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Volumn 47, Issue 6, 2014, Pages 2178-2192

Moments and root-mean-square error of the Bayesian MMSE estimator of classification error in the Gaussian model

Author keywords

Bayesian minimum mean square error estimator; Double asymptotics; Kolmogorov asymptotics; Linear discriminant analysis; Performance metrics; RMS

Indexed keywords


EID: 84894366246     PISSN: 00313203     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.patcog.2013.11.022     Document Type: Article
Times cited : (34)

References (35)
  • 2
    • 0015395891 scopus 로고
    • Considerations of sample and feature size
    • D. Foley Considerations of sample and feature size IEEE Trans. Inf. Theory IT18 1972 618 626
    • (1972) IEEE Trans. Inf. Theory , vol.18 IT , pp. 618-626
    • Foley, D.1
  • 3
    • 80051734868 scopus 로고
    • Estimating the conditional probability of misclassification
    • M.J. Sorum Estimating the conditional probability of misclassification Technometrics 13 1971 333 343
    • (1971) Technometrics , vol.13 , pp. 333-343
    • Sorum, M.J.1
  • 4
    • 84990495134 scopus 로고
    • An asymptotic expansion of the expectation of the estimated error rate in discriminant analysis
    • G.J. McLachlan An asymptotic expansion of the expectation of the estimated error rate in discriminant analysis Aust. J. Stat. 15 1973 210 214
    • (1973) Aust. J. Stat. , vol.15 , pp. 210-214
    • McLachlan, G.J.1
  • 5
    • 85041937814 scopus 로고
    • On the expectation of errors of allocation associated with a linear discriminant function
    • M. Moran On the expectation of errors of allocation associated with a linear discriminant function Biometrika 62 1975 141 148
    • (1975) Biometrika , vol.62 , pp. 141-148
    • Moran, M.1
  • 6
    • 0041665444 scopus 로고    scopus 로고
    • A priori estimates of recognition quality for discrete features
    • V.B. Berikov A priori estimates of recognition quality for discrete features Pattern Recognit. Image Anal. 12 2002 235 242
    • (2002) Pattern Recognit. Image Anal. , vol.12 , pp. 235-242
    • Berikov, V.B.1
  • 7
    • 0041876267 scopus 로고    scopus 로고
    • The influence of prior knowledge on the expected performance of a classifier
    • V.B. Berikov, and A.G. Litvinenko The influence of prior knowledge on the expected performance of a classifier Pattern Recognit. Lett. 24 2003 2537 2548
    • (2003) Pattern Recognit. Lett. , vol.24 , pp. 2537-2548
    • Berikov, V.B.1    Litvinenko, A.G.2
  • 8
    • 24044535745 scopus 로고    scopus 로고
    • Exact performance measures and distributions of error estimators for discrete classifiers
    • U. Braga-Neto, and E.R. Dougherty Exact performance measures and distributions of error estimators for discrete classifiers Pattern Recognit. 38 2005 1799 1814
    • (2005) Pattern Recognit. , vol.38 , pp. 1799-1814
    • Braga-Neto, U.1    Dougherty, E.R.2
  • 9
    • 0018179125 scopus 로고
    • Additive estimators for probabilities of correct classification
    • N. Glick Additive estimators for probabilities of correct classification Pattern Recognit. 10 1978 211 222
    • (1978) Pattern Recognit. , vol.10 , pp. 211-222
    • Glick, N.1
  • 12
    • 67649390743 scopus 로고    scopus 로고
    • On the sampling distribution of resubstitution and leave-one-out error estimators for linear classifiers
    • 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. 42 2009 2705 2723
    • (2009) Pattern Recognit. , vol.42 , pp. 2705-2723
    • Zollanvari, A.1    Braga-Neto, U.M.2    Dougherty, E.R.3
  • 13
    • 75149170858 scopus 로고    scopus 로고
    • Exact correlation between actual and estimated errors in discrete classification
    • U.M. Braga-Neto, and E.R. Dougherty Exact correlation between actual and estimated errors in discrete classification Pattern Recognit. Lett. 31 2010 407 413
    • (2010) Pattern Recognit. Lett. , vol.31 , pp. 407-413
    • Braga-Neto, U.M.1    Dougherty, E.R.2
  • 14
    • 80052964854 scopus 로고    scopus 로고
    • Exact representation of the second-order moments for resubstitution and leave-one-out error estimation for linear discriminant analysis in the univariate heteroskedastic gaussian model
    • A. Zollanvari, U.M. Braga-Neto, and E.R. Dougherty Exact representation of the second-order moments for resubstitution and leave-one-out error estimation for linear discriminant analysis in the univariate heteroskedastic gaussian model Pattern Recognit. 45 2012 908 917
    • (2012) Pattern Recognit. , vol.45 , pp. 908-917
    • Zollanvari, A.1    Braga-Neto, U.M.2    Dougherty, E.R.3
  • 15
    • 77649305686 scopus 로고    scopus 로고
    • Joint sampling distribution between actual and estimated classification errors for linear discriminant analysis
    • A. Zollanvari, U.M. Braga-Neto, and E.R. Dougherty Joint sampling distribution between actual and estimated classification errors for linear discriminant analysis IEEE Trans. Inf. Theory 56 2010 784 804
    • (2010) IEEE Trans. Inf. Theory , vol.56 , pp. 784-804
    • Zollanvari, A.1    Braga-Neto, U.M.2    Dougherty, E.R.3
  • 16
    • 79960987402 scopus 로고    scopus 로고
    • Analytic study of performance of error estimators for linear discriminant analysis
    • 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. 59 2011 4238 4255
    • (2011) IEEE Trans. Signal Process. , vol.59 , pp. 4238-4255
    • Zollanvari, A.1    Braga-Neto, U.M.2    Dougherty, E.R.3
  • 17
    • 0025659671 scopus 로고
    • A comparison of asymptotic error rate expansions for the sample linear discriminant function
    • F. Wyman, D. Young, and D. Turner A comparison of asymptotic error rate expansions for the sample linear discriminant function Pattern Recognit. 23 1990 775 783
    • (1990) Pattern Recognit. , vol.23 , pp. 775-783
    • Wyman, F.1    Young, D.2    Turner, D.3
  • 18
    • 0344422338 scopus 로고
    • Comparison of methods of computing the expected classification errors
    • V. Pikelis Comparison of methods of computing the expected classification errors Autom. Remote Control 5 1976 59 63
    • (1976) Autom. Remote Control , vol.5 , pp. 59-63
    • Pikelis, V.1
  • 19
    • 0007826528 scopus 로고
    • On the amount of a priori information in designing the classification algorithm
    • In Russian
    • S. Raudys On the amount of a priori information in designing the classification algorithm Tech. Cybern. 4 1972 168 174 In Russian
    • (1972) Tech. Cybern. , vol.4 , pp. 168-174
    • Raudys, S.1
  • 20
    • 0039070785 scopus 로고
    • Representation of statistics of discriminant analysis and asymptotic expansion when space dimensions are comparable with sample size
    • (in Russian)
    • A. Deev Representation of statistics of discriminant analysis and asymptotic expansion when space dimensions are comparable with sample size Dokl. Akad. Nauk SSSR 195 1970 759 762 (in Russian)
    • (1970) Dokl. Akad. Nauk SSSR , vol.195 , pp. 759-762
    • Deev, A.1
  • 21
    • 0042494547 scopus 로고    scopus 로고
    • Error bounds for asymptotic approximations of the linear discriminant function when the sample size and dimensionality are large
    • Y. Fujikoshi Error bounds for asymptotic approximations of the linear discriminant function when the sample size and dimensionality are large J. Multivar. Anal. 73 2000 1 17
    • (2000) J. Multivar. Anal. , vol.73 , pp. 1-17
    • Fujikoshi, Y.1
  • 23
    • 33745156863 scopus 로고    scopus 로고
    • Some theory for Fisher's linear discriminant function, 'naive bayes', and some alternatives when there are many more variables than observations
    • P.J. Bickel, and E. Levina Some theory for Fisher's linear discriminant function, 'naive bayes', and some alternatives when there are many more variables than observations Bernoulli 10 2004 989 1010
    • (2004) Bernoulli , vol.10 , pp. 989-1010
    • Bickel, P.J.1    Levina, E.2
  • 24
    • 1442331023 scopus 로고    scopus 로고
    • Results in statistical discriminant analysis a review of the former soviet union literature
    • S. Raudys, and D.M. Young Results in statistical discriminant analysis a review of the former soviet union literature J. Multivar. Anal. 89 2004 1 35
    • (2004) J. Multivar. Anal. , vol.89 , pp. 1-35
    • Raudys, S.1    Young, D.M.2
  • 26
    • 79961007365 scopus 로고    scopus 로고
    • The illusion of distribution-free small-sample classification in genomics
    • E.R. Dougherty, A. Zollanvari, and U.M. Braga-Neto The illusion of distribution-free small-sample classification in genomics Curr. Genomics 12 2011 333 341
    • (2011) Curr. Genomics , vol.12 , pp. 333-341
    • Dougherty, E.R.1    Zollanvari, A.2    Braga-Neto, U.M.3
  • 27
    • 79959465085 scopus 로고    scopus 로고
    • Bayesian minimum mean-square error estimation for classification error-Part i definition and the Bayesian MMSE error estimator for discrete classification
    • L. 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. 59 2011 115 129
    • (2011) IEEE Trans. Signal Process. , vol.59 , pp. 115-129
    • Dalton, L.1    Dougherty, E.R.2
  • 28
    • 79959394813 scopus 로고    scopus 로고
    • Bayesian minimum mean-square error estimation for classification error - Part II linear classification of Gaussian models
    • L. Dalton, and E.R. Dougherty Bayesian minimum mean-square error estimation for classification error - Part II linear classification of Gaussian models IEEE Trans. Signal Process. 59 2011 130 144
    • (2011) IEEE Trans. Signal Process. , vol.59 , pp. 130-144
    • Dalton, L.1    Dougherty, E.R.2
  • 29
    • 84859974404 scopus 로고    scopus 로고
    • Exact sample conditioned MSE performance of the Bayesian MMSE estimator for classification error - Part i Representation
    • L. Dalton, and E.R. Dougherty Exact sample conditioned MSE performance of the Bayesian MMSE estimator for classification error - Part I Representation IEEE Trans. Signal Process. 60 2012 2575 2587
    • (2012) IEEE Trans. Signal Process. , vol.60 , pp. 2575-2587
    • Dalton, L.1    Dougherty, E.R.2
  • 30
    • 84859950916 scopus 로고    scopus 로고
    • Exact sample conditioned MSE performance of the Bayesian MMSE estimator for classification error - Part II Consistency and performance analysis
    • L. Dalton, and E.R. Dougherty Exact sample conditioned MSE performance of the Bayesian MMSE estimator for classification error - Part II Consistency and performance analysis IEEE Trans. Signal Process. 60 2012 2588 2603
    • (2012) IEEE Trans. Signal Process. , vol.60 , pp. 2588-2603
    • Dalton, L.1    Dougherty, E.R.2
  • 31
    • 0001893585 scopus 로고
    • Classification by multivariate analysis
    • T. Anderson Classification by multivariate analysis Psychometrika 16 1951 31 50
    • (1951) Psychometrika , vol.16 , pp. 31-50
    • Anderson, T.1
  • 32
    • 0007284561 scopus 로고
    • Errors in discrimination
    • S. John Errors in discrimination Ann. Math. Stat. 32 1961 1125 1144
    • (1961) Ann. Math. Stat. , vol.32 , pp. 1125-1144
    • John, S.1
  • 34
    • 38349151562 scopus 로고    scopus 로고
    • From moments of sum to moments of product
    • R. Kan From moments of sum to moments of product J. Multivar. Anal. 99 2008 542 554
    • (2008) J. Multivar. Anal. , vol.99 , pp. 542-554
    • Kan, R.1
  • 35
    • 74149094589 scopus 로고    scopus 로고
    • Expectation of quadratic forms in normal and nonnormal variables with econometric applications
    • Y. Bao, and A. Ullah Expectation of quadratic forms in normal and nonnormal variables with econometric applications J. Stat. Plan. Inference 140 2010 1193 1205
    • (2010) J. Stat. Plan. Inference , vol.140 , pp. 1193-1205
    • Bao, Y.1    Ullah, A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.