Maximizing the Bregman divergence from a Bregman family

Johannes Rauh; František Matúš

Kybernetika (2020)

  • Volume: 56, Issue: 5, page 875-885
  • ISSN: 0023-5954

Abstract

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The problem to maximize the information divergence from an exponential family is generalized to the setting of Bregman divergences and suitably defined Bregman families.

How to cite

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Rauh, Johannes, and Matúš, František. "Maximizing the Bregman divergence from a Bregman family." Kybernetika 56.5 (2020): 875-885. <http://eudml.org/doc/297237>.

@article{Rauh2020,
abstract = {The problem to maximize the information divergence from an exponential family is generalized to the setting of Bregman divergences and suitably defined Bregman families.},
author = {Rauh, Johannes, Matúš, František},
journal = {Kybernetika},
keywords = {Bregman divergence; relative entropy; exponential family; optimization},
language = {eng},
number = {5},
pages = {875-885},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Maximizing the Bregman divergence from a Bregman family},
url = {http://eudml.org/doc/297237},
volume = {56},
year = {2020},
}

TY - JOUR
AU - Rauh, Johannes
AU - Matúš, František
TI - Maximizing the Bregman divergence from a Bregman family
JO - Kybernetika
PY - 2020
PB - Institute of Information Theory and Automation AS CR
VL - 56
IS - 5
SP - 875
EP - 885
AB - The problem to maximize the information divergence from an exponential family is generalized to the setting of Bregman divergences and suitably defined Bregman families.
LA - eng
KW - Bregman divergence; relative entropy; exponential family; optimization
UR - http://eudml.org/doc/297237
ER -

References

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  2. Ay, N., Knauf, A., Maximizing multi-information., Kybernetika 42 (2006), 517-538. Zbl1249.82011MR2283503
  3. Barndorff-Nielsen, O., Information and Exponential Families in Statistical Theory., Wiley, 1978. Zbl1288.62007MR0489333
  4. Csiszár, I., Matúš, F., 10.1214/009117904000000766, Ann. Probab. 33 (2005), 582-600. Zbl1068.60008MR2123202DOI10.1214/009117904000000766
  5. Csiszár, I., Matúš, F., 10.1007/s00440-007-0084-z, Probab. Theory Related Fields 141 (2008), 213-246. MR2372970DOI10.1007/s00440-007-0084-z
  6. Geiger, D., Meek, C., Sturmfels, B., 10.1214/009053606000000263, Ann. Statist. 34 (2006), 1463-1492. Zbl1104.60007MR2278364DOI10.1214/009053606000000263
  7. Matúš, F., Maximization of information divergences from binary i.i.d. sequences., In: Proc. IPMU 2 (2004), 1303-1306. 
  8. Matúš, F., Optimality conditions for maximizers of the information divergence from an exponential family., Kybernetika 43 (2007), 731-746. MR2376334
  9. Matúš, F., 10.1109/tit.2009.2032806, IEEE Trans. Inform. Theory 55 (2009), 5375-5381. MR2597169DOI10.1109/tit.2009.2032806
  10. Matúš, F., Ay, N., On maximization of the information divergence from an exponential family., In: Proc. WUPES 2003, University of Economics, Prague 2003, pp. 199-204. 
  11. Matúš, F., Csiszár, I., Generalized minimizers of convex integral functionals, Bregman distance, Pythagorean identities., Kybernetika 48 (2012), 637-689. MR3013394
  12. Matúš, F., Rauh, J., 10.1109/isit.2011.6034269, In: Proc. IEEE International Symposium on Information Theory (ISIT2011), 2011. MR2817016DOI10.1109/isit.2011.6034269
  13. Montúfar, G., Rauh, J., Ay, N., Expressive power and approximation errors of Restricted Boltzmann Machines., In: Proc. NIPS 2011. 
  14. Montúfar, G., Rauh, J., Ay, N., 10.1007/978-3-642-40020-9_85, In: Proc. GSI, 2013, pp. 759-766. DOI10.1007/978-3-642-40020-9_85
  15. Rauh, J., 10.1109/tit.2011.2136230, IEEE Trans. Inform. Theory 57 (2011), 3236-3247. MR2817016DOI10.1109/tit.2011.2136230
  16. Rauh, J., Finding the Maximizers of the Information Divergence from an Exponential Family, Ph.D. Dissertation, Universität Leipzig, 2011. MR2817016
  17. Rockafellar, R. T., 10.1017/s0013091500010142, Princeton University Press, 1970. Zbl1011.49013MR0274683DOI10.1017/s0013091500010142
  18. Wang, N., Rauh, J., Massam, H., 10.1214/18-aos1710, Ann. Statist. 47 (2019), 1203-1233. MR3911110DOI10.1214/18-aos1710

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