Game theory, maximum entropy, minimum discrepancy and robust Bayesian decision theory

Keywords

Mathematics, Minimax, Decision theory, Entropy (arrow of time), Information theory

References

• Shannon-Optimal Priors on iid Statistical Experiments Converge Weakly to Jeffreys PriorHolger Scholl — 1999
• Reference Posterior Distributions for Bayesian InferenceJosé M. Bernardo — 1979
• Search for a naturalistic world view: Natural Science and MetaphysicsAbner Shimony — 1993
• Information Theory: 1948-1998 - Guest EditorialSergio Verdú — 1998
• Convexity and Optimization in Finite Dimensions IJosef Stoer, Christoph Witzgall — 1970
• Entropy optimization principles with applicationsJ. N. Kapur, H. K. Kesavan — 1992
• Duality and Auxiliary Functions for Bregman DistancesS. Della Pietra, V. Della Pietra, John Lafferty — 2001
• Relative Loss Bounds for On-Line Density Estimation with the Exponential Family of DistributionsKaty S. Azoury, Manfred K. Warmuth — 1999
• Coherent dispersion criteria for optimal experimental designA. P. Dawid, Paola Sebastiani — 1999
• An algorithm for calculating Γ-minimax decision rules under generalized moment conditionsRoger Fandom Noubiap, Wilfried Seidel — 2001
• A Minimax Result for the Kullback Leibler Bayes RiskJürgen Krob, Holger Scholl — 1997
• Unified approach to optimization techniques in Shannon theoryPeter Harremoës, Flemming Topsøe — 2002
• Statistical Reasoning with Imprecise ProbabilitiesL. H. Wasserman, Peter Walley — 1990
• Maximum Entropy Reconstruction Using Derivative Information, Part 1: Fisher Information and Convex DualityJonathan M. Borwein, Adrian S. Lewis, Dominikus Noll — 1996
• Probability Theory, An Analytic ViewDaniel W. Stroock — 2024
• Boosting as entropy projectionJyrki Kivinen, Manfred K. Warmuth — 1999
• Additive models, boosting, and inference for generalized divergencesJohn Lafferty — 1999
• Statistical Decision Theory and Bayesian Analysis, Second EditionJames O. Berger — 1993
• Uncertainty, Information, and Sequential ExperimentsMorris H. DeGroot — 1962
• Optimal Statistical DecisionsDavid Siegmund, Morris H. DeGroot — 1970

Cited by

• Qualitative Aspects in Numerical Data: Structure, Interaction, and CorrelationAleks Jakulin — 2004
• Penalized Bregman divergence for large-dimensional regression and classification.弘 山本, 昭夫 角田, 寿治 西 — 2010
• Computing conditional probabilities in large domains by maximizing renyi's quadratic entropyC. Lawrence Zitnick, Takeo Kanade — 2003
• Modeling Purposeful Adaptive Behavior with the Principle of Maximum Causal EntropyZiebart, Brian D. — 2010
• Derivation of Probability Distributions for Risk AssessmentAdam Duracz — 2006
• Collective reasoning under uncertainty and inconsistencyMartin Adamčík — 2014
• Existence and uniqueness of the measure of maximal entropy of the domino tiling process on ZDeutsch, Philipp — 2010
• On the Fundamental Relationships Among Path Planning AlternativesRoss A. Knepper — 2011
• Graphical ModelsSteffen L. Lauritzen — 2026
• Decision Making Under Uncertainty: A Robust OptimizationEmmanouil Androulakis — 2014
• Probabilistic Search for Tracking Targets: Theory and Modern ApplicationsIrad Ben‐Gal, Eugene Kagan — 2013
• Inference after checking multiple Bayesian models for data conflict and applications to mitigating the influence of rejected priorsDavid R. Bickel — 2014
• Algebraic and Geometric Methods in Statistics: Contingency tablesPaolo Gibilisco, Paolo Gibilisco, Stephen E. Fienberg — 2009
• Privacy preserving data mining for numerical matrices, social networks, and big dataLian Liu — 2015
• Probabilism, entropies and strictly proper scoring rulesJürgen Landes — 2015
• Applications of Bregman Divergence Measures in Bayesian ModelingGyuhyeong Goh — 2015
• Information and SymmetryAleks Jakulin — 2004
• Extensions of Expected Utility Theory and Some Limitations of Pairwise ComparisonsMark J. Schervish, Teddy Seidenfeld, Joseph B. Kadane — 2003
• Evaluating credal set theory as a belief framework in high-level information fusion for automated decision-makingAlexander Karlsson — 2010
• Is ignorance BlissJoseph B. Kadane, Mark J. Schervish, Teddy Seidenfeld — 2008

Related papers

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• deBruijn identities: From Shannon, Kullback-Leibler and Fisher to generalized φ-entropies, φ-divergences and φ-Fisher informationsSteeve Zozor, Jean-Marc Brossier — 2015
• The Information Volume of Uncertain Information: (5) Divergence MeasureLipeng Pan, Yong Deng — 2020