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

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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.

Original languageEnglish
Pages (from-to)1-25
Number of pages25
JournalAdvances in Data Analysis and Classification
DOIs
Publication statusAccepted/In press - 2016 Jul 27

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Linear Discriminant Function
Normal Population
Asymptotic Relative Efficiency
Discriminant Function
Covariance matrix
Labels
Heteroscedasticity
Receiver Operating Characteristic Curve
Discriminant
Normality

Keywords

  • Area under the ROC curve
  • Labeling mechanism
  • Linear discriminant function
  • Missing data
  • Receiver operating characteristic curve
  • Semi-supervised learning

ASJC Scopus subject areas

  • Computer Science Applications
  • Applied Mathematics

Cite this

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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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