Optimal measures and Markov transition kernels

Journal of Global Optimization - Tập 55 Số 2 - Trang 387-416 - 2013
Roman V. Belavkin1
1School of Engineering and Information Sciences, Middlesex University, London NW4 4BT, UK

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Accardi L., Cecchini C.: Conditional expectations in von Neumann algebras and a theorem of Takesaki. J. Funct. Anal. 45(2), 245–273 (1982)

Alesker S.: Integrals of smooth and analytic functions over Minkowski’s sums of convex sets. In: Ball, K.M., Milman, V. (eds) Convex Geometric Analysis, vol. 34, pp. 1–15. MSRI, Berkeley, CA (1998)

Amari S.I.: Differential-Geometrical Methods of Statistics Lecture Notes in Statistics vol 25. Springer, Berlin (1985)

Amari S.I., Ohara A.: Geometry of q-exponential family of probability distributions. Entropy 13, 1170–1185 (2011)

Asplund E., Rockafellar R.T.: Gradients of convex functions. Trans. Am. Math. Soc. 139, 443–467 (1969)

Banerjee A., Merugu S., Dhillon I.S., Ghosh J.: Clustering with Bregman divergences. J. Mach. Learn. Res. 6, 1705–1749 (2005)

Belavkin, R.V.: Utility and value of information in cognitive science, biology and quantum theory. In: Accardi, L., Freudenberg, W., Ohya, M. (eds.) Quantum Bio-Informatics III. QP-PQ: Quantum Probability and White Noise Analysis, vol. 26. World Scientific, Singapore (2010)

Belavkin, R.V.: On evolution of an information dynamic system and its generating operator. Optim. Lett. 1–14 (2011). doi: 10.1007/s11590-011-0325-z

Belavkin V.P.: New types of quantum entropies and additive information capacities. In: Accardi, L., Freudenberg, W., Ohya, M. (eds) Quantum Bio-Informatics IV, QP-PQ: Quantum Probability and White Noise Analysis, pp. 61–89. World Scientific, Singapore (2011)

Bobkov, S.G., Zegarlinski, B.: Entropy Bounds and Isoperimetry. Memoirs of the American Mathematical Society, vol. 176. AMS, New York, USA (2005)

Bourbaki N.: Eléments de mathématiques. Intégration. Hermann, Paris (1963)

Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. Nauka, Moscow, USSR (1972). In Russian, English translation: AMS, Providence, RI (1982)

Cramér H.: Mathematical Methods of Statistics. Princeton University Press, Princeton, NJ (1946)

Csiszár I.: Why least squares and maximum entropy? An axiomatic approach to inference for linear inverse problems. Ann. Stat. 19(4), 2032–2066 (1991)

Dixmier J.: von Neumann Algebras. North-Holland, Amsterdam, New York, NY (1981)

Goldreich O.: Computational Complexity: A Conceptual Perspective. Cambridge University Press, Cambridge (2008)

Jaynes, E.T.: Information theory and statistical mechanics. Phys. Rev. 106, 108, 620–630, 171–190 (1957)

Kachurovskii R.I.: Nonlinear monotone operators in Banach spaces. Russ. Math. Surv. 23(2), 117–165 (1968)

Khinchin A.I.: Mathematical Foundations of Information Theory. Dover, New York, NY (1957)

Kirkpatrick S., Gelatt C.D., Vecchi J.M.P.: Optimization by simulated annealing. Science 220(4598), 671–680 (1983)

Kolmogorov, A.N., Uspenskii, V.A.: On the definition of an algorithm. Uspekhi Mat. Nauk 13(4), 3–28 (1958) In Russian

Kozen D., Ruozzi N.: Applications of metric coinduction. Log. Methods Comput. Sci. 5(3), 10–119 (2009)

Kullback S.: Information Theory and Statistics. Wiley, New York, NY (1959)

Markov, A.A., Nagornyi, N.M.: The theory of algorithms. Kluwer, Dordrecht, Boston, London (1988). Translated from Russian

Moreau, J.J.: Functionelles convexes. Lectrue Notes, Séminaire sur les équations aux derivées partielles. Collége de France, Paris (1967)

Naudts J.: Generalised exponential families and associated entropy functions. Entropy 10, 131–149 (2008)

Petz D.: Conditional expectation in quantum probability. Lecture Notes in Mathematics 1303, 251–260 (1988)

Phelps R.R.: Lectures on Choquet’s theorem Lecture Notes in Mathematics vol 1757 2nd edn. Springer, Berlin (2001)

Pistone G., Sempi C.: An infinite-dimensional geometric structure on the space of all the probability measures equivalent to a given one. Ann. Stat. 23(5), 1543–1561 (1995)

Rao C.R.: Information and the accuracy attainable in the estimation of statistical parameters. Bull. Calc. Math. Soc. 37, 81–89 (1945)

Rockafellar, R.T.: Conjugate Duality and Optimization. CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 16. Society for Industrial and Applied Mathematics, PA (1974)

Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27, 379–423 and 623–656 (1948)

Stratonovich R.L.: On value of information. Izvestiya USSR Acad. Sci. Tech. Cybern 5, 3–12 (1965) In Russian

Stratonovich, R.L.: Information Theory. Sovetskoe Radio, Moscow, USSR (1975). In Russian

Streater, R.F.: Quantum Orlicz spaces in information geometry. In: The 36th Conference on Mathematical Physics. Open Systems and Information Dynamics, vol. 11, pp. 350–375. Torun (2004)

Takesaki M.: Conditional expectations in von Neumann algebras. J. Funct. Anal. 9(3), 306–321 (1972)

Tikhomirov, V.M.: Analysis II. Encyclopedia of Mathematical Sciences, vol. 14, chap. Convex Analysis, pp. 1–92. Springer (1990)

von Neumann J., Morgenstern O.: Theory of Games and Economic Behavior, 1st edn. Princeton University Press, Princeton, NJ (1944)

Wainwright, M.J., Jordan, M.I.: Graphical models, exponential families, and variational inference. Tech. Rep. 649, University of California, Berkeley (2003)