zbMATH — the first resource for mathematics

A variational Bayes approach to variable selection. (English) Zbl 1384.62240
Markov chain Monte Carlo (MCMC) methods are slow in practice for sufficiently large scale problems. Methods based on mean field variational Bayes (VB) are typically a much faster alternative to stochastic search algorithms and induce sparsity upon the regression coefficients.
The VB method selects the true model at an exponential rate (either it gives the rate of convergence or it can be empirically competitive to other methods in the considered simulation settings), so this approach can provide a useful tool when it is not computationally feasible to enumerate all possible models using exact Bayesian approaches. Numerical examples are given: diets simulation, communities and crime data, simulated single-nucleotide polymorphism data.

62J05 Linear regression; mixed models
62F15 Bayesian inference
62C10 Bayesian problems; characterization of Bayes procedures
Full Text: DOI Euclid