Information geometry最新文献_第2页

Half a century of information geometry, part 1 信息几何半个世纪，第 1 部分

Information geometry Pub Date : 2023-12-21 DOI: 10.1007/s41884-023-00127-8

Hiroshi Matsuzoe

引用次数: 0

Correction: Geometric thermodynamics for the Fokker–Planck equation: stochastic thermodynamic links between information geometry and optimal transport 更正：福克-普朗克方程的几何热力学：信息几何与最佳传输之间的随机热力学联系

Information geometry Pub Date : 2023-11-29 DOI: 10.1007/s41884-023-00119-8

Sosuke Ito

引用次数: 0

Estimation with infinite-dimensional exponential family and Fisher divergence 无限维指数族估计与Fisher散度

Information geometry Pub Date : 2023-11-13 DOI: 10.1007/s41884-023-00122-z

Kenji Fukumizu

引用次数: 0

Legendre duality: from thermodynamics to information geometry 勒让德对偶:从热力学到信息几何

Information geometry Pub Date : 2023-11-08 DOI: 10.1007/s41884-023-00121-0

Jan Naudts, Jun Zhang

引用次数: 0

On the geometric mechanics of assignment flows for metric data labeling 度量数据标注分配流的几何力学研究

Information geometry Pub Date : 2023-11-03 DOI: 10.1007/s41884-023-00120-1

Fabrizio Savarino, Peter Albers, Christoph Schnörr

{"title":"On the geometric mechanics of assignment flows for metric data labeling","authors":"Fabrizio Savarino, Peter Albers, Christoph Schnörr","doi":"10.1007/s41884-023-00120-1","DOIUrl":"https://doi.org/10.1007/s41884-023-00120-1","url":null,"abstract":"Abstract Metric data labeling refers to the task of assigning one of multiple predefined labels to every given datapoint based on the metric distance between label and data. This assignment of labels typically takes place in a spatial or spatio-temporal context. Assignment flows are a class of dynamical models for metric data labeling that evolve on a basic statistical manifold, the so called assignment manifold, governed by a system of coupled replicator equations. In this paper we generalize the result of a recent paper for uncoupled replicator equations and adopting the viewpoint of geometric mechanics, relate assignment flows to critical points of an action functional via the associated Euler–Lagrange equation. We also show that not every assignment flow is a critical point and characterize precisely the class of coupled replicator equations fulfilling this relation, a condition that has been missing in recent related work. Finally, some consequences of this connection to Lagrangian mechanics are investigated including the fact that assignment flows are, up to initial conditions of measure zero, reparametrized geodesics of the so-called Jacobi metric.","PeriodicalId":93762,"journal":{"name":"Information geometry","volume":"218 S705","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135775002","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Conelike radiant structures 锥形辐射结构

Information geometry Pub Date : 2023-10-04 DOI: 10.1007/s41884-023-00115-y

Daniel J. F. Fox

{"title":"Conelike radiant structures","authors":"Daniel J. F. Fox","doi":"10.1007/s41884-023-00115-y","DOIUrl":"https://doi.org/10.1007/s41884-023-00115-y","url":null,"abstract":"Abstract Analogues of the classical affine-projective correspondence are developed in the context of statistical manifolds compatible with a radiant vector field. These utilize a formulation of Einstein equations for special statistical structures that generalizes the usual Einstein equations for pseudo-Riemannian metrics and is of independent interest. A conelike radiant structure is a not necessarily flat affine connection equipped with a family of surfaces that behave like the intersections of the planes through the origin with a convex cone in a real vector space. A radiant structure is a torsion-free affine connection and a vector field whose covariant derivative is the identity endomorphism. A radiant structure is conelike if for every point and every two-dimensional subspace containing the radiant vector field there is a totally geodesic surface passing through the point and tangent to the subspace. Such structures exist on the total space of any principal bundle with one-dimensional fiber and on any Lie group with a quadratic structure on its Lie algebra. The affine connection of a conelike radiant structure can be normalized in a canonical way to have antisymmetric Ricci tensor. Applied to a conelike radiant structure on the total space of a principal bundle with one-dimensional fiber this yields a generalization of the classical Thomas connection of a projective structure. The compatibility of radiant and conelike structures with metrics is investigated and yields a construction of connections for which the symmetrized Ricci curvature is a constant multiple of a compatible metric that generalizes well-known constructions of Riemannian and Lorentzian Einstein–Weyl structures over Kähler–Einstein manifolds having nonzero scalar curvature. A formulation of Einstein equations for special statistical manifolds is given that generalizes the Einstein–Weyl equations and encompasses these more general examples. There are constructed left-invariant conelike radiant structures on a Lie group endowed with a left-invariant nondegenerate bilinear form, and the case of three-dimensional unimodular Lie groups is described in detail.","PeriodicalId":93762,"journal":{"name":"Information geometry","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135547708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Publisher Correction: Object embedding using an information geometrical perspective 发布者更正:使用信息几何透视图嵌入对象

Information geometry Pub Date : 2023-08-24 DOI: 10.1007/s41884-023-00118-9

Taiki Sugiura, Noboru Murata

引用次数: 0

Object embedding using an information geometrical perspective 基于信息几何视角的对象嵌入

Information geometry Pub Date : 2023-07-27 DOI: 10.1007/s41884-023-00114-z

Taiki Sugiura, Noboru Murata

引用次数: 0

Doubly autoparallel structure and curvature integrals 二重自平行结构与曲率积分

Information geometry Pub Date : 2023-07-27 DOI: 10.1007/s41884-023-00116-x

A. Ohara, H. Ishi, T. Tsuchiya