Open problems in information geometry: a discussion at FDIG 2025

2025/09/02 by Tomonari Sei, Sei, Tomonari, Hiroshi Matsuzoe +1 · 1 citation
Computer Science · #Rough Sets and Fuzzy Logic

paper · pdf · doi:10.48550/arxiv.2509.06989

Abstract

Open problems in information geometry are collected and discussed in the conference ``Further Developments of Information Geometry (FDIG) 2025'' held at the University of Tokyo, Japan, from March 18 to 21, 2025.

Citations

• The moduli spaces of left-invariant statistical structures on Lie groups
• Infinite variety of thermodynamic speed limits with general activities
• Generalized free energy and excess/housekeeping decomposition in nonequilibrium systems: from large deviations to thermodynamic speed limits
• Homogeneous statistical manifolds
• Information Geometry of Wasserstein Statistics on Shapes and Affine Deformations
• Autoparallelity of Quantum Statistical Manifolds in Light of Quantum Estimation Theory
• A characterization of the alpha-connections on the statistical manifold of multivariate normal distributions
• Information Geometry of Dynamics on Graphs and Hypergraphs
• Information geometry of operator scaling
• Wasserstein Distributionally Robust Optimization: Theory and\n Applications in Machine Learning
• A review of matrix scaling and Sinkhorn's normal form for matrices and\n positive maps
• A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem

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