Bayesian generalized horseshoe estimation of generalized linear models

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Abstract

Bayesian global-local shrinkage estimation with the generalized horseshoe prior represents the state-of-the-art for Gaussian regression models. The extension to non-Gaussian data, such as binary or Student-t regression, is usually done by exploiting a scale-mixture-of-normals approach. However, many standard distributions, such as the gamma and the Poisson, do not admit such a representation. We contribute two extensions to global-local shrinkage methodology. The first is an adaption of recent auxiliary gradient based-sampling schemes to the global-local shrinkage framework, which yields simple algorithms for sampling from generalized linear models. We also introduce two new samplers for the hyperparameters in the generalized horseshoe model, one based on an inverse-gamma mixture of inverse-gamma distributions, and the second a rejection sampler. Results show that these new samplers are highly competitive with the no U-turn sampler for small numbers of predictors, and potentially perform better for larger numbers of predictors. Results for hyperparameter sampling show our new inverse-gamma inverse-gamma based sampling scheme outperforms the standard sampler based on a gamma mixture of gamma distributions.

Original languageEnglish
Title of host publicationMachine Learning and Knowledge Discovery in Databases
Subtitle of host publicationEuropean Conference, ECML PKDD 2019 Würzburg, Germany, September 16–20, 2019 Proceedings, Part II
EditorsUlf Brefeld, Elisa Fromont, Andreas Hotho, Arno Knobbe, Marloes Maathuis, Céline Robardet
Place of PublicationCham Switzerland
PublisherSpringer
Pages598-613
Number of pages16
ISBN (Electronic)9783030461478
ISBN (Print)9783030461461
DOIs
Publication statusPublished - 2020
EventEuropean Conference on Machine Learning European Conference on Principles and Practice of Knowledge Discovery in Databases 2019 - Wurzburg, Germany
Duration: 16 Sept 201920 Sept 2019
https://link.springer.com/book/10.1007/978-3-030-46147-8 (Proceedings)
https://ecmlpkdd2019.org (Website)

Publication series

NameLecture Notes in Computer Science
PublisherSpringer
Volume11907
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

ConferenceEuropean Conference on Machine Learning European Conference on Principles and Practice of Knowledge Discovery in Databases 2019
Abbreviated titleECML PKDD 2019
Country/TerritoryGermany
CityWurzburg
Period16/09/1920/09/19
Internet address

Keywords

  • Bayesian regression
  • Horseshoe regression
  • Markov Chain Monte Carlo sampling
  • Shrinkage

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