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- Publisher Website: 10.1016/j.csda.2018.01.006
- Scopus: eid_2-s2.0-85041431600
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Article: Approximate nonparametric maximum likelihood for mixture models: A convex optimization approach to fitting arbitrary multivariate mixing distributions
Title | Approximate nonparametric maximum likelihood for mixture models: A convex optimization approach to fitting arbitrary multivariate mixing distributions |
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Authors | |
Keywords | Convex optimization Kiefer–Wolfowitz estimator Multivariate mixture models Nonparametric maximum likelihood |
Issue Date | 2018 |
Citation | Computational Statistics and Data Analysis, 2018, v. 122, p. 80-91 How to Cite? |
Abstract | Nonparametric maximum likelihood (NPML) for mixture models is a technique for estimating mixing distributions that has a long and rich history in statistics going back to the 1950s, and is closely related to empirical Bayes methods. Historically, NPML-based methods have been considered to be relatively impractical because of computational and theoretical obstacles. However, recent work focusing on approximate NPML methods suggests that these methods may have great promise for a variety of modern applications. Building on this recent work, a class of flexible, scalable, and easy to implement approximate NPML methods is studied for problems with multivariate mixing distributions. Concrete guidance on implementing these methods is provided, with theoretical and empirical support; topics covered include identifying the support set of the mixing distribution, and comparing algorithms (across a variety of metrics) for solving the simple convex optimization problem at the core of the approximate NPML problem. Additionally, three diverse real data applications are studied to illustrate the methods’ performance: (i) A baseball data analysis (a classical example for empirical Bayes methods), (ii) high-dimensional microarray classification, and (iii) online prediction of blood-glucose density for diabetes patients. Among other things, the empirical results demonstrate the relative effectiveness of using multivariate (as opposed to univariate) mixing distributions for NPML-based approaches. |
Persistent Identifier | http://hdl.handle.net/10722/318700 |
ISSN | 2023 Impact Factor: 1.5 2023 SCImago Journal Rankings: 1.008 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Feng, Long | - |
dc.contributor.author | Dicker, Lee H. | - |
dc.date.accessioned | 2022-10-11T12:24:21Z | - |
dc.date.available | 2022-10-11T12:24:21Z | - |
dc.date.issued | 2018 | - |
dc.identifier.citation | Computational Statistics and Data Analysis, 2018, v. 122, p. 80-91 | - |
dc.identifier.issn | 0167-9473 | - |
dc.identifier.uri | http://hdl.handle.net/10722/318700 | - |
dc.description.abstract | Nonparametric maximum likelihood (NPML) for mixture models is a technique for estimating mixing distributions that has a long and rich history in statistics going back to the 1950s, and is closely related to empirical Bayes methods. Historically, NPML-based methods have been considered to be relatively impractical because of computational and theoretical obstacles. However, recent work focusing on approximate NPML methods suggests that these methods may have great promise for a variety of modern applications. Building on this recent work, a class of flexible, scalable, and easy to implement approximate NPML methods is studied for problems with multivariate mixing distributions. Concrete guidance on implementing these methods is provided, with theoretical and empirical support; topics covered include identifying the support set of the mixing distribution, and comparing algorithms (across a variety of metrics) for solving the simple convex optimization problem at the core of the approximate NPML problem. Additionally, three diverse real data applications are studied to illustrate the methods’ performance: (i) A baseball data analysis (a classical example for empirical Bayes methods), (ii) high-dimensional microarray classification, and (iii) online prediction of blood-glucose density for diabetes patients. Among other things, the empirical results demonstrate the relative effectiveness of using multivariate (as opposed to univariate) mixing distributions for NPML-based approaches. | - |
dc.language | eng | - |
dc.relation.ispartof | Computational Statistics and Data Analysis | - |
dc.subject | Convex optimization | - |
dc.subject | Kiefer–Wolfowitz estimator | - |
dc.subject | Multivariate mixture models | - |
dc.subject | Nonparametric maximum likelihood | - |
dc.title | Approximate nonparametric maximum likelihood for mixture models: A convex optimization approach to fitting arbitrary multivariate mixing distributions | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1016/j.csda.2018.01.006 | - |
dc.identifier.scopus | eid_2-s2.0-85041431600 | - |
dc.identifier.volume | 122 | - |
dc.identifier.spage | 80 | - |
dc.identifier.epage | 91 | - |
dc.identifier.isi | WOS:000427339400006 | - |