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

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    Type
    Article
    Authors
    Park, Chiwoo
    Huang, Jianhua Z.
    Ding, Yu
    KAUST Grant Number
    KUS-CI-016-04
    Date
    2010-10
    Permanent link to this record
    http://hdl.handle.net/10754/597240
    
    Metadata
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    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. ©2010 INFORMS.
    Citation
    Park C, Huang JZ, Ding Y (2010) A Computable Plug-In Estimator of Minimum Volume Sets for Novelty Detection. Operations Research 58: 1469–1480. Available: http://dx.doi.org/10.1287/opre.1100.0825.
    Sponsors
    Park and Ding's research was partially supported by grants from the National Science Foundation (CMMI-0348150 and CMMI-0529026). Huang's research was partially supported by grants from the National Science Foundation (DMS-0606580 and DMS-0907170), the National Cancer Institute (CA57030), and award number KUS-CI-016-04, made by King Abdullah University of Science and Technology (KAUST). The authors are also grateful for the insightful comments and constructive suggestions made by the associate editor and two reviewers that helped improve the paper.
    Publisher
    Institute for Operations Research and the Management Sciences (INFORMS)
    Journal
    Operations Research
    DOI
    10.1287/opre.1100.0825
    ae974a485f413a2113503eed53cd6c53
    10.1287/opre.1100.0825
    Scopus Count
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