Shinto Eguchi

Information Geometry · Robust Statistics · Generative AI

The Institute of Statistical Mathematics, Japan

About

My research explores how the geometry of probability distributions can guide statistical inference and machine learning. I am particularly interested in divergence and entropy as tools for understanding estimation, robustness, and learning.

A recurring question in my work is how statistical methods behave when models are imperfect or data contain contamination. This question connects my studies of information geometry and minimum divergence estimation with statistical learning and applications in biostatistics and ecology. Recent work extends these connections to Stein operators and flow matching, bringing geometric ideas into computational inference and generative modeling.

A single thread runs through this work: a divergence induces a geometry, and the geometry guides inference. Contrast functions generate a metric and a pair of dual connections on a statistical manifold (1983, 1985, 1992); the γ-divergence, introduced with H. Fujisawa (2008), carries this structure into robust estimation; its first variation under escort transport motivates the γ-Stein operator (2026); and the associated γ-Stein metric gives a geometric account of density-weighted flow matching (2026).

Recent highlights

2026 — Density-powered Stein operators

Robust inference using density-powered Stein operators in Information Geometry. It develops a γ-Stein framework for robust inference with unnormalized models, with applications to score matching, goodness-of-fit diagnostics, and variational inference.

Journal article · Preprint · Code

2026 — Geometry and flow matching

Implicit geometric regularization in flow matching via density weighted Stein operators in Transactions on Machine Learning Research. It investigates density weighting in flow matching and its connections to the geometry and smoothness of learned velocity fields.

Journal article · Preprint · Code

Books

S. Eguchi (2026). Statistical Inference via Generative Models: Flow Matching and Causal Inference. Book manuscript. arXiv

S. Eguchi (2025). Minimum Gamma-Divergence for Regression and Classification Problems. SpringerBriefs in Statistics. Springer, Singapore. Springer · arXiv

S. Eguchi and O. Komori (2022). Minimum Divergence Methods in Statistical Machine Learning: From an Information Geometric Viewpoint. Springer, Tokyo. Springer

O. Komori and S. Eguchi (2019). Statistical Methods for Imbalanced Data in Ecological and Biological Studies. SpringerBriefs in Statistics. Springer, Tokyo. Springer

Profiles and contact

Professor Emeritus, The Institute of Statistical Mathematics (ISM) and
Project Professor, Research Center for Medical and Health Data Science, ISM

Email: eguchi [at] ism.ac.jp

Google Scholar · researchmap · GitHub