Bregman divergence (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Bregman divergence" in English language version.

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6doi.org

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2utexas.edu

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1univ-ag.fr

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arxiv.org

Nielsen, Frank (28 October 2021). "Fast Approximations of the Jeffreys Divergence between Univariate Gaussian Mixtures via Mixture Conversions to Exponential-Polynomial Distributions". Entropy. 23 (11): 1417. arXiv:2107.05901. Bibcode:2021Entrp..23.1417N. doi:10.3390/e23111417. ISSN 1099-4300. PMC 8619509. PMID 34828115.
Nielsen, Frank; Boissonnat, Jean-Daniel; Nock, Richard (September 2010). "Bregman Voronoi Diagrams: Properties, Algorithms and Applications". Discrete & Computational Geometry. 44 (2): 281–307. arXiv:0709.2196. doi:10.1007/s00454-010-9256-1. ISSN 0179-5376. S2CID 1327029.
Jiao, Jiantao; Courtade, Thomas; No, Albert; Venkat, Kartik; Weissman, Tsachy (December 2014). "Information Measures: the Curious Case of the Binary Alphabet". IEEE Transactions on Information Theory. 60 (12): 7616–7626. arXiv:1404.6810. doi:10.1109/TIT.2014.2360184. ISSN 0018-9448. S2CID 13108908.
Nielsen, Frank; Nock, Richard (2019). "The Bregman Chord Divergence". Geometric Science of Information. Lecture Notes in Computer Science. Vol. 11712. pp. 299–308. arXiv:1810.09113. doi:10.1007/978-3-030-26980-7_31. ISBN 978-3-030-26979-1. S2CID 53046425.

doi.org

Adamčík, Martin (2014). "The Information Geometry of Bregman Divergences and Some Applications in Multi-Expert Reasoning". Entropy. 16 (12): 6338–6381. Bibcode:2014Entrp..16.6338A. doi:10.3390/e16126338.
Nielsen, Frank (28 October 2021). "Fast Approximations of the Jeffreys Divergence between Univariate Gaussian Mixtures via Mixture Conversions to Exponential-Polynomial Distributions". Entropy. 23 (11): 1417. arXiv:2107.05901. Bibcode:2021Entrp..23.1417N. doi:10.3390/e23111417. ISSN 1099-4300. PMC 8619509. PMID 34828115.
Nielsen, Frank; Boissonnat, Jean-Daniel; Nock, Richard (September 2010). "Bregman Voronoi Diagrams: Properties, Algorithms and Applications". Discrete & Computational Geometry. 44 (2): 281–307. arXiv:0709.2196. doi:10.1007/s00454-010-9256-1. ISSN 0179-5376. S2CID 1327029.
Jiao, Jiantao; Courtade, Thomas; No, Albert; Venkat, Kartik; Weissman, Tsachy (December 2014). "Information Measures: the Curious Case of the Binary Alphabet". IEEE Transactions on Information Theory. 60 (12): 7616–7626. arXiv:1404.6810. doi:10.1109/TIT.2014.2360184. ISSN 0018-9448. S2CID 13108908.
Nielsen, Frank; Nock, Richard (2019). "The Bregman Chord Divergence". Geometric Science of Information. Lecture Notes in Computer Science. Vol. 11712. pp. 299–308. arXiv:1810.09113. doi:10.1007/978-3-030-26980-7_31. ISBN 978-3-030-26979-1. S2CID 53046425.
"Matrix Information Geometry", R. Nock, B. Magdalou, E. Briys and F. Nielsen, pdf, from this book

harvard.edu

ui.adsabs.harvard.edu

Adamčík, Martin (2014). "The Information Geometry of Bregman Divergences and Some Applications in Multi-Expert Reasoning". Entropy. 16 (12): 6338–6381. Bibcode:2014Entrp..16.6338A. doi:10.3390/e16126338.
Nielsen, Frank (28 October 2021). "Fast Approximations of the Jeffreys Divergence between Univariate Gaussian Mixtures via Mixture Conversions to Exponential-Polynomial Distributions". Entropy. 23 (11): 1417. arXiv:2107.05901. Bibcode:2021Entrp..23.1417N. doi:10.3390/e23111417. ISSN 1099-4300. PMC 8619509. PMID 34828115.

nih.gov

ncbi.nlm.nih.gov

Nielsen, Frank (28 October 2021). "Fast Approximations of the Jeffreys Divergence between Univariate Gaussian Mixtures via Mixture Conversions to Exponential-Polynomial Distributions". Entropy. 23 (11): 1417. arXiv:2107.05901. Bibcode:2021Entrp..23.1417N. doi:10.3390/e23111417. ISSN 1099-4300. PMC 8619509. PMID 34828115.

pubmed.ncbi.nlm.nih.gov

Nielsen, Frank (28 October 2021). "Fast Approximations of the Jeffreys Divergence between Univariate Gaussian Mixtures via Mixture Conversions to Exponential-Polynomial Distributions". Entropy. 23 (11): 1417. arXiv:2107.05901. Bibcode:2021Entrp..23.1417N. doi:10.3390/e23111417. ISSN 1099-4300. PMC 8619509. PMID 34828115.

nips.cc

papers.nips.cc

Ehsan Amid, Manfred K. Warmuth, Rohan Anil, Tomer Koren (2019). "Robust Bi-Tempered Logistic Loss Based on Bregman Divergences". Conference on Neural Information Processing Systems. pp. 14987-14996. pdf

semanticscholar.org

api.semanticscholar.org

Nielsen, Frank; Boissonnat, Jean-Daniel; Nock, Richard (September 2010). "Bregman Voronoi Diagrams: Properties, Algorithms and Applications". Discrete & Computational Geometry. 44 (2): 281–307. arXiv:0709.2196. doi:10.1007/s00454-010-9256-1. ISSN 0179-5376. S2CID 1327029.
Jiao, Jiantao; Courtade, Thomas; No, Albert; Venkat, Kartik; Weissman, Tsachy (December 2014). "Information Measures: the Curious Case of the Binary Alphabet". IEEE Transactions on Information Theory. 60 (12): 7616–7626. arXiv:1404.6810. doi:10.1109/TIT.2014.2360184. ISSN 0018-9448. S2CID 13108908.
Nielsen, Frank; Nock, Richard (2019). "The Bregman Chord Divergence". Geometric Science of Information. Lecture Notes in Computer Science. Vol. 11712. pp. 299–308. arXiv:1810.09113. doi:10.1007/978-3-030-26980-7_31. ISBN 978-3-030-26979-1. S2CID 53046425.

univ-ag.fr

www1.univ-ag.fr

"Matrix Information Geometry", R. Nock, B. Magdalou, E. Briys and F. Nielsen, pdf, from this book

utexas.edu

cs.utexas.edu

"Learning with Bregman Divergences" (PDF). utexas.edu. Retrieved 19 August 2023.
Dhillon, Inderjit; Tropp, Joel (2008). "Matrix Nearness Problems with Bregman Divergence" (PDF). SIAM Journal on Matrix Analysis and Applications. 29 (4). Supposed D_\varphi is a Bregman divergence, supposed that {C_k} is a finite collection of closed, convex sets whose intersection is nonempty. Given an input matrix Y our goal is to produce a matrix \mathbf{X} in the intersection that diverges the least from \textbf{Y}, i.e. to solve \min_{\mathbf{X} } D_\varphi(\mathbf{X};\mathbf{Y}) subject to \mathbf{X} \in \big\cap_k C_k. Under mild conditions, the solution is unique and it has a variational characterization analogous with the characterization of an orthogonal projection onto a convex set" (see s2.4, page 1125 for more)

worldcat.org

search.worldcat.org

Nielsen, Frank (28 October 2021). "Fast Approximations of the Jeffreys Divergence between Univariate Gaussian Mixtures via Mixture Conversions to Exponential-Polynomial Distributions". Entropy. 23 (11): 1417. arXiv:2107.05901. Bibcode:2021Entrp..23.1417N. doi:10.3390/e23111417. ISSN 1099-4300. PMC 8619509. PMID 34828115.
Nielsen, Frank; Boissonnat, Jean-Daniel; Nock, Richard (September 2010). "Bregman Voronoi Diagrams: Properties, Algorithms and Applications". Discrete & Computational Geometry. 44 (2): 281–307. arXiv:0709.2196. doi:10.1007/s00454-010-9256-1. ISSN 0179-5376. S2CID 1327029.
Jiao, Jiantao; Courtade, Thomas; No, Albert; Venkat, Kartik; Weissman, Tsachy (December 2014). "Information Measures: the Curious Case of the Binary Alphabet". IEEE Transactions on Information Theory. 60 (12): 7616–7626. arXiv:1404.6810. doi:10.1109/TIT.2014.2360184. ISSN 0018-9448. S2CID 13108908.