Spherical Hamiltonian Monte Carlo for constrained target distributions

Shiwei Lan, Bo Zhou, Babak Shahbaba

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Scopus citations

Abstract

Statistical models with constrained probability distributions are abundant in machine learning. Some examples include regression models with norm constraints (e.g., Lasso), probit models, many copula models, and Latent Dirichlet Allocation (LDA) models. Bayesian inference involving probability distributions confined to constrained domains could be quite challenging for commonly used sampling algorithms. For such problems, we propose a novel Markov Chain Monte Carlo (MCMC) method that provides a general and computationally efficient framework for handling boundary conditions. Our method first maps the -D-dimensional constrained domain of parameters to the unit ball BD0(1), then augments it to a D-dimensional sphere SD such that the original boundary corresponds to the equator of SD. This way, our method handles the constraints implicitly by moving freely on the sphere generating proposals that remain within boundaries when mapped back to the original space.

Original languageEnglish (US)
Title of host publication31st International Conference on Machine Learning, ICML 2014
PublisherInternational Machine Learning Society (IMLS)
Pages960-968
Number of pages9
ISBN (Electronic)9781634393973
StatePublished - 2014
Event31st International Conference on Machine Learning, ICML 2014 - Beijing, China
Duration: Jun 21 2014Jun 26 2014

Publication series

Name31st International Conference on Machine Learning, ICML 2014
Volume2

Other

Other31st International Conference on Machine Learning, ICML 2014
CountryChina
CityBeijing
Period6/21/146/26/14

ASJC Scopus subject areas

  • Artificial Intelligence
  • Computer Networks and Communications
  • Software

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