On the optimality of conditional expectation as a Bregman predictor

IEEE Transactions on Information Theory

Volumn 51, Issue 7, 2005, Pages 2664-2669

  Banerjee, Arindam ^a   Guo, Xin ^b   Wang, Hui ^c  

^a The University of Texas at Austin   (United States)

^b Cornell University   (United States)

^c BROWN UNIVERSITY   (United States)

Author keywords

Bregman loss functions (BLFs); Conditional expectation; Prediction

Indexed keywords

DIFFERENTIAL EQUATIONS; FUNCTIONS; OPTIMIZATION; PROBABILITY DISTRIBUTIONS; THEOREM PROVING;

BREGNAN LOSS FUNCTIONS (BLFS); CONDITIONAL EXPECTATION;

INFORMATION THEORY;

EID: 23744473964     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2005.850145     Document Type: Article

References (20)

1. S. Karlin and H. M. Taylor, A First Course in Stochastic Processes, 2nd ed. San Diego, CA: Academic, 1974.
2. O. Knill, "Probability," Course notes from Caifornia Institute of Technology, Pasadena, CA, 1994.
3. D. Williams, Probability With Martingales. Cambridge, U.K.: Cambridge Univ. Press, 1991.
4. E. L. Lehmann and G. Casella, Theory of Point Estimation, 2nd ed. New York: Springer-Verlag, 1998.
5. K. B. Athreya, "Prediction Under Convex Loss," Dept. Mathematics and Statistics, Iowa State Univ., Ames, IA, Tech. Rep. 99-2, 1999.
6. L. M. Bregman, "The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming," USSR Comput. Math. Phys., vol. 7, pp. 200-217, 1967.
7. I. Ekeland and R. Témam, Convex Analysis and Variational Problems, ser. SIAM Classics in Applied Mathematics. Philadelphia, PA: SIAM, 1999.
8. R. T. Rockafellar, Convex Analysis, ser. Princeton Landmarks in Mathematics. Princeton, NJ: Princeton Univ. Press, 1970.
9. A. Banerjee, S. Merugu, I. Dhillon, and J. Ghosh, "Clustering with Bregman divergences," in Proc. SIAM Int. Conf. Data Mining, 2004, pp. 234-245.
10. D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order, 3rd ed. New York: Springer-Verlag, 2001.
11. C. H. Edwards, Advanced Calculus of Several Variables. Mineola, NY: Dover, 1995.
12. H. L. V. Trees, Detection, Estimation and Modulation Theory (Part I). New York: Wiley, 1968.
13. Y. Censor and S. Zenios, Parallel Optimization: Theory, Algorithms, and Applications. London, U.K.: Oxford Univ. Press, 1998.
14. I. Csiszár, "Why least sqaures and maximum entropy? An axiomatic approach to inference for linear inverse problems," Annals Stat., vol. 19, no. 4, pp. 2032-2066, 1991.
15. A. Ben-Tal, A. Charnes, and M. Teboulle, "Entropic means," J. Math. Anal. Appl., vol. 139, pp. 537-551, 1989.
16. I. Csisár, "Information-type measures of difference of probability distributions and indirect observations," Studia Sci. Math. Hungar, vol. 2, pp. 299-318, 1967.
17. I. Csiszár, "Generalized projections for nonnegative functions," Acta Mathematica Hungarica, vol. 68, no. 1-2, pp. 161-185, 1995.
18. A. Gersho and R. M. Gray, Vector Quantization and Signal Compression. Norwell, MA: Kluwer, 1991.
19. J. Li, N. Chaddha, and R. M. Gray, "Asymptotic performance of vector quantizers with a perceptual distortion measure," IEEE Trans. Inf. Theory, vol. 45, pp. 1082-1091, 1999.
20. T. M. Cover and J. A. Thomas, Elements of Information Theory. New York: Wiley-Interscience, 1991.