Found 46 Documents (Results 1–46)
Information theory. From coding to learning (to appear). (English) Zbl 07887869
Cambridge: Cambridge University Press (ISBN 978-1-108-83290-8/hbk). (2024).
Improvements of Jensen’s inequality and its converse for strongly convex functions with applications to strongly \(f\)-divergences. (English) Zbl 07852443
A precise bare simulation approach to the minimization of some distances. I: Foundations. (English) Zbl 1542.94034
Aggregated tests based on supremal divergence estimators for non-regular statistical models. (English) Zbl 07789191
Nielsen, Frank (ed.) et al., Geometric science of information. 6th international conference, GSI 2023, St. Malo, France, August 30 – September 1, 2023. Proceedings. Part I. Cham: Springer. Lect. Notes Comput. Sci. 14071, 136-144 (2023).
MSC:
62H15
f-Betas and portfolio optimization with f-divergence induced risk measures. (English) Zbl 1530.91524
Quant. Finance 23, No. 10, 1483-1496 (2023); correction ibid. 23, No. 11, 11 (2023).
MSC:
91G10
\((f,\Gamma)\)-divergences: interpolating between \(f\)-divergences and integral probability metrics. (English) Zbl 07625192
Refinements of the integral Jensen’s inequality generated by finite or infinite permutations. (English) Zbl 1504.26052
Chain rule optimal transport. (English) Zbl 1473.49052
Nielsen, Frank (ed.), Progress in information geometry. Theory and applications. Based on discussions of the fourth international conference on geometric science of information, GSI’2019, Toulouse, France, August 27–29, 2019. Cham: Springer. Signals Commun. Technol., 191-217 (2021).
MSC:
49Q22
More accurate majorization inequalities obtained via superquadraticity and convexity with application to entropies. (English) Zbl 1462.94020
A new refinement of Jensen’s inequality with applications in information theory. (English) Zbl 1483.26020
Variational regularisation for inverse problems with imperfect forward operators and general noise models. (English) Zbl 1454.49037
Reviewer: Sorin-Mihai Grad (Wien)
A strengthened data processing inequality for the Belavkin-Staszewski relative entropy. (English) Zbl 1439.81015
Monotonicity of the Jensen functional for \(f\)-divergences with applications to the Zipf-Mandelbrot law. (English) Zbl 1430.94045
Zipf-Mandelbrot law and superadditivity of the Jensen functional. (English) Zbl 1476.94020
Pečarić, Đilda (ed.) et al., Inequalities and Zipf-Mandelbrot law. Selected topics in information theory. Zagreb: Element. Monogr. Inequal. 15, 61-88 (2019).
A note on reverse Pinsker inequalities. (English) Zbl 1432.94046
MSC:
94A17
Zipf-Mandelbrot law, \(f\)-divergences and the Jensen-type interpolating inequalities. (English) Zbl 1412.94137
Different quantum \(f\)-divergences and the reversibility of quantum operations. (English) Zbl 1378.81016
Reviewer: Bassano Vacchini (Milano)
Quantum \(f\)-divergence preserving maps on positive semidefinite operators acting on finite dimensional Hilbert spaces. (English) Zbl 1341.47044
Mixed \(f\)-divergence and inequalities for log-concave functions. (English) Zbl 1331.52009
Reviewer: A. E. Litvak (Edmonton)
A generalization of \(f\)-divergence measure to convex functions defined on linear spaces. (English) Zbl 1277.26034
Quantum \(f\)-divergences and error correction. (English) Zbl 1230.81007
Rev. Math. Phys. 23, No. 7, 691-747 (2011); erratum ibid. 29, No. 7, Article ID 1792001, 2 p. (2017).
A new refinement of Jensen’s inequality in linear spaces with applications. (English) Zbl 1205.26032
Superadditivity of some functionals associated with Jensen’s inequality for convex functions on linear spaces with applications. (English) Zbl 1204.26033
Reviewer: Bicheng Yang (Guangdong)
An improvement on Vajda’s inequality. (English) Zbl 1235.94036
Sidoravicius, Vladas (ed.) et al., In and out of equilibrium 2. Papers celebrating the 10th edition of the Brazilian school of probability (EBP), Rio de Janiero, Brazil, July 30 to August 4, 2006. Basel: Birkhäuser (ISBN 978-3-7643-8785-3/hbk). Progress in Probability 60, 299-304 (2008).
Extensions of the parametric families of divergences used in statistical inference. (English) Zbl 1142.62002
MSC:
62B10
Robust utility maximization, \(f\)-projections, and risk constraints. (English) Zbl 1192.91006
Berlin: Humboldt-Univ., Mathematisch-Naturwissenschaftliche Fakultät (Diss.). 142 p. (2006).
Robust utility maximization for complete and incomplete markets. (English) Zbl 1106.91027
Reviewer: Yuliya Mishura (Kyïv)
A symmetric information divergence measure of the Csiszár’s \(f\)-divergence class and its bounds. (English) Zbl 1077.94509
MSC:
94A17
Approximating Csiszár \(f\)-divergence by the use of Taylor’s formula with integral remainder. (English) Zbl 1011.26014
Reviewer: J.E.Pečarić (Zagreb)
Minimax and minimal distance martingale measures and their relationship to portfolio optimization. (English) Zbl 0997.91022
Reviewer: Mikhail Moklyachuk (Kyïv)
Testing in stationary models based on divergences of observed and theoretical frequencies. (English) Zbl 0907.62007
Why least squares and maximum entropy? An axiomatic approach to inference for linear inverse problems. (English) Zbl 0753.62003
Geometry of \(f\)-divergence. (English) Zbl 0761.62027
A note on f-divergences. (English) Zbl 0725.62005
f-projection of \(\sigma\)-finite measures and its information-theoretic and statistical applications. (English) Zbl 0679.62003
Information theory, statistical decision functions, random processes, Trans. 10th Prague Conf., Prague/Czech. 1986, Vol. B, 381-388 (1989).
Some recent results on characterizations of measures of information. (English) Zbl 0482.94011
Theorie de l’information, developpements recents et applications, Colloq. int. CNRS 276, Cachan/Fr. 1977, 19-26 (1978).
On robust estimates. (Hungarian) Zbl 0435.62040
On topological properties of f-divergences. (English) Zbl 0157.25803
Reviewer: J. Wolfowitz
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