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Multilevel Gibbs Sampling for Bayesian Regression

Computation 2020-09-28 v1 Machine Learning Numerical Analysis Numerical Analysis Machine Learning

Abstract

Bayesian regression remains a simple but effective tool based on Bayesian inference techniques. For large-scale applications, with complicated posterior distributions, Markov Chain Monte Carlo methods are applied. To improve the well-known computational burden of Markov Chain Monte Carlo approach for Bayesian regression, we developed a multilevel Gibbs sampler for Bayesian regression of linear mixed models. The level hierarchy of data matrices is created by clustering the features and/or samples of data matrices. Additionally, the use of correlated samples is investigated for variance reduction to improve the convergence of the Markov Chain. Testing on a diverse set of data sets, speed-up is achieved for almost all of them without significant loss in predictive performance.

Keywords

Cite

@article{arxiv.2009.12132,
  title  = {Multilevel Gibbs Sampling for Bayesian Regression},
  author = {Joris Tavernier and Jaak Simm and Adam Arany and Karl Meerbergen and Yves Moreau},
  journal= {arXiv preprint arXiv:2009.12132},
  year   = {2020}
}
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