Generalized projections for non-negative functions

Keywords

Bregman divergence, Mathematics, Convex function, Regular polygon, Entropy (arrow of time)

References

• A General Class of Coefficients of Divergence of One Distribution from AnotherSyed Mustafa Ali, S. D. Silvey — 1966
• Approximation-theoretic derivation of logarithmic entropy principles for inverse problems and unique extension of the maximum entropy method to incorporate prior knowledgeLee K. Jones — 1989
• Maximum entropy in action: Buck, Brian and Macaulay, Vincent A., 1991, 220 pp., Clarendon Press, Oxford, £30 pb, ISBN 0-19-8539630Walter T. Grandy — 1995
• Convergence of best phi-entropy estimatesMarc Teboulle, Igor Vajda — 1993
• The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programmingL.M. Bregman — 1967
• General entropy criteria for inverse problems, with applications to data compression, pattern classification, and cluster analysisLee K. Jones, C.L. Byrne — 1990
• Sanov Property, Generalized I-Projection and a Conditional Limit TheoremImre Csiszár — 1984
• Information-theoretical optimization techniquesFlemming Topsøe — 1979
• Partially-Finite Programming in L1 and the Existence of Maximum Entropy EstimatesJonathan M. Borwein, Adrian S. Lewis — 1993
• I-Divergence Geometry of Probability Distributions and Minimization ProblemsImre Csiszár — 1975
• Maximum d'entropie et problème des momentsDidier Dacunha‐Castelle, Fabrice Gamboa — 1990
• Papers on probability, statistics and statistical physicsE. Jaynes — 1983
• Why least squares and maximum entropy? An axiomatic approach to inverse problemsI. Csiszár — 1990

Cited by

• Applications of Bregman Divergence Measures in Bayesian ModelingGyuhyeong Goh — 2015
• Existence and Uniqueness of Semiparametric ProjectionsIvana Komunjer, Giuseppe Ragusa — 2009
• Logistic Regression, AdaBoost and Bregman DistancesMichael Collins, Robert E. Schapire, Yoram Singer — 2000
• On entropies, divergences, and mean valuesMichèle Basseville, J.-F. Cardoso — 1995
• Relative entropy and covariance type constraints yielding ARMA modelsValérie Girardin — 2001
• Minimization of entropy functionalsChristian Léonard — 2007
• Generalized minimizers of convex integral functionals, Bregman distance, Pythagorean identitiesImre Csiszár, František Matúš — 2012
• Clustering Longitudinal Health Data Using Hidden Markov ModelsShima Ghassem Pour — 2014
• Minimizers of energy functionalsChristian Léonard — 2001
• On two extensions of the vector quantization schemeAurélie Fischer — 2015
• Rescaling Entropy and Divergence RatesValérie Girardin, Loïck Lhote — 2015
• Functional Bregman Divergence and Bayesian Estimation of DistributionsBéla A. Frigyik, Santosh Kumar Srivastava, Maya R. Gupta — 2006
• On Bregman Distances and Divergences of Probability MeasuresWolfgang Stummer, Igor Vajda — 2009
• Additive models, boosting, and inference for generalized divergencesJohn Lafferty — 1999
• Bayesian model diagnostics using functional Bregman divergenceGyuhyeong Goh, Dipak K. Dey — 2014
• NEW BAYESIAN METHODS FOR ILL POSED PROBLEMSFabrice Gamboa — 1999
• Inference in ϕ-families of distributionsBruno Pelletier — 2011
• Minimization of entropy functionals revisitedImre Csiszár, František Matúš — 2012
• Minimization of Energy Functionals Applied to Some Inverse ProblemsChristian Léonard — 2001
• Solving Fredholm equations by maximum entropy on the mean. application to superresolutionFabrice Gamboa, Henryk Gzyl — 1997

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