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Asymptotic comparison of semi-supervised and supervised linear discriminant functions for heteroscedastic normal populations

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  • Kenichi Hayashi

    (Keio University)

Abstract

It has been reported that using unlabeled data together with labeled data to construct a discriminant function works successfully in practice. However, theoretical studies have implied that unlabeled data can sometimes adversely affect the performance of discriminant functions. Therefore, it is important to know what situations call for the use of unlabeled data. In this paper, asymptotic relative efficiency is presented as the measure for comparing analyses with and without unlabeled data under the heteroscedastic normality assumption. The linear discriminant function maximizing the area under the receiver operating characteristic curve is considered. Asymptotic relative efficiency is evaluated to investigate when and how unlabeled data contribute to improving discriminant performance under several conditions. The results show that asymptotic relative efficiency depends mainly on the heteroscedasticity of the covariance matrices and the stochastic structure of observing the labels of the cases.

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  • Kenichi Hayashi, 2018. "Asymptotic comparison of semi-supervised and supervised linear discriminant functions for heteroscedastic normal populations," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 12(2), pages 315-339, June.
    • Handle: RePEc:spr:advdac:v:12:y:2018:i:2:d:10.1007_s11634-016-0266-6
    DOI: 10.1007/s11634-016-0266-6
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    References listed on IDEAS

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    1. Shinto Eguchi, 2002. "A class of logistic-type discriminant functions," Biometrika, Biometrika Trust, vol. 89(1), pages 1-22, March.
    2. Boldea, Otilia & Magnus, Jan R., 2009. "Maximum Likelihood Estimation of the Multivariate Normal Mixture Model," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1539-1549.
    3. Osamu Komori, 2011. "A boosting method for maximization of the area under the ROC curve," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(5), pages 961-979, October.
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