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Bounds on Performance for Recovery of Corrupted Labels in Supervised Learning: A Finite Query-Testing Approach

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  • Jin-Taek Seong

    (Graduate School of Data Science, Chonnam National University, Gwangju 61186, Republic of Korea)

Abstract

Label corruption leads to a significant challenge in supervised learning, particularly in deep neural networks. This paper considers recovering a small corrupted subset of data samples which are typically caused by non-expert sources, such as automatic classifiers. Our aim is to recover the corrupted data samples by exploiting a finite query-testing system as an additional expert. The task involves identifying the corrupted data samples with minimal expert queries and finding them to their true label values. The proposed query-testing system uses a random selection of a subset of data samples and utilizes finite field operations to construct combined responses. In this paper, we demonstrate an information-theoretic lower bound on the minimum number of queries required for recovering corrupted labels. The lower bound can be represented as a function of joint entropy with an imbalanced rate of data samples and mislabeled probability. In addition, we find an upper bound on the error probability using maximum a posteriori decoding.

Suggested Citation

  • Jin-Taek Seong, 2023. "Bounds on Performance for Recovery of Corrupted Labels in Supervised Learning: A Finite Query-Testing Approach," Mathematics, MDPI, vol. 11(17), pages 1-16, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:17:p:3636-:d:1223045
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    References listed on IDEAS

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    1. Viv Cothey, 2004. "Web‐crawling reliability," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 55(14), pages 1228-1238, December.
    2. Jin-Taek Seong, 2022. "Theoretical Bounds on the Number of Tests in Noisy Threshold Group Testing Frameworks," Mathematics, MDPI, vol. 10(14), pages 1-14, July.
    3. Jin-Taek Seong, 2020. "Theoretical Bounds on Performance in Threshold Group Testing Schemes," Mathematics, MDPI, vol. 8(4), pages 1-13, April.
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