The efficiency of logistic regression compared to normal discriminant analysis under class-conditional classification noise

Yingtao Bi, Daniel R. Jeske*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

Abstract

In many real world classification problems, class-conditional classification noise (CCC-Noise) frequently deteriorates the performance of a classifier that is naively built by ignoring it. In this paper, we investigate the impact of CCC-Noise on the quality of a popular generative classifier, normal discriminant analysis (NDA), and its corresponding discriminative classifier, logistic regression (LR). We consider the problem of two multivariate normal populations having a common covariance matrix. We compare the asymptotic distribution of the misclassification error rate of these two classifiers under CCC-Noise. We show that when the noise level is low, the asymptotic error rates of both procedures are only slightly affected. We also show that LR is less deteriorated by CCC-Noise compared to NDA. Under CCC-Noise contexts, the Mahalanobis distance between the populations plays a vital role in determining the relative performance of these two procedures. In particular, when this distance is small, LR tends to be more tolerable to CCC-Noise compared to NDA.

Original languageEnglish (US)
Pages (from-to)1622-1637
Number of pages16
JournalJournal of Multivariate Analysis
Volume101
Issue number7
DOIs
StatePublished - Aug 2010

Keywords

  • Asymptotic distribution
  • Class noise
  • Misclassification rate
  • Misspecified model

ASJC Scopus subject areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

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