint: MDPI Books provides the opportunity to republish successful Special Issues in book format, both online and in print.

Further information on MDPI's Special Issue policies can be found here.

Published Papers (1 paper)

Order results

Result details

Show export options Show export options

Select all

Export citation of selected articles as:

Research

15 pages, 545 KB

Open AccessArticle

Geometry of Statistical Manifolds

by Paul W. Vos

Entropy 2025, 27(11), 1110; https://doi.org/10.3390/e27111110 - 27 Oct 2025

Viewed by 588

Abstract

A statistical manifold M can be defined as a Riemannian manifold each of whose points is a probability distribution on the same support. In fact, statistical manifolds possess a richer geometric structure beyond the Fisher information metric defined on the tangent bundle [...] Read more.

T M

. Recognizing that points in M are distributions and not just generic points in a manifold,

T M

can be extended to a Hilbert bundle

H M

. This extension proves fundamental when we generalize the classical notion of a point estimate—a single point in M—to a function on M that characterizes the relationship between observed data and each distribution in M. The log likelihood and score functions are important examples of generalized estimators. In terms of a parameterization

θ : M \to Θ \subset R^{k}

\hat{θ}

is a distribution on

Θ

while its generalization

g_{\hat{θ}} = \hat{θ} - E \hat{θ}

as an estimate is a function over

Θ

that indicates inconsistency between the model and data. As an estimator,

g_{\hat{θ}}

is a distribution of functions. Geometric properties of these functions describe statistical properties of

g_{\hat{θ}}

. In particular, the expected slopes of

g_{\hat{θ}}

are used to define

Λ (g_{\hat{θ}})

, the

Λ

-information of

g_{\hat{θ}}

. The Fisher information I is an upper bound for the

Λ

-information: for all g,

Λ (g) \leq I

. We demonstrate the utility of this geometric perspective using the two-sample problem. Full article

(This article belongs to the Special Issue SUURI of Information Geometry: Dedicated to SUURI Engineer Professor Shun’ichi Amari on the Occasion of His 90th Birthday)

► Show Figures

Journal Menu

Journal Browser

SUURI of Information Geometry: Dedicated to SUURI Engineer Professor Shun’ichi Amari on the Occasion of His 90th Birthday

Share This Special Issue

Special Issue Editors

Special Issue Information

Keywords

Benefits of Publishing in a Special Issue

Published Papers (1 paper)

Research

Further Information

Guidelines

MDPI Initiatives

Follow MDPI