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We consider the space of $w$-mixtures which is defined as the set of finite statistical mixtures sharing the same prescribed component distributions closed under convex combinations.
On a measure of divergence between two multinomial populations
Anil Bhattacharyya · 1946
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Eine informationstheoretische ungleichung und ihre anwendung auf den beweis der ergodizitat von markoffschen ketten
Imre Csiszár · 1963
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Markov processes and the H H -theorem
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A general class of coefficients of divergence of one distribution from another
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Inferences for the Cauchy distribution based on maximum likelihood estimators
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Convex analysis
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Statistical manifolds
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Convex Statistical Distances
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Proof without Words: The Mediant Property
Richard A Gibbs · 1990
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Divergence measures based on the Shannon entropy
Jianhua Lin · 1991
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Geometry of f f -divergence
Paul W Vos · 1991
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Geometry of minimum contrast
Shinto Eguchi · 1992
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Kernel smoothing
Matt P Wand and M Chris Jones · 1994
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About distances of discrete distributions satisfying the data processing theorem of information theory
MC Pardo and Igor Vajda · 1997
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Information geometry on hierarchy of probability distributions
Shun-ichi Amari · 2001
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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
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Farey sequences and discrete radon transform projection angles
Imants Svalbe and Andrew Kingston · 2003
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Information theory and statistics: A tutorial
Imre Csiszár and Paul C Shields · 2004
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Finite Mixture Models
G. McLachlan and D. Peel · 2004
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Kullback information of normal mixture is not an analytic function
Sumio Watanabe, Keisuke Yamazaki, and Miki Aoyagi · 2004
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Divergence function, duality, and convex analysis
Jun Zhang · 2004
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Clustering with Bregman divergences
Arindam Banerjee, Srujana Merugu, Inderjit S Dhillon, and Joydeep Ghosh · 2005
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A distance measure between GMMs based on the unscented transform and its application to speaker recognition
Jacob Goldberger and Hagai Aronowitz · 2005
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Convex functions and their applications: a contemporary approach
Constantin Niculescu and Lars-Erik Persson · 2006
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Integration of stochastic models by minimizing α \alpha -divergence
Shun-ichi Amari · 2007
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Local mixtures of the exponential distribution
KA Anaya-Izquierdo and PK Marriott · 2007
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Differential entropic clustering of multivariate gaussians
Jason V Davis and Inderjit S Dhillon · 2007
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Confliction of the convexity and metric properties in f f -divergences
Mohammadali Khosravifard, Dariush Fooladivanda, and T Aaron Gulliver · 2007
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Calculation of differential entropy for a mixed Gaussian distribution
Joseph V Michalowicz, Jonathan M Nichols, and Frank Bucholtz · 2008
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The information geometric structure of generalized empirical likelihood estimators
Tomoaki Nishimura and Fumiyasu Komaki · 2008
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α \alpha -divergence is unique, belonging to both f f -divergence and Bregman divergence classes
Shun-ichi Amari · 2009
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Computation of multivariate normal and t t probabilities
Alan Genz and Frank Bretz · 2009
Learning mixtures by simplifying kernel density estimators
Olivier Schwander and Frank Nielsen · 2013
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Geometric modeling in probability and statistics
Ovidiu Calin and Constantin Udriste · 2014
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Information geometry approach to parameter estimation in Markov chains
Masahito Hayashi and Shun Watanabe · 2014
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Information measures: the curious case of the binary alphabet
Jiantao Jiao, Thomas A Courtade, Albert No, Kartik Venkat, and Tsachy Weissman · 2014
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Distributed estimation, information loss and exponential families
Qiang Liu and Alexander T Ihler · 2014
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Multivariate f f -divergence estimation with confidence
Kevin Moon and Alfred Hero · 2014
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On the discontinuity of the Shannon information measures
Siu-Wai Ho and Raymond W Yeung · 2009
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Statistical exponential families: A digest with flash cards
Frank Nielsen and Vincent Garcia · 2009
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Clustering multivariate normal distributions
Frank Nielsen and Richard Nock · 2009
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Sided and symmetrized Bregman centroids
Frank Nielsen and Richard Nock · 2009
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Generalised Pinsker inequalities
Mark D. Reid and Robert C. Williamson · 2009
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Information geometry of divergence functions
Shun-ichi Amari and Andrzej Cichocki · 2010
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On the chi square and higher-order chi distances for approximating f f -divergences
Frank Nielsen and Richard Nock · 2014
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Maximum likelihood estimates for gaussian mixtures are transcendental
Carlos Améndola, Mathias Drton, and Bernd Sturmfels · 2015
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Reference duality and representation duality in information geometry
Jun Zhang · 2015
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Information Geometry and Its Applications
Shun-ichi Amari · 2016
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Deep Learning
Ian Goodfellow, Yoshua Bengio, and Aaron Courville · 2016
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A note on divergences
Xiao Liang · 2016
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Arbitrarily tight bounds on differential entropy of gaussian mixtures
Kamyar Moshksar and Amir K. Khandani · 2016
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Guaranteed bounds on information-theoretic measures of univariate mixtures using piecewise log-sum-exp inequalities
Frank Nielsen and Ke Sun · 2016
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Guaranteed bounds on the Kullback-Leibler divergence of univariate mixtures
Frank Nielsen and Ke Sun · 2016
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Comix: Joint estimation and lightspeed comparison of mixture models
Olivier Schwander, Stéphane Marchand-Maillet, and Frank Nielsen · 2016
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Estimating mixture entropy with pairwise distances
Artemy Kolchinsky and Brendan D. Tracey · 2017
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Ensemble estimation of distributional functionals via k k -nearest neighbors
Kevin R Moon, Kumar Sricharan, and Alfred O Hero III · 2017
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Statistical inference of w w -mixtures
Frank Nielsen and Richard Nock · 2017
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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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On the Jensen–Shannon symmetrization of distances relying on abstract means
Frank Nielsen · 2019
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Monte carlo information-geometric structures
Frank Nielsen and Gaëtan Hadjeres · 2019
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On a generalization of the Jensen–Shannon divergence and the Jensen–Shannon centroid
Frank Nielsen · 2020
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The dually flat information geometry of the mixture family of two prescribed Cauchy components
Frank Nielsen · 2021
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