Information geometry最新文献_第6页

Laplacian operator on statistical manifold 统计流形上的拉普拉斯算子

Information geometry Pub Date : 2022-02-17 DOI: 10.1007/s41884-022-00070-0

Ruichao Jiang, J. Tavakoli, Yiqiang Q. Zhao

引用次数: 0

Information geometry of warped product spaces 扭曲产品空间的信息几何

Information geometry Pub Date : 2022-02-06 DOI: 10.1007/s41884-022-00091-9

Yasuaki Fujitani

引用次数: 1

Pseudo-Riemannian geometry encodes information geometry in optimal transport. 伪黎曼几何编码最优传输中的信息几何。

Information geometry Pub Date : 2022-01-01 Epub Date: 2021-07-30 DOI: 10.1007/s41884-021-00053-7

Ting-Kam Leonard Wong, Jiaowen Yang

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引用次数: 13

The information geometry of two-field functional integrals. 双域泛函积分的信息几何。

Information geometry Pub Date : 2022-01-01 Epub Date: 2022-10-19 DOI: 10.1007/s41884-022-00071-z

Eric Smith

{"title":"The information geometry of two-field functional integrals.","authors":"Eric Smith","doi":"10.1007/s41884-022-00071-z","DOIUrl":"https://doi.org/10.1007/s41884-022-00071-z","url":null,"abstract":"Two-field functional integrals (2FFI) are an important class of solution methods for generating functions of dissipative processes, including discrete-state stochastic processes, dissipative dynamical systems, and decohering quantum densities. The stationary trajectories of these integrals describe a conserved current by Liouville's theorem, despite the absence of a conserved kinematic phase space current in the underlying stochastic process. We develop the information geometry of generating functions for discrete-state classical stochastic processes in the Doi-Peliti 2FFI form, and exhibit two quantities conserved along stationary trajectories. One is a Wigner function, familiar as a semiclassical density from quantum-mechanical time-dependent density-matrix methods. The second is an overlap function, between directions of variation in an underlying distribution and those in the directions of relative large-deviation probability that can be used to interrogate the distribution, and expressed as an inner product of vector fields in the Fisher information metric. To give an interpretation to the time invertibility implied by current conservation, we use generating functions to represent importance sampling protocols, and show that the conserved Fisher information is the differential of a sample volume under deformations of the nominal distribution and the likelihood ratio. We derive a pair of dual affine connections particular to Doi-Peliti theory for the way they separate the roles of the nominal distribution and likelihood ratio, distinguishing them from the standard dually-flat connection of Nagaoka and Amari defined on the importance distribution, and show that dual flatness in the affine coordinates of the coherent-state basis captures the special role played by coherent states in Doi-Peliti theory.","PeriodicalId":93762,"journal":{"name":"Information geometry","volume":"5 2","pages":"427-492"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9700636/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40503370","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: 3

Plücker coordinates of the best-fit Stiefel tropical linear space to a mixture of Gaussian distributions 混合高斯分布的Stiefel热带线性空间的最佳拟合Plücker坐标

Information geometry Pub Date : 2021-12-22 DOI: 10.1007/s41884-023-00098-w

K. Miura, R. Yoshida

引用次数: 0

Optimal transportation plans with escort entropy regularization 具有护送熵正则化的最优运输方案

Information geometry Pub Date : 2021-11-09 DOI: 10.1007/s41884-021-00058-2

Takashi Kurose, Shintaro Yoshizawa, S. Amari

引用次数: 3

Transport information geometry: Riemannian calculus on probability simplex 传输信息几何：概率单纯形上的黎曼微积分

Information geometry Pub Date : 2021-11-08 DOI: 10.1007/s41884-021-00059-1

Wuchen Li