Information geometry最新文献

Feature learning and generalization error analysis of two-layer linear neural networks for high-dimensional inputs 高维输入双层线性神经网络的特征学习和泛化误差分析

Information geometry Pub Date : 2024-07-28 DOI: 10.1007/s41884-024-00142-3

Hayato Nishimori, Taiji Suzuki

引用次数: 0

Robust estimation for kernel exponential families with smoothed total variation distances 具有平滑总变异距离的核指数族的稳健估计

Information geometry Pub Date : 2024-07-27 DOI: 10.1007/s41884-024-00141-4

Takafumi Kanamori, Kodai Yokoyama, Takayuki Kawashima

引用次数: 0

Infinite-dimensional distances and divergences between positive definite operators, Gaussian measures, and Gaussian processes 正定算子、高斯度量和高斯过程之间的无穷维距离和发散

Information geometry Pub Date : 2024-05-21 DOI: 10.1007/s41884-024-00134-3

Hà Quang Minh

引用次数: 0

Dually flat structure of binary choice models 二元选择模型的双平面结构

Information geometry Pub Date : 2024-05-18 DOI: 10.1007/s41884-024-00136-1

Hisatoshi Tanaka

引用次数: 0

On the complete integrability of gradient systems on manifold of the beta family of the first kind 论第一类贝塔族流形上梯度系统的完全可积分性

Information geometry Pub Date : 2024-01-29 DOI: 10.1007/s41884-023-00130-z

Prosper Rosaire Mama Assandje, Joseph Dongho, Thomas Bouetou Bouetou

引用次数: 0

On partial likelihood and the construction of factorisable transformations. 关于偏似然与可因子变换的构造

Information geometry Pub Date : 2024-01-01 Epub Date: 2022-06-28 DOI: 10.1007/s41884-022-00068-8

H S Battey, D R Cox, Su Hyeong Lee

{"title":"On partial likelihood and the construction of factorisable transformations.","authors":"H S Battey, D R Cox, Su Hyeong Lee","doi":"10.1007/s41884-022-00068-8","DOIUrl":"10.1007/s41884-022-00068-8","url":null,"abstract":"Models whose associated likelihood functions fruitfully factorise are an important minority allowing elimination of nuisance parameters via partial likelihood, an operation that is valuable in both Bayesian and frequentist inferences, particularly when the number of nuisance parameters is not small. After some general discussion of partial likelihood, we focus on marginal likelihood factorisations, which are particularly difficult to ascertain from elementary calculations. We suggest a systematic approach for deducing transformations of the data, if they exist, whose marginal likelihood functions are free of the nuisance parameters. This is based on the solution to an integro-differential equation constructed from aspects of the Laplace transform of the probability density function, for which candidate solutions solve a simpler first-order linear homogeneous differential equation. The approach is generalised to the situation in which such factorisable structure is not exactly present. Examples are used in illustration. Although motivated by inferential problems in statistics, the proposed construction is of independent interest and may find application elsewhere.","PeriodicalId":93762,"journal":{"name":"Information geometry","volume":" ","pages":"9-28"},"PeriodicalIF":0.0,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12630320/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47426676","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Projections of SDEs onto submanifolds. sde在子流形上的投影

Information geometry Pub Date : 2024-01-01 Epub Date: 2023-02-02 DOI: 10.1007/s41884-022-00093-7

John Armstrong, Damiano Brigo, Emilio Ferrucci

{"title":"Projections of SDEs onto submanifolds.","authors":"John Armstrong, Damiano Brigo, Emilio Ferrucci","doi":"10.1007/s41884-022-00093-7","DOIUrl":"10.1007/s41884-022-00093-7","url":null,"abstract":"In Armstrong et al. (Proc Lond Math Soc (3) 119(1):176-213, 2019) the authors define three projections of <math> <msup><mrow><mi>R</mi></mrow> <mi>d</mi></msup> </math> -valued stochastic differential equations (SDEs) onto submanifolds: the Stratonovich, Itô-vector and Itô-jet projections. In this paper, after a brief survey of SDEs on manifolds, we begin by giving these projections a natural, coordinate-free description, each in terms of a specific representation of manifold-valued SDEs. We proceed by deriving formulae for the three projections in ambient <math> <msup><mrow><mi>R</mi></mrow> <mi>d</mi></msup> </math> -coordinates. We use these to show that the Itô-vector and Itô-jet projections satisfy respectively a weak and mean-square optimality criterion \"for small t\": this is achieved by solving constrained optimisation problems. These results confirm, but do not rely on the approach taken in Armstrong et al. (Proc Lond Math Soc (3) 119(1):176-213, 2019), which is formulated in terms of weak and strong Itô-Taylor expansions. In the final section we exhibit examples showing how the three projections can differ, and explore alternative notions of optimality.","PeriodicalId":93762,"journal":{"name":"Information geometry","volume":"1 1","pages":"397-427"},"PeriodicalIF":0.0,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12630303/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42931848","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Gibbs manifolds. 吉布斯流形

Information geometry Pub Date : 2024-01-01 Epub Date: 2023-07-03 DOI: 10.1007/s41884-023-00111-2

Dmitrii Pavlov, Bernd Sturmfels, Simon Telen

引用次数: 0

Foreword: Half a Century of Information Geometry 前言：半个世纪的信息几何

Information geometry Pub Date : 2023-12-21 DOI: 10.1007/s41884-023-00128-7

S. Amari

引用次数: 0

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