Kullback–Leibler divergence (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Kullback–Leibler divergence" in English language version.

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Kullback, S.; Leibler, R.A. (1951). "On information and sufficiency". Annals of Mathematical Statistics. 22 (1): 79–86. doi:10.1214/aoms/1177729694. JSTOR 2236703. MR 0039968.

archive.org

Burnham, K. P.; Anderson, D. R. (2002). Model Selection and Multi-Model Inference (2nd ed.). Springer. p. 51. ISBN 9780387953649.

archive.today

Fraundorf, P. (2007). "Thermal roots of correlation-based complexity". Complexity. 13 (3): 18–26. arXiv:1103.2481. Bibcode:2008Cmplx..13c..18F. doi:10.1002/cplx.20195. S2CID 20794688. Archived from the original on 2011-08-13.

arxiv.org

Matassa, Marco (December 2021). "Fubini-Study metrics and Levi-Civita connections on quantum projective spaces". Advances in Mathematics. 393: 108101. arXiv:2010.03291. doi:10.1016/j.aim.2021.108101. ISSN 0001-8708.
Soklakov, A. N. (2020). "Economics of Disagreement—Financial Intuition for the Rényi Divergence". Entropy. 22 (8): 860. arXiv:1811.08308. Bibcode:2020Entrp..22..860S. doi:10.3390/e22080860. PMC 7517462. PMID 33286632.
Bonnici, V. (2020). "Kullback-Leibler divergence between quantum distributions, and its upper-bound". arXiv:2008.05932 [cs.LG].
Fraundorf, P. (2007). "Thermal roots of correlation-based complexity". Complexity. 13 (3): 18–26. arXiv:1103.2481. Bibcode:2008Cmplx..13c..18F. doi:10.1002/cplx.20195. S2CID 20794688. Archived from the original on 2011-08-13.
Nielsen, Frank (2019). "On the Jensen–Shannon Symmetrization of Distances Relying on Abstract Means". Entropy. 21 (5): 485. arXiv:1904.04017. Bibcode:2019Entrp..21..485N. doi:10.3390/e21050485. PMC 7514974. PMID 33267199.
Nielsen, Frank (2020). "On a Generalization of the Jensen–Shannon Divergence and the Jensen–Shannon Centroid". Entropy. 22 (2): 221. arXiv:1912.00610. Bibcode:2020Entrp..22..221N. doi:10.3390/e22020221. PMC 7516653. PMID 33285995.

books.google.com

MacKay, David J.C. (2003). Information Theory, Inference, and Learning Algorithms (1st ed.). Cambridge University Press. p. 34. ISBN 9780521642989 – via Google Books.
Tribus, Myron (1959). Thermostatics and Thermodynamics: An Introduction to Energy, Information and States of Matter, with Engineering Applications. Van Nostrand.
Gibbs, Josiah Willard (1871). A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces. The Academy. footnote page 52.

doi.org

Csiszar, I (February 1975). "I-Divergence Geometry of Probability Distributions and Minimization Problems". Ann. Probab. 3 (1): 146–158. doi:10.1214/aop/1176996454.
Kullback, S.; Leibler, R.A. (1951). "On information and sufficiency". Annals of Mathematical Statistics. 22 (1): 79–86. doi:10.1214/aoms/1177729694. JSTOR 2236703. MR 0039968.
Amari 2016, p. 11. Amari, Shun-ichi (2016). Information Geometry and Its Applications. Applied Mathematical Sciences. Vol. 194. Springer Japan. pp. XIII, 374. doi:10.1007/978-4-431-55978-8. ISBN 978-4-431-55977-1.
Amari 2016, p. 28. Amari, Shun-ichi (2016). Information Geometry and Its Applications. Applied Mathematical Sciences. Vol. 194. Springer Japan. pp. XIII, 374. doi:10.1007/978-4-431-55978-8. ISBN 978-4-431-55977-1.
Kullback, S. (1987). "Letter to the Editor: The Kullback–Leibler distance". The American Statistician. 41 (4): 340–341. doi:10.1080/00031305.1987.10475510. JSTOR 2684769.
Abdulkadirov, Ruslan; Lyakhov, Pavel; Nagornov, Nikolay (January 2023). "Survey of Optimization Algorithms in Modern Neural Networks". Mathematics. 11 (11): 2466. doi:10.3390/math11112466. ISSN 2227-7390.
Matassa, Marco (December 2021). "Fubini-Study metrics and Levi-Civita connections on quantum projective spaces". Advances in Mathematics. 393: 108101. arXiv:2010.03291. doi:10.1016/j.aim.2021.108101. ISSN 0001-8708.
Lan, Guanghui (March 2023). "Policy mirror descent for reinforcement learning: linear convergence, new sampling complexity, and generalized problem classes". Mathematical Programming. 198 (1): 1059–1106. doi:10.1007/s10107-022-01816-5. ISSN 1436-4646.
Kelly, J. L. Jr. (1956). "A New Interpretation of Information Rate". Bell Syst. Tech. J. 2 (4): 917–926. doi:10.1002/j.1538-7305.1956.tb03809.x.
Soklakov, A. N. (2020). "Economics of Disagreement—Financial Intuition for the Rényi Divergence". Entropy. 22 (8): 860. arXiv:1811.08308. Bibcode:2020Entrp..22..860S. doi:10.3390/e22080860. PMC 7517462. PMID 33286632.
Henide, Karim (30 September 2024). "Flow Rider: Tradable Ecosystems' Relative Entropy of Flows As a Determinant of Relative Value". The Journal of Investing. 33 (6): 34–58. doi:10.3905/joi.2024.1.321.
Donsker, Monroe D.; Varadhan, SR Srinivasa (1983). "Asymptotic evaluation of certain Markov process expectations for large time. IV". Communications on Pure and Applied Mathematics. 36 (2): 183–212. doi:10.1002/cpa.3160360204.
Belov, Dmitry I.; Armstrong, Ronald D. (2011-04-15). "Distributions of the Kullback-Leibler divergence with applications". British Journal of Mathematical and Statistical Psychology. 64 (2): 291–309. doi:10.1348/000711010x522227. ISSN 0007-1102. PMID 21492134.
Chaloner, K.; Verdinelli, I. (1995). "Bayesian experimental design: a review". Statistical Science. 10 (3): 273–304. doi:10.1214/ss/1177009939. hdl:11299/199630.
Jaynes, E. T. (1957). "Information theory and statistical mechanics" (PDF). Physical Review. 106 (4): 620–630. Bibcode:1957PhRv..106..620J. doi:10.1103/physrev.106.620. S2CID 17870175.
Jaynes, E. T. (1957). "Information theory and statistical mechanics II" (PDF). Physical Review. 108 (2): 171–190. Bibcode:1957PhRv..108..171J. doi:10.1103/physrev.108.171.
Tribus, M.; McIrvine, E. C. (1971). "Energy and information". Scientific American. 224 (3): 179–186. Bibcode:1971SciAm.225c.179T. doi:10.1038/scientificamerican0971-179.
Fraundorf, P. (2007). "Thermal roots of correlation-based complexity". Complexity. 13 (3): 18–26. arXiv:1103.2481. Bibcode:2008Cmplx..13c..18F. doi:10.1002/cplx.20195. S2CID 20794688. Archived from the original on 2011-08-13.
Burnham, K.P.; Anderson, D.R. (2001). "Kullback–Leibler information as a basis for strong inference in ecological studies". Wildlife Research. 28 (2): 111–119. doi:10.1071/WR99107.
Nielsen, Frank (2019). "On the Jensen–Shannon Symmetrization of Distances Relying on Abstract Means". Entropy. 21 (5): 485. arXiv:1904.04017. Bibcode:2019Entrp..21..485N. doi:10.3390/e21050485. PMC 7514974. PMID 33267199.
Nielsen, Frank (2020). "On a Generalization of the Jensen–Shannon Divergence and the Jensen–Shannon Centroid". Entropy. 22 (2): 221. arXiv:1912.00610. Bibcode:2020Entrp..22..221N. doi:10.3390/e22020221. PMC 7516653. PMID 33285995.
Bretagnolle, J.; Huber, C. (1978), "Estimation des densités : Risque minimax", Séminaire de Probabilités XII, Lecture Notes in Mathematics (in French), vol. 649, Berlin, Heidelberg: Springer Berlin Heidelberg, pp. 342–363, doi:10.1007/bfb0064610, ISBN 978-3-540-08761-8, S2CID 122597694, retrieved 2023-02-14 Lemma 2.1
Rubner, Y.; Tomasi, C.; Guibas, L. J. (2000). "The earth mover's distance as a metric for image retrieval". International Journal of Computer Vision. 40 (2): 99–121. doi:10.1023/A:1026543900054. S2CID 14106275.

dx.doi.org

Belov, Dmitry I.; Armstrong, Ronald D. (2011-04-15). "Distributions of the Kullback-Leibler divergence with applications". British Journal of Mathematical and Statistical Psychology. 64 (2): 291–309. doi:10.1348/000711010x522227. ISSN 0007-1102. PMID 21492134.
Bretagnolle, J.; Huber, C. (1978), "Estimation des densités : Risque minimax", Séminaire de Probabilités XII, Lecture Notes in Mathematics (in French), vol. 649, Berlin, Heidelberg: Springer Berlin Heidelberg, pp. 342–363, doi:10.1007/bfb0064610, ISBN 978-3-540-08761-8, S2CID 122597694, retrieved 2023-02-14 Lemma 2.1

elsevier.com

linkinghub.elsevier.com

Matassa, Marco (December 2021). "Fubini-Study metrics and Levi-Civita connections on quantum projective spaces". Advances in Mathematics. 393: 108101. arXiv:2010.03291. doi:10.1016/j.aim.2021.108101. ISSN 0001-8708.

handle.net

hdl.handle.net

Chaloner, K.; Verdinelli, I. (1995). "Bayesian experimental design: a review". Statistical Science. 10 (3): 273–304. doi:10.1214/ss/1177009939. hdl:11299/199630.

harvard.edu

ui.adsabs.harvard.edu

Soklakov, A. N. (2020). "Economics of Disagreement—Financial Intuition for the Rényi Divergence". Entropy. 22 (8): 860. arXiv:1811.08308. Bibcode:2020Entrp..22..860S. doi:10.3390/e22080860. PMC 7517462. PMID 33286632.
Jaynes, E. T. (1957). "Information theory and statistical mechanics" (PDF). Physical Review. 106 (4): 620–630. Bibcode:1957PhRv..106..620J. doi:10.1103/physrev.106.620. S2CID 17870175.
Jaynes, E. T. (1957). "Information theory and statistical mechanics II" (PDF). Physical Review. 108 (2): 171–190. Bibcode:1957PhRv..108..171J. doi:10.1103/physrev.108.171.
Tribus, M.; McIrvine, E. C. (1971). "Energy and information". Scientific American. 224 (3): 179–186. Bibcode:1971SciAm.225c.179T. doi:10.1038/scientificamerican0971-179.
Fraundorf, P. (2007). "Thermal roots of correlation-based complexity". Complexity. 13 (3): 18–26. arXiv:1103.2481. Bibcode:2008Cmplx..13c..18F. doi:10.1002/cplx.20195. S2CID 20794688. Archived from the original on 2011-08-13.
Nielsen, Frank (2019). "On the Jensen–Shannon Symmetrization of Distances Relying on Abstract Means". Entropy. 21 (5): 485. arXiv:1904.04017. Bibcode:2019Entrp..21..485N. doi:10.3390/e21050485. PMC 7514974. PMID 33267199.
Nielsen, Frank (2020). "On a Generalization of the Jensen–Shannon Divergence and the Jensen–Shannon Centroid". Entropy. 22 (2): 221. arXiv:1912.00610. Bibcode:2020Entrp..22..221N. doi:10.3390/e22020221. PMC 7516653. PMID 33285995.

jstor.org

Kullback, S.; Leibler, R.A. (1951). "On information and sufficiency". Annals of Mathematical Statistics. 22 (1): 79–86. doi:10.1214/aoms/1177729694. JSTOR 2236703. MR 0039968.
Kullback, S. (1987). "Letter to the Editor: The Kullback–Leibler distance". The American Statistician. 41 (4): 340–341. doi:10.1080/00031305.1987.10475510. JSTOR 2684769.

nih.gov

pubmed.ncbi.nlm.nih.gov

Soklakov, A. N. (2020). "Economics of Disagreement—Financial Intuition for the Rényi Divergence". Entropy. 22 (8): 860. arXiv:1811.08308. Bibcode:2020Entrp..22..860S. doi:10.3390/e22080860. PMC 7517462. PMID 33286632.
Belov, Dmitry I.; Armstrong, Ronald D. (2011-04-15). "Distributions of the Kullback-Leibler divergence with applications". British Journal of Mathematical and Statistical Psychology. 64 (2): 291–309. doi:10.1348/000711010x522227. ISSN 0007-1102. PMID 21492134.
Nielsen, Frank (2019). "On the Jensen–Shannon Symmetrization of Distances Relying on Abstract Means". Entropy. 21 (5): 485. arXiv:1904.04017. Bibcode:2019Entrp..21..485N. doi:10.3390/e21050485. PMC 7514974. PMID 33267199.
Nielsen, Frank (2020). "On a Generalization of the Jensen–Shannon Divergence and the Jensen–Shannon Centroid". Entropy. 22 (2): 221. arXiv:1912.00610. Bibcode:2020Entrp..22..221N. doi:10.3390/e22020221. PMC 7516653. PMID 33285995.

ncbi.nlm.nih.gov

Soklakov, A. N. (2020). "Economics of Disagreement—Financial Intuition for the Rényi Divergence". Entropy. 22 (8): 860. arXiv:1811.08308. Bibcode:2020Entrp..22..860S. doi:10.3390/e22080860. PMC 7517462. PMID 33286632.
Nielsen, Frank (2019). "On the Jensen–Shannon Symmetrization of Distances Relying on Abstract Means". Entropy. 21 (5): 485. arXiv:1904.04017. Bibcode:2019Entrp..21..485N. doi:10.3390/e21050485. PMC 7514974. PMID 33267199.
Nielsen, Frank (2020). "On a Generalization of the Jensen–Shannon Divergence and the Jensen–Shannon Centroid". Entropy. 22 (2): 221. arXiv:1912.00610. Bibcode:2020Entrp..22..221N. doi:10.3390/e22020221. PMC 7516653. PMID 33285995.

nrbook.com

apps.nrbook.com

Press, W.H.; Teukolsky, S.A.; Vetterling, W.T.; Flannery, B.P. (2007). "Section 14.7.2. Kullback–Leibler Distance". Numerical Recipes: The Art of Scientific Computing (3rd ed.). Cambridge University Press. ISBN 978-0-521-88068-8.

semanticscholar.org

api.semanticscholar.org

Jaynes, E. T. (1957). "Information theory and statistical mechanics" (PDF). Physical Review. 106 (4): 620–630. Bibcode:1957PhRv..106..620J. doi:10.1103/physrev.106.620. S2CID 17870175.
Fraundorf, P. (2007). "Thermal roots of correlation-based complexity". Complexity. 13 (3): 18–26. arXiv:1103.2481. Bibcode:2008Cmplx..13c..18F. doi:10.1002/cplx.20195. S2CID 20794688. Archived from the original on 2011-08-13.
Bretagnolle, J.; Huber, C. (1978), "Estimation des densités : Risque minimax", Séminaire de Probabilités XII, Lecture Notes in Mathematics (in French), vol. 649, Berlin, Heidelberg: Springer Berlin Heidelberg, pp. 342–363, doi:10.1007/bfb0064610, ISBN 978-3-540-08761-8, S2CID 122597694, retrieved 2023-02-14 Lemma 2.1
Rubner, Y.; Tomasi, C.; Guibas, L. J. (2000). "The earth mover's distance as a metric for image retrieval". International Journal of Computer Vision. 40 (2): 99–121. doi:10.1023/A:1026543900054. S2CID 14106275.

springer.com

link.springer.com

Lan, Guanghui (March 2023). "Policy mirror descent for reinforcement learning: linear convergence, new sampling complexity, and generalized problem classes". Mathematical Programming. 198 (1): 1059–1106. doi:10.1007/s10107-022-01816-5. ISSN 1436-4646.

ssrn.com

papers.ssrn.com

Soklakov, A. N. (2023). "Information Geometry of Risks and Returns". Risk. June. SSRN 4134885.

stackexchange.com

stats.stackexchange.com

"What's the maximum value of Kullback-Leibler (KL) divergence?". Machine learning. Statistics Stack Exchange (stats.stackexchange.com). Cross validated.

math.stackexchange.com

"In what situations is the integral equal to infinity?". Integration. Mathematics Stack Exchange (math.stackexchange.com).

stanford.edu

web.stanford.edu

Duchi J. "Derivations for Linear Algebra and Optimization" (PDF). p. 13.

videolectures.net

See the section "differential entropy – 4" in Relative Entropy video lecture by Sergio Verdú NIPS 2009

wiley.com

www3.interscience.wiley.com

Fraundorf, P. (2007). "Thermal roots of correlation-based complexity". Complexity. 13 (3): 18–26. arXiv:1103.2481. Bibcode:2008Cmplx..13c..18F. doi:10.1002/cplx.20195. S2CID 20794688. Archived from the original on 2011-08-13.

worldcat.org

search.worldcat.org

Bishop, Christopher M. Pattern recognition and machine learning. p. 55. OCLC 1334664824.
Abdulkadirov, Ruslan; Lyakhov, Pavel; Nagornov, Nikolay (January 2023). "Survey of Optimization Algorithms in Modern Neural Networks". Mathematics. 11 (11): 2466. doi:10.3390/math11112466. ISSN 2227-7390.
Matassa, Marco (December 2021). "Fubini-Study metrics and Levi-Civita connections on quantum projective spaces". Advances in Mathematics. 393: 108101. arXiv:2010.03291. doi:10.1016/j.aim.2021.108101. ISSN 0001-8708.
Lan, Guanghui (March 2023). "Policy mirror descent for reinforcement learning: linear convergence, new sampling complexity, and generalized problem classes". Mathematical Programming. 198 (1): 1059–1106. doi:10.1007/s10107-022-01816-5. ISSN 1436-4646.
Belov, Dmitry I.; Armstrong, Ronald D. (2011-04-15). "Distributions of the Kullback-Leibler divergence with applications". British Journal of Mathematical and Statistical Psychology. 64 (2): 291–309. doi:10.1348/000711010x522227. ISSN 0007-1102. PMID 21492134.
Buchner, Johannes (2022-04-29). An intuition for physicists: information gain from experiments. OCLC 1363563215.
Burnham, Kenneth P. (December 2010). Model selection and multimodel inference : a practical information-theoretic approach. Springer. ISBN 978-1-4419-2973-0. OCLC 878132909.
B.), Tsybakov, A. B. (Alexandre (2010). Introduction to nonparametric estimation. Springer. ISBN 978-1-4419-2709-5. OCLC 757859245.{{cite book}}: CS1 maint: multiple names: authors list (link) Equation 2.25.

worldcat.org

Bishop, Christopher M. Pattern recognition and machine learning. p. 55. OCLC 1334664824.
Buchner, Johannes (2022-04-29). An intuition for physicists: information gain from experiments. OCLC 1363563215.
Burnham, Kenneth P. (December 2010). Model selection and multimodel inference : a practical information-theoretic approach. Springer. ISBN 978-1-4419-2973-0. OCLC 878132909.
B.), Tsybakov, A. B. (Alexandre (2010). Introduction to nonparametric estimation. Springer. ISBN 978-1-4419-2709-5. OCLC 757859245.{{cite book}}: CS1 maint: multiple names: authors list (link) Equation 2.25.

wustl.edu

bayes.wustl.edu

Jaynes, E. T. (1957). "Information theory and statistical mechanics" (PDF). Physical Review. 106 (4): 620–630. Bibcode:1957PhRv..106..620J. doi:10.1103/physrev.106.620. S2CID 17870175.
Jaynes, E. T. (1957). "Information theory and statistical mechanics II" (PDF). Physical Review. 108 (2): 171–190. Bibcode:1957PhRv..108..171J. doi:10.1103/physrev.108.171.