Loading…

On the Hyperprior Choice for the Global Shrinkage Parameter in the Horseshoe Prior

The horseshoe prior has proven to be a noteworthy alternative for sparse Bayesian estimation, but as shown in this paper, the results can be sensitive to the prior choice for the global shrinkage hyperparameter. We argue that the previous default choices are dubious due to their tendency to favor so...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2017-04
Main Authors: Piironen, Juho, Vehtari, Aki
Format: Article
Language:English
Subjects:
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites
container_end_page
container_issue
container_start_page
container_title arXiv.org
container_volume
creator Piironen, Juho
Vehtari, Aki
description The horseshoe prior has proven to be a noteworthy alternative for sparse Bayesian estimation, but as shown in this paper, the results can be sensitive to the prior choice for the global shrinkage hyperparameter. We argue that the previous default choices are dubious due to their tendency to favor solutions with more unshrunk coefficients than we typically expect a priori. This can lead to bad results if this parameter is not strongly identified by data. We derive the relationship between the global parameter and the effective number of nonzeros in the coefficient vector, and show an easy and intuitive way of setting up the prior for the global parameter based on our prior beliefs about the number of nonzero coefficients in the model. The results on real world data show that one can benefit greatly -- in terms of improved parameter estimates, prediction accuracy, and reduced computation time -- from transforming even a crude guess for the number of nonzero coefficients into the prior for the global parameter using our framework.
format article
fullrecord <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2076384620</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2076384620</sourcerecordid><originalsourceid>FETCH-proquest_journals_20763846203</originalsourceid><addsrcrecordid>eNqNjMEKgkAURYcgSMp_eNBamGZ0dC-Vu6LayxTPZswce6OL_j4FP6DVvXDOvQsWCCl3URYLsWKh9zXnXKhUJIkM2OXUQm8Qim-H1JF1BLlx9oFQjXUix8bddQNXQ7Z96SfCWZN-Y48Edt468uiNG9F0sGHLSjcewznXbHvY3_Ii6sh9BvR9WbuB2hGVgqdKZrESXP5n_QCOlz8K</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2076384620</pqid></control><display><type>article</type><title>On the Hyperprior Choice for the Global Shrinkage Parameter in the Horseshoe Prior</title><source>Publicly Available Content Database</source><creator>Piironen, Juho ; Vehtari, Aki</creator><creatorcontrib>Piironen, Juho ; Vehtari, Aki</creatorcontrib><description>The horseshoe prior has proven to be a noteworthy alternative for sparse Bayesian estimation, but as shown in this paper, the results can be sensitive to the prior choice for the global shrinkage hyperparameter. We argue that the previous default choices are dubious due to their tendency to favor solutions with more unshrunk coefficients than we typically expect a priori. This can lead to bad results if this parameter is not strongly identified by data. We derive the relationship between the global parameter and the effective number of nonzeros in the coefficient vector, and show an easy and intuitive way of setting up the prior for the global parameter based on our prior beliefs about the number of nonzero coefficients in the model. The results on real world data show that one can benefit greatly -- in terms of improved parameter estimates, prediction accuracy, and reduced computation time -- from transforming even a crude guess for the number of nonzero coefficients into the prior for the global parameter using our framework.</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Bayesian analysis ; Coefficients ; Parameter estimation ; Parameter identification ; Shrinkage</subject><ispartof>arXiv.org, 2017-04</ispartof><rights>2017. 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>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.proquest.com/docview/2076384620?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>780,784,25752,37011,44589</link.rule.ids></links><search><creatorcontrib>Piironen, Juho</creatorcontrib><creatorcontrib>Vehtari, Aki</creatorcontrib><title>On the Hyperprior Choice for the Global Shrinkage Parameter in the Horseshoe Prior</title><title>arXiv.org</title><description>The horseshoe prior has proven to be a noteworthy alternative for sparse Bayesian estimation, but as shown in this paper, the results can be sensitive to the prior choice for the global shrinkage hyperparameter. We argue that the previous default choices are dubious due to their tendency to favor solutions with more unshrunk coefficients than we typically expect a priori. This can lead to bad results if this parameter is not strongly identified by data. We derive the relationship between the global parameter and the effective number of nonzeros in the coefficient vector, and show an easy and intuitive way of setting up the prior for the global parameter based on our prior beliefs about the number of nonzero coefficients in the model. The results on real world data show that one can benefit greatly -- in terms of improved parameter estimates, prediction accuracy, and reduced computation time -- from transforming even a crude guess for the number of nonzero coefficients into the prior for the global parameter using our framework.</description><subject>Bayesian analysis</subject><subject>Coefficients</subject><subject>Parameter estimation</subject><subject>Parameter identification</subject><subject>Shrinkage</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><sourceid>PIMPY</sourceid><recordid>eNqNjMEKgkAURYcgSMp_eNBamGZ0dC-Vu6LayxTPZswce6OL_j4FP6DVvXDOvQsWCCl3URYLsWKh9zXnXKhUJIkM2OXUQm8Qim-H1JF1BLlx9oFQjXUix8bddQNXQ7Z96SfCWZN-Y48Edt468uiNG9F0sGHLSjcewznXbHvY3_Ii6sh9BvR9WbuB2hGVgqdKZrESXP5n_QCOlz8K</recordid><startdate>20170427</startdate><enddate>20170427</enddate><creator>Piironen, Juho</creator><creator>Vehtari, Aki</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>20170427</creationdate><title>On the Hyperprior Choice for the Global Shrinkage Parameter in the Horseshoe Prior</title><author>Piironen, Juho ; Vehtari, Aki</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_20763846203</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Bayesian analysis</topic><topic>Coefficients</topic><topic>Parameter estimation</topic><topic>Parameter identification</topic><topic>Shrinkage</topic><toplevel>online_resources</toplevel><creatorcontrib>Piironen, Juho</creatorcontrib><creatorcontrib>Vehtari, Aki</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</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>Publicly Available Content Database</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>Piironen, Juho</au><au>Vehtari, Aki</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>On the Hyperprior Choice for the Global Shrinkage Parameter in the Horseshoe Prior</atitle><jtitle>arXiv.org</jtitle><date>2017-04-27</date><risdate>2017</risdate><eissn>2331-8422</eissn><abstract>The horseshoe prior has proven to be a noteworthy alternative for sparse Bayesian estimation, but as shown in this paper, the results can be sensitive to the prior choice for the global shrinkage hyperparameter. We argue that the previous default choices are dubious due to their tendency to favor solutions with more unshrunk coefficients than we typically expect a priori. This can lead to bad results if this parameter is not strongly identified by data. We derive the relationship between the global parameter and the effective number of nonzeros in the coefficient vector, and show an easy and intuitive way of setting up the prior for the global parameter based on our prior beliefs about the number of nonzero coefficients in the model. The results on real world data show that one can benefit greatly -- in terms of improved parameter estimates, prediction accuracy, and reduced computation time -- from transforming even a crude guess for the number of nonzero coefficients into the prior for the global parameter using our framework.</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, 2017-04
issn 2331-8422
language eng
recordid cdi_proquest_journals_2076384620
source Publicly Available Content Database
subjects Bayesian analysis
Coefficients
Parameter estimation
Parameter identification
Shrinkage
title On the Hyperprior Choice for the Global Shrinkage Parameter in the Horseshoe Prior
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-08T18%3A42%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=On%20the%20Hyperprior%20Choice%20for%20the%20Global%20Shrinkage%20Parameter%20in%20the%20Horseshoe%20Prior&rft.jtitle=arXiv.org&rft.au=Piironen,%20Juho&rft.date=2017-04-27&rft.eissn=2331-8422&rft_id=info:doi/&rft_dat=%3Cproquest%3E2076384620%3C/proquest%3E%3Cgrp_id%3Ecdi_FETCH-proquest_journals_20763846203%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2076384620&rft_id=info:pmid/&rfr_iscdi=true