Exact sample conditioned MSE performance of the Bayesian MMSE estimator for classification error - Part I: Representation

IEEE Transactions on Signal Processing

Volumn 60, Issue 5, 2012, Pages 2575-2587

  Dalton, Lori A ^a   Dougherty, Edward R ^a,b,c  

^a Department of Electrical and Computer Engineering   (United States)

^b TRANSLATIONAL GENOMICS RESEARCH INSTITUTE   (United States)

^c UNIVERSITY OF TEXAS MD ANDERSON CANCER CENTER   (United States)

Author keywords

Bayesian estimation; classification; error estimation; genomics; minimum mean square estimation; small samples

Indexed keywords

BAYESIAN APPROACHES; BAYESIAN ERROR ESTIMATION; BAYESIAN ESTIMATIONS; BAYESIAN MODEL; CENSORED SAMPLING; CLASSIFICATION ERRORS; CLOSED FORM SOLUTIONS; CRITICAL ISSUES; DIRICHLET PRIOR; DISCRETE CLASSIFICATION; ERROR ESTIMATORS; GENOMICS; HIGH-THROUGHPUT; LINEAR CLASSIFICATION; MATHEMATICAL FRAMEWORKS; MEASURE OF PERFORMANCE; MINIMUM MEAN SQUARES; OBSERVED SAMPLES; RIGOROUS SOLUTION; SIGNAL ESTIMATION; SMALL SAMPLES; TRAINING AND TESTING;

BAYESIAN NETWORKS; CLASSIFICATION (OF INFORMATION); ERROR ANALYSIS; IMAGE SEGMENTATION; INVERSE PROBLEMS;

ESTIMATION;

EID: 84859974404     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2012.2184101     Document Type: Article

References (32)

1. E. R. Dougherty, A. Datta, and C. Sima, "Research issues in genomic signal processing," IEEE Signal Process. Mag., vol. 22, no. 6, pp. 46-68, Jun. 2005. (Pubitemid 46404903)
2. E. R. Dougherty and U. Braga-Neto, "Epistemology of computational biology:Mathematical models and experimental prediction as the basis of their validity," Biol. Syst., vol. 14, no. 1, pp. 65-90, 2006. (Pubitemid 43289707)
3. L. Devroye, L. Gyrfi, and G. Lugosi, A Probabilistic Theory of Pattern Recognition, ser. StochasticModelling and Applied Probability. Berlin, Germany: Springer-Verlag, 1996.
4. E. R. Dougherty, A. Zollanvari, and U. M. Braga-Neto, "The illusion of distribution-free small-sample classification in genomics," Current Genomics, 2011.
5. M. Hills, "Allocation rules and their error rates," J. Roy. Statist. Soc. Series B (Methodol.), vol. 28, no. 1, pp. 1-31, 1966.
6. D. Foley, "Considerations of sample and feature size," IEEE Trans. Inf. Theory, vol. IT-18, no. 5, pp. 618-626, Sep. 1972.
7. M. J. Sorum, "Estimating the expected probability of misclassification for a rule based on the linear discriminant function: univariate normal case," Technometrics, vol. 15, pp. 329-339, 1973.
8. G. J. McLachlan, "An asymptotic expansion of the expectation of the estimated error rate in discriminant analysis," Austr. J. Statist., vol. 15, pp. 210-214, 1973.
9. M.Moran, "On the expectation of errors of allocation associated with a linear discriminant function," Biometrika, vol. 62, no. 1, pp. 141-148, 1975.
10. M. Goldstein and E. Wolf, "On the problem of bias in multinomial classification," Biometrics, vol. 33, pp. 325-31, Jun. 1977. (Pubitemid 8131510)
11. A. Davison and P. Hall, "On the bias and variability of bootstrap and crossvalidation estimates of error rates in discrimination problems," Biometrica, vol. 79, pp. 274-284, 1992.
12. U. Braga-Neto and E. R. Dougherty, "Exact correlation between actual and estimated errors in discrete classification," Pattern Recognit. Lett., vol. 31, no. 5, pp. 407-412, Apr. 2010.
13. A. Zollanvari, U. M. Braga-Neto, and E. R. Dougherty, "On the sampling distribution of resubstitution and leave-one-out error estimators for linear classifiers," Pattern Recognit., vol. 42, no. 11, pp. 2705-2723, Nov. 2009.
14. A. Zollanvari, U. M. Braga-Neto, and E. R. Dougherty, "On the joint sampling distribution between the actual classification error and the resubstitution and leave-one-out error estimators for linear classifiers," IEEE Trans. Inf. Theory, vol. 56, no. 2, pp. 784-804, Feb. 2010.
15. A. Zollanvari, U.M. Braga-Neto, and E. R. Dougherty, "Analytic study of performance of error estimators for linear discriminant analysis," IEEE Trans. Signal Process., vol. 59, no. 9, pp. 4238-4255, Sep. 2011.
16. F. Wyman, D. Young, and D. Turner, "A comparison of asymptotic error rate expansions for the sample linear discriminant function," Pattern Recognit., vol. 23, pp. 775-783, 1990.
17. V. Pikelis, "Comparison of methods of computing the expected classification errors," Autom. Remote Contr., vol. 5, pp. 59-63, 1976.
18. L. A. Dalton and E. R. Dougherty, "Bayesian minimum mean-square error estimation for classification error-Part I: Definition and the Bayesian MMSE error estimator for discrete classification," IEEE Trans. Signal Process., vol. 59, no. 1, pp. 115-129, Jan. 2011.
19. L. A. Dalton and E. R. Dougherty, "Bayesian minimum mean-square error estimation for classification error-Part II: The Bayesian MMSE error estimator for linear classification of Gaussian distributions," IEEE Trans. Signal Process., vol. 59, no. 1, pp. 130-144, Jan. 2011.
20. H. V. Poor, "On robust wiener filtering," IEEE Trans. Autom. Control, vol. 25, no. 4, pp. 531-536, Apr. 1980.
21. K. S. Vastola and H. V. Poor, "Robust wiener-kolmogorov theory," IEEE Trans. Inf. Theory, vol. IT-30, no. 2, pp. 316-327, Mar. 1984.
22. S. Verdu and H. V. Poor, "On minimax robustness: A general approach and applications," IEEE Trans. Inf. Theory, vol. IT-30, no. 2, pp. 328-340, Mar. 1984. (Pubitemid 14566142)
23. A.M. Grigoryan and E. R. Dougherty, "Bayesian robust optimal linear filters," Signal Process., vol. 81, no. 12, pp. 2503-2521, Dec. 2001. (Pubitemid 33089138)
24. R. Pal, A. Datta, and E. R. Dougherty, "Robust intervention in probabilistic boolean networks," IEEE Trans. Signal Process., vol. 56, no. 3, pp. 1280-1294, Mar. 2008. (Pubitemid 351386284)
25. R. Pal, A. Datta, and E. R. Dougherty, "Bayesian robustness in the control of gene regulatory networks," IEEE Trans. Signal Process., vol. 57, no. 9, pp. 3667-3678, Sep. 2009.
26. A. Nilim and L. E. Ghaoui, "Robust control of markov decision processes with uncertain transitionmatrices," Operations Res., vol. 53, no. 5, pp. 780-798, 2005. (Pubitemid 41525849)
27. A. Gelman, J. B. Carlin, H. S. Stern, and D. B. Rubin, Bayesian Data Analysis, 2nd ed. Boca Raton, FL: CRC Press, 2004.
28. J. W. Craig, "A new, simple and exact result for calculating the probability of error for two-dimensional signal constellations," in Proc. IEEE Military Commun. Conf. (MILCOM91), McLean, VA, Nov. 1991, pp. 571-575.
29. L. J. Slater, Generalized Hypergeometric Functions. Cambridge, U.K.: Cambridge Univ. Press, 1966.
30. S. F. Arnold, The Theory of Linear Models and Multivariate Analysis. New York: Wiley, 1981.
31. A.M.Mathai and H. J.Haubold, Special Functions for Applied Scientists. New York: Springer-Verlag, 2008.
32. K. E. Muller and P. W. Stewart, Linear model theory: Univariate, multivariate, and mixed models. Hoboken, NJ: Wiley, 2006.