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Boosting in the Presence of Outliers: Adaptive Classification With Nonconvex Loss Functions

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  • Alexander Hanbo Li
  • Jelena Bradic

Abstract

This article examines the role and the efficiency of nonconvex loss functions for binary classification problems. In particular, we investigate how to design adaptive and effective boosting algorithms that are robust to the presence of outliers in the data or to the presence of errors in the observed data labels. We demonstrate that nonconvex losses play an important role for prediction accuracy because of the diminishing gradient properties—the ability of the losses to efficiently adapt to the outlying data. We propose a new boosting framework called ArchBoost that uses diminishing gradient property directly and leads to boosting algorithms that are provably robust. Along with the ArchBoost framework, a family of nonconvex losses is proposed, which leads to the new robust boosting algorithms, named adaptive robust boosting (ARB). Furthermore, we develop a new breakdown point analysis and a new influence function analysis that demonstrate gains in robustness. Moreover, based only on local curvatures, we establish statistical and optimization properties of the proposed ArchBoost algorithms with highly nonconvex losses. Extensive numerical and real data examples illustrate theoretical properties and reveal advantages over the existing boosting methods when data are perturbed by an adversary or otherwise. Supplementary materials for this article are available online.

Suggested Citation

  • Alexander Hanbo Li & Jelena Bradic, 2018. "Boosting in the Presence of Outliers: Adaptive Classification With Nonconvex Loss Functions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 660-674, April.
  • Handle: RePEc:taf:jnlasa:v:113:y:2018:i:522:p:660-674
    DOI: 10.1080/01621459.2016.1273116
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    Cited by:

    1. Tengyuan Liang & Pragya Sur, 2020. "A Precise High-Dimensional Asymptotic Theory for Boosting and Minimum-L1-Norm Interpolated Classifiers," Working Papers 2020-152, Becker Friedman Institute for Research In Economics.
    2. Ju, Xiaomeng & Salibián-Barrera, Matías, 2021. "Robust boosting for regression problems," Computational Statistics & Data Analysis, Elsevier, vol. 153(C).
    3. Zhu Wang, 2022. "MM for penalized estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 54-75, March.
    4. Piotr Skórka & Beata Grzywacz & Dawid Moroń & Magdalena Lenda, 2020. "The macroecology of the COVID-19 pandemic in the Anthropocene," PLOS ONE, Public Library of Science, vol. 15(7), pages 1-17, July.

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