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

Handle URI:
http://hdl.handle.net/10754/597240
Title:
A Computable Plug-In Estimator of Minimum Volume Sets for Novelty Detection
Authors:
Park, Chiwoo; Huang, Jianhua Z.; Ding, Yu
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.
Publisher:
Institute for Operations Research and the Management Sciences (INFORMS)
Journal:
Operations Research
KAUST Grant Number:
KUS-CI-016-04
Issue Date:
Oct-2010
DOI:
10.1287/opre.1100.0825
Type:
Article
ISSN:
0030-364X; 1526-5463
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.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorPark, Chiwooen
dc.contributor.authorHuang, Jianhua Z.en
dc.contributor.authorDing, Yuen
dc.date.accessioned2016-02-25T12:28:44Zen
dc.date.available2016-02-25T12:28:44Zen
dc.date.issued2010-10en
dc.identifier.citationPark 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.en
dc.identifier.issn0030-364Xen
dc.identifier.issn1526-5463en
dc.identifier.doi10.1287/opre.1100.0825en
dc.identifier.urihttp://hdl.handle.net/10754/597240en
dc.description.abstractA 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.en
dc.description.sponsorshipPark 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.en
dc.publisherInstitute for Operations Research and the Management Sciences (INFORMS)en
dc.subjectAsymptotic consistencyen
dc.subjectDensity level setsen
dc.subjectGeneralized statistical control charten
dc.subjectMinimum volume setsen
dc.subjectNovelty detectionen
dc.subjectPlug-in estimatoren
dc.titleA Computable Plug-In Estimator of Minimum Volume Sets for Novelty Detectionen
dc.typeArticleen
dc.identifier.journalOperations Researchen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
kaust.grant.numberKUS-CI-016-04en
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