Sampling Constrained Probability Distributions Using Spherical Augmentation

Shiwei Lan, Babak Shahbaba

Research output: Chapter in Book/Report/Conference proceedingChapter

8 Scopus citations


Statistical models with constrained probability distributions are abundant in machine learning. Some examples include regression models with norm constraints (e.g., Lasso), probit, many copula models, and latent Dirichlet allocation (LDA). Bayesian inference involving probability distributions confined to constrained domains could be quite challenging for commonly used sampling algorithms. In this work, we propose a novel augmentation technique that handles a wide range of constraints by mapping the constrained domain to a sphere in the augmented space. By moving freely on the surface of this sphere, sampling algorithms handle constraints implicitly and generate proposals that remain within boundaries when mapped back to the original space. Our proposed method, called Spherical Augmentation, provides a mathematically natural and computationally efficient framework for sampling from constrained probability distributions. We show the advantages of our method over state-of-the-art sampling algorithms, such as exact Hamiltonian Monte Carlo, using several examples including truncated Gaussian distributions, Bayesian Lasso, Bayesian bridge regression, reconstruction of quantized stationary Gaussian process, and LDA for topic modeling.

Original languageEnglish (US)
Title of host publicationAdvances in Computer Vision and Pattern Recognition
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages47
StatePublished - 2016
Externally publishedYes

Publication series

NameAdvances in Computer Vision and Pattern Recognition
ISSN (Print)2191-6586
ISSN (Electronic)2191-6594

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Artificial Intelligence


Dive into the research topics of 'Sampling Constrained Probability Distributions Using Spherical Augmentation'. Together they form a unique fingerprint.

Cite this