Some decision procedures based on scaled Bregman distance surfaces

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 8085 LNCS, Issue , 2013, Pages 479-486

  Kißlinger, Anna Lena ^a   Stummer, Wolfgang ^a  

^a UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

Author keywords

exponential families; goodness of fit; parameter estimation; Scaled Bregman distances

Indexed keywords

BREGMAN DISTANCES; DISTRIBUTION MIXTURES; EMPIRICAL DISTRIBUTIONS; EXPLORATORY ANALYSIS; EXPONENTIAL FAMILY; GOODNESS OF FIT; RELATIVE FREQUENCIES; STATISTICAL DECISION-MAKING;

DECISION MAKING; PARAMETER ESTIMATION;

INFORMATION SCIENCE;

EID: 84884927783     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-40020-9_52     Document Type: Conference Paper

References (21)

1. Amari, S.-I.: Integration of stochastic models by minimizing α-divergence. Neural Computation 19(10), 2780-2796 (2007)
2. Banerjee, A., Merugu, S., Dhillon, I.S., Ghosh, J.: Clustering with Bregman divergences. J. Machine Learning Research 6, 1705-1749 (2005)
3. Bartlett, P.L., Jordan, M.I., McAuliffe, J.D.: Convexity, classification and risk bounds. JASA 101, 138-156 (2006)
4. Boratynska, A.: Stability of Bayesian inference in exponential families. Statist. & Probab. Letters 36, 173-178 (1997)
5. Carlson, B.A., Clements, M.A.: A computationally compact divergence measure for speech processing. IEEE Transactions on PAMI 13, 1255-1260 (1991)
6. Censor, Y., Zenios, S.A.: Parallel Optimization - Theory, Algorithms, and Applications. Oxford University Press, New York (1997)
7. Cesa-Bianchi, N., Lugosi, G.: Prediction, Learning, Games. Cambridge University Press, Cambridge (2006)
8. Do, M.N., Vetterli, M.: Wavelet-based texture retrieval using generalized Gaussian density and Kullback-Leibler distance. IEEE Transactions on Image Processing 11, 146-158 (2002)
9. Freund, Y., Schapire, R.E.: A decision-theoretic generalization of on-line learning and an application to boosting. J. Comput. Syst. Sci. 55, 119-139 (1997)
10. Hertz, T., Bar-Hillel, A., Weinshall, D.: Learning distance functions for information retrieval. In: Proc. IEEE Comput. Soc. Conf. on Computer Vision and Pattern Rec. CVPR, vol. 2, pp. II-570-II-577 (2004)
11. Lafferty, J.D.: Additive models, boosting, and inference for generalized divergences. In: Proceedings of the Twelfth Annual Conference on Computational Learning Theory, pp. 125-133. ACM Press, New York (1999)
12. Marquina, A., Osher, S.J.: Image super-resolution by TV-regularization and Bregman iteration. J. Sci. Comput. 37, 367-382 (2008)
13. Nock, R., Nielsen, F.: Bregman divergences and surrogates for learning. IEEE Transactions on PAMI 31(11), 2048-2059 (2009)
14. Pardo, M.C., Vajda, I.: On asymptotic properties of information-theoretic divergences. IEEE Transaction on Information Theory 49(7), 1860-1868 (2003)
15. Scherzer, O., Grasmair, M., Grossauer, H., Haltmeier, M., Lenzen, F.: Variational methods in imaging. Springer, New York (2008)
16. Stummer, W.: Some Bregman distances between financial diffusion processes. Proc. Appl. Math. Mech. 7(1), 1050503-1050504 (2007)
17. Stummer, W., Vajda, I.: On Bregman Distances and Divergences of Probability Measures. IEEE Transaction on Information Theory 58(3), 1277-1288 (2012)
18. Teboulle, M.: A unified continuous optimization framework for center-based clustering methods. Journal of Machine Learning Research 8, 65-102 (2007)
19. Vajda, I., Zvárová, J.: On generalized entropies, Bayesian decisions and statistical diversity. Kybernetika 43(5), 675-696 (2007)
20. Veldhuis, R.N.J.: The centroid of the Kullback-Leibler distance. IEEE Signal Processing Letters 9(3), 96-99 (2002)
21. Xu, J., Osher, S.: Iterative regularization and nonlinear inverse scale space applied to wavelet-based denoising. IEEE Transaction on Image Processing 16(2), 534-544 (2007)