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The dualistic structure of statistical manifolds in information geometry yields eight types of geodesic triangles passing through three given points, the triangle vertices.
On the generalized distance in statistics
Prasanta Chandra Mahalanobis · 1936
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On pairs of conjugate parallel displacements in multidimensional spaces
Aleksandr Petrovich Norden · 1945
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Parallel displacement and scalar product of vectors
R. N. Sen · 1948
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The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming
Lev M. Bregman · 1967
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Information-type measures of difference of probability distributions and indirect observation
Imre Csiszár · 1967
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Spaces of constant curvature
Joseph Albert Wolf · 1972
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A relationship between the second derivatives of a convex function and of its conjugate
Jean-Pierre Crouzeix · 1977
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Statistical manifolds
Stefan L. Lauritzen · 1987
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Dual connections and affine geometry
Takashi Kurose · 1990
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Geometry of minimum contrast
Shinto Eguchi et al · 1992
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On the Lambert W function
Robert M Corless, Gaston H Gonnet, David EG Hare, David J Jeffrey, and Donald E Knuth · 1996
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Inducing features of random fields
Stephen Della Pietra, Vincent Della Pietra, and John Lafferty · 1997
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Riemannian geometry
Luther Pfahler Eisenhart · 1997
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Relative loss bounds for on-line density estimation with the exponential family of distributions
Katy S Azoury and Manfred K Warmuth · 2001
Cited alongside, same era.
Solving systems of polynomial equations
Bernd Sturmfels · 2002
Cited alongside, same era.
Clustering with Bregman divergences
Arindam Banerjee, Srujana Merugu, Inderjit S Dhillon, and Joydeep Ghosh · 2005
Cited alongside, same era.
The geometry of Hessian structures
Hirohiko Shima · 2007
Cited alongside, same era.
Statistical exponential families: A digest with flash cards
Frank Nielsen and Vincent Garcia · 2009
Cited alongside, same era.
Sided and symmetrized Bregman centroids
Frank Nielsen and Richard Nock · 2009
Cited alongside, same era.
Matrix information geometry
Frank Nielsen and Rajendra Bhatia · 2013
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Mining matrix data with Bregman matrix divergences for portfolio selection
Richard Nock, Brice Magdalou, Eric Briys, and Frank Nielsen · 2013
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Information geometry of positive measures and positive-definite matrices: Decomposable dually flat structure
Shun-ichi Amari · 2014
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Information geometry and its applications
Shun-ichi Amari · 2016
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Classification with mixtures of curved Mahalanobis metrics
Frank Nielsen, Boris Muzellec, and Richard Nock · 2016
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Topological data analysis with Bregman divergences
Herbert Edelsbrunner and Hubert Wagner · 2017
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Bregman Voronoi diagrams
Jean-Daniel Boissonnat, Frank Nielsen, and Richard Nock · 2010
Cited alongside, same era.
Legendre transformation and information geometry, 2010
Frank Nielsen · 2010
Cited alongside, same era.
The Burbea-Rao and Bhattacharyya centroids
Frank Nielsen and Sylvain Boltz · 2011
Cited alongside, same era.
Skew Jensen-Bregman voronoi diagrams
Frank Nielsen and Richard Nock · 2011
Cited alongside, same era.
A history of non-Euclidean geometry: Evolution of the concept of a geometric space
Boris A. Rosenfeld · 2012
Cited alongside, same era.
Cramér-Rao lower bound and information geometry
Frank Nielsen · 2013
Cited alongside, same era.
An elementary introduction to information geometry
Frank Nielsen · 2018
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Monte Carlo information geometry: The dually flat case
Frank Nielsen and Gaëtan Hadjeres · 2018
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On the geometry of mixtures of prescribed distributions
Frank Nielsen and Richard Nock · 2018
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Logarithmic divergences from optimal transport and Rényi geometry
Ting-Kam Leonard Wong · 2018
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On a convergence property of a geometrical algorithm for statistical manifolds
Shotaro Akaho, Hideitsu Hino, and Noboru Murata · 2019
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On geodesic triangles with right angles in a dually flat space
Frank Nielsen · 2021
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