On the hyperprior choice for the global shrinkage parameter in the horseshoe prior

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

Researchers

Research units

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.

Details

Original languageEnglish
Title of host publicationProceedings of the 20th International Conference on Artificial Intelligence and Statistics
Publication statusPublished - 2017
MoE publication typeA4 Article in a conference publication
EventInternational Conference on Artificial Intelligence and Statistics - Hyatt Pier 66 Hotel, Fort Lauderdale, United States
Duration: 20 Apr 201722 Apr 2017
Conference number: 20

Publication series

NameProceedings of Machine Learning Research
PublisherPMLR
Volume54
ISSN (Electronic)1938-7228

Conference

ConferenceInternational Conference on Artificial Intelligence and Statistics
Abbreviated titleAISTATS
CountryUnited States
CityFort Lauderdale
Period20/04/201722/04/2017

ID: 14258530