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A Computable Plug-In Estimator of Minimum Volume Sets for Novelty Detection

Author

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  • Chiwoo Park

    (Department of Industrial and Systems Engineering, Texas A&M University, College Station, Texas 77843)

  • Jianhua Z. Huang

    (Department of Statistics, Texas A&M University, College Station, Texas 77843)

  • Yu Ding

    (Department of Industrial and Systems Engineering, Texas A&M University, College Station, Texas 77843)

Abstract

A minimum volume set of a probability density is a region of minimum size among the regions covering a given probability mass of the density. Effective methods for finding the minimum volume sets are very useful for detecting failures or anomalies in commercial and security applications---a problem known as novelty detection . One theoretical approach of estimating the minimum volume set is to use a density level set where a kernel density estimator is plugged into the optimization problem that yields the appropriate level. Such a plug-in estimator is not of practical use because solving the corresponding minimization problem is usually intractable. A modified plug-in estimator was proposed by Hyndman in 1996 to overcome the computation difficulty of the theoretical approach but is not well studied in the literature. In this paper, we provide theoretical support to this estimator by showing its asymptotic consistency. We also show that this estimator is very competitive to other existing novelty detection methods through an extensive empirical study.

Suggested Citation

  • Chiwoo Park & Jianhua Z. Huang & Yu Ding, 2010. "A Computable Plug-In Estimator of Minimum Volume Sets for Novelty Detection," Operations Research, INFORMS, vol. 58(5), pages 1469-1480, October.
    • Handle: RePEc:inm:oropre:v:58:y:2010:i:5:p:1469-1480
    DOI: 10.1287/opre.1100.0825
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    References listed on IDEAS

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    1. Baíllo, Amparo, 2003. "Total error in a plug-in estimator of level sets," Statistics & Probability Letters, Elsevier, vol. 65(4), pages 411-417, December.
    2. Dolia, A.N. & Harris, C.J. & Shawe-Taylor, J.S. & Titterington, D.M., 2007. "Kernel ellipsoidal trimming," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 309-324, September.
    3. Cadre, BenoI^t, 2006. "Kernel estimation of density level sets," Journal of Multivariate Analysis, Elsevier, vol. 97(4), pages 999-1023, April.
    4. Rocco S., Claudio M. & Zio, Enrico, 2007. "A support vector machine integrated system for the classification of operation anomalies in nuclear components and systems," Reliability Engineering and System Safety, Elsevier, vol. 92(5), pages 593-600.
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    Cited by:

    1. Qianying JIN & Kristiaan KERSTENS & Ignace VAN DE WOESTYNE, 2023. "Convex and Nonconvex Nonparametric Frontier-based Classification Methods for Anomaly Detection," Working Papers 2023-EQM-01, IESEG School of Management.
    2. Qianying Jin & Kristiaan Kerstens & Ignace Van de Woestyne, 2024. "Convex and nonconvex nonparametric frontier-based classification methods for anomaly detection," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 46(4), pages 1213-1239, December.
    3. Irad Ben-Gal & Marcelo Bacher & Morris Amara & Erez Shmueli, 2023. "A Nonparametric Subspace Analysis Approach with Application to Anomaly Detection Ensembles," INFORMS Joural on Data Science, INFORMS, vol. 2(2), pages 99-115, October.
    4. J Morio & R Pastel, 2012. "Plug-in estimation of d-dimensional density minimum volume set of a rare event in a complex system," Journal of Risk and Reliability, , vol. 226(3), pages 337-345, June.

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