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

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  • Bi, Yingtao
  • Jeske, Daniel R.

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.

Suggested Citation

  • Bi, Yingtao & Jeske, Daniel R., 2010. "The efficiency of logistic regression compared to normal discriminant analysis under class-conditional classification noise," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1622-1637, August.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:7:p:1622-1637
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    1. Yutaka Yasui & Margaret Pepe & Li Hsu & Bao-Ling Adam & Ziding Feng, 2004. "Partially Supervised Learning Using an EM-Boosting Algorithm," Biometrics, The International Biometric Society, vol. 60(1), pages 199-206, March.
    2. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
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    1. Huiqing Chang & Linlin Huang & Panpan Song & Liyang Ru, 2022. "Prediction of arsenic accumulation in a calcareous soil-wheat/maize rotation system with continuous amendment of sewage sludge," Plant, Soil and Environment, Czech Academy of Agricultural Sciences, vol. 68(11), pages 516-524.
    2. Baiyun Chen & Longhai Huang & Zizhong Chen & Guoyin Wang, 2022. "An Ensemble and Iterative Recovery Strategy Based k GNN Method to Edit Data with Label Noise," Mathematics, MDPI, vol. 10(15), pages 1-28, August.
    3. Ahfock, Daniel & McLachlan, Geoffrey J., 2021. "Harmless label noise and informative soft-labels in supervised classification," Computational Statistics & Data Analysis, Elsevier, vol. 161(C).

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