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

    17 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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