A New Monte Carlo Based Algorithm for the Gaussian Process Classification Problem
Gaussian process is a very promising novel technology that has been applied to both the regression problem and the classification problem. While for the regression problem it yields simple exact solutions, this is not the case for the classification problem, because we encounter intractable integral...
Gespeichert in:
Veröffentlicht in: | arXiv.org 2013-10 |
---|---|
Hauptverfasser: | , , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
container_end_page | |
---|---|
container_issue | |
container_start_page | |
container_title | arXiv.org |
container_volume | |
creator | Atiya, Amir F Fayed, Hatem A Abdel-Gawad, Ahmed H |
description | Gaussian process is a very promising novel technology that has been applied to both the regression problem and the classification problem. While for the regression problem it yields simple exact solutions, this is not the case for the classification problem, because we encounter intractable integrals. In this paper we develop a new derivation that transforms the problem into that of evaluating the ratio of multivariate Gaussian orthant integrals. Moreover, we develop a new Monte Carlo procedure that evaluates these integrals. It is based on some aspects of bootstrap sampling and acceptancerejection. The proposed approach has beneficial properties compared to the existing Markov Chain Monte Carlo approach, such as simplicity, reliability, and speed. |
format | Article |
fullrecord | <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2086076578</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2086076578</sourcerecordid><originalsourceid>FETCH-proquest_journals_20860765783</originalsourceid><addsrcrecordid>eNqNiksKwjAUAIMgWLR3eOC6EBP72dbiZ6MouC-xpjYl7dO8FK9vEQ_gamBmJiwQUq6ibC3EjIVELedcJKmIYxmwSw4n_YYj9l5DoZxF2CjSd8jtA53xTQc1OvCNhr0aiIzq4eyw0kRQWDWK2lTKG_zqm9Xdgk1rZUmHP87Zcre9Fofo6fA1aPJli4Prx1QKniU8TeI0k_9dHxjUPpw</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2086076578</pqid></control><display><type>article</type><title>A New Monte Carlo Based Algorithm for the Gaussian Process Classification Problem</title><source>Free E- Journals</source><creator>Atiya, Amir F ; Fayed, Hatem A ; Abdel-Gawad, Ahmed H</creator><creatorcontrib>Atiya, Amir F ; Fayed, Hatem A ; Abdel-Gawad, Ahmed H</creatorcontrib><description>Gaussian process is a very promising novel technology that has been applied to both the regression problem and the classification problem. While for the regression problem it yields simple exact solutions, this is not the case for the classification problem, because we encounter intractable integrals. In this paper we develop a new derivation that transforms the problem into that of evaluating the ratio of multivariate Gaussian orthant integrals. Moreover, we develop a new Monte Carlo procedure that evaluates these integrals. It is based on some aspects of bootstrap sampling and acceptancerejection. The proposed approach has beneficial properties compared to the existing Markov Chain Monte Carlo approach, such as simplicity, reliability, and speed.</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Algorithms ; Classification ; Gaussian process ; Integrals ; Markov analysis ; Markov chains ; Monte Carlo simulation</subject><ispartof>arXiv.org, 2013-10</ispartof><rights>2013. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>780,784</link.rule.ids></links><search><creatorcontrib>Atiya, Amir F</creatorcontrib><creatorcontrib>Fayed, Hatem A</creatorcontrib><creatorcontrib>Abdel-Gawad, Ahmed H</creatorcontrib><title>A New Monte Carlo Based Algorithm for the Gaussian Process Classification Problem</title><title>arXiv.org</title><description>Gaussian process is a very promising novel technology that has been applied to both the regression problem and the classification problem. While for the regression problem it yields simple exact solutions, this is not the case for the classification problem, because we encounter intractable integrals. In this paper we develop a new derivation that transforms the problem into that of evaluating the ratio of multivariate Gaussian orthant integrals. Moreover, we develop a new Monte Carlo procedure that evaluates these integrals. It is based on some aspects of bootstrap sampling and acceptancerejection. The proposed approach has beneficial properties compared to the existing Markov Chain Monte Carlo approach, such as simplicity, reliability, and speed.</description><subject>Algorithms</subject><subject>Classification</subject><subject>Gaussian process</subject><subject>Integrals</subject><subject>Markov analysis</subject><subject>Markov chains</subject><subject>Monte Carlo simulation</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNqNiksKwjAUAIMgWLR3eOC6EBP72dbiZ6MouC-xpjYl7dO8FK9vEQ_gamBmJiwQUq6ibC3EjIVELedcJKmIYxmwSw4n_YYj9l5DoZxF2CjSd8jtA53xTQc1OvCNhr0aiIzq4eyw0kRQWDWK2lTKG_zqm9Xdgk1rZUmHP87Zcre9Fofo6fA1aPJli4Prx1QKniU8TeI0k_9dHxjUPpw</recordid><startdate>20131017</startdate><enddate>20131017</enddate><creator>Atiya, Amir F</creator><creator>Fayed, Hatem A</creator><creator>Abdel-Gawad, Ahmed H</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20131017</creationdate><title>A New Monte Carlo Based Algorithm for the Gaussian Process Classification Problem</title><author>Atiya, Amir F ; Fayed, Hatem A ; Abdel-Gawad, Ahmed H</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_20860765783</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>Algorithms</topic><topic>Classification</topic><topic>Gaussian process</topic><topic>Integrals</topic><topic>Markov analysis</topic><topic>Markov chains</topic><topic>Monte Carlo simulation</topic><toplevel>online_resources</toplevel><creatorcontrib>Atiya, Amir F</creatorcontrib><creatorcontrib>Fayed, Hatem A</creatorcontrib><creatorcontrib>Abdel-Gawad, Ahmed H</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Access via ProQuest (Open Access)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Atiya, Amir F</au><au>Fayed, Hatem A</au><au>Abdel-Gawad, Ahmed H</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>A New Monte Carlo Based Algorithm for the Gaussian Process Classification Problem</atitle><jtitle>arXiv.org</jtitle><date>2013-10-17</date><risdate>2013</risdate><eissn>2331-8422</eissn><abstract>Gaussian process is a very promising novel technology that has been applied to both the regression problem and the classification problem. While for the regression problem it yields simple exact solutions, this is not the case for the classification problem, because we encounter intractable integrals. In this paper we develop a new derivation that transforms the problem into that of evaluating the ratio of multivariate Gaussian orthant integrals. Moreover, we develop a new Monte Carlo procedure that evaluates these integrals. It is based on some aspects of bootstrap sampling and acceptancerejection. The proposed approach has beneficial properties compared to the existing Markov Chain Monte Carlo approach, such as simplicity, reliability, and speed.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><oa>free_for_read</oa></addata></record> |
fulltext | fulltext |
identifier | EISSN: 2331-8422 |
ispartof | arXiv.org, 2013-10 |
issn | 2331-8422 |
language | eng |
recordid | cdi_proquest_journals_2086076578 |
source | Free E- Journals |
subjects | Algorithms Classification Gaussian process Integrals Markov analysis Markov chains Monte Carlo simulation |
title | A New Monte Carlo Based Algorithm for the Gaussian Process Classification Problem |
url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-23T01%3A37%3A32IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=document&rft.atitle=A%20New%20Monte%20Carlo%20Based%20Algorithm%20for%20the%20Gaussian%20Process%20Classification%20Problem&rft.jtitle=arXiv.org&rft.au=Atiya,%20Amir%20F&rft.date=2013-10-17&rft.eissn=2331-8422&rft_id=info:doi/&rft_dat=%3Cproquest%3E2086076578%3C/proquest%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2086076578&rft_id=info:pmid/&rfr_iscdi=true |