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Robust mislabel logistic regression without modeling mislabel probabilities

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  • Hung Hung
  • Zhi†Yu Jou
  • Su†Yun Huang

Abstract

Logistic regression is among the most widely used statistical methods for linear discriminant analysis. In many applications, we only observe possibly mislabeled responses. Fitting a conventional logistic regression can then lead to biased estimation. One common resolution is to fit a mislabel logistic regression model, which takes into consideration of mislabeled responses. Another common method is to adopt a robust M†estimation by down†weighting suspected instances. In this work, we propose a new robust mislabel logistic regression based on γ†divergence. Our proposal possesses two advantageous features: (1) It does not need to model the mislabel probabilities. (2) The minimum γ†divergence estimation leads to a weighted estimating equation without the need to include any bias correction term, that is, it is automatically bias†corrected. These features make the proposed γ†logistic regression more robust in model fitting and more intuitive for model interpretation through a simple weighting scheme. Our method is also easy to implement, and two types of algorithms are included. Simulation studies and the Pima data application are presented to demonstrate the performance of γ†logistic regression.

Suggested Citation

  • Hung Hung & Zhi†Yu Jou & Su†Yun Huang, 2018. "Robust mislabel logistic regression without modeling mislabel probabilities," Biometrics, The International Biometric Society, vol. 74(1), pages 145-154, March.
    • Handle: RePEc:bla:biomet:v:74:y:2018:i:1:p:145-154
    DOI: 10.1111/biom.12726
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    References listed on IDEAS

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    1. Fujisawa, Hironori & Eguchi, Shinto, 2008. "Robust parameter estimation with a small bias against heavy contamination," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 2053-2081, October.
    2. Takafumi Kanamori & Hironori Fujisawa, 2015. "Robust estimation under heavy contamination using unnormalized models," Biometrika, Biometrika Trust, vol. 102(3), pages 559-572.
    3. Kenichi Hayashi, 2012. "A boosting method with asymmetric mislabeling probabilities which depend on covariates," Computational Statistics, Springer, vol. 27(2), pages 203-218, June.
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    Cited by:

    1. Takayuki Kawashima & Hironori Fujisawa, 2023. "Robust regression against heavy heterogeneous contamination," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(4), pages 421-442, May.
    2. Miron, Julien & Poilane, Benjamin & Cantoni, Eva, 2022. "Robust polytomous logistic regression," Computational Statistics & Data Analysis, Elsevier, vol. 176(C).
    3. Mingyang Ren & Sanguo Zhang & Qingzhao Zhang, 2021. "Robust high-dimensional regression for data with anomalous responses," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(4), pages 703-736, August.
    4. Dries Cornilly & Lise Tubex & Stefan Van Aelst & Tim Verdonck, 2024. "Robust and sparse logistic regression," 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. 18(3), pages 663-679, September.

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