Scalable Variational Inference for Bayesian Variable Selection in Regression, and Its Accuracy in Genetic Association Studies

By Peter Carbonetto, Matthew Stephens. 2012

292 citations recorded by the source corpus.

The Bayesian approach to variable selection in regression is a powerful tool for tackling many scientiflc problems. Inference for variable selection models is usually implemented using Markov chain Monte Carlo (MCMC). Because MCMC can impose a high computational cost in studies with a large number of variables, we assess an alternative to MCMC based on a simple variational approximation. Our aim is to retain useful features of Bayesian variable selection at a reduced cost. Using simulations designed to mimic genetic association studies, we show that this simple variational approximation yields posterior inferences in some settings that closely match exact values. In less restrictive (and more realistic) conditions, we show that posterior probabilities of inclusion for individual variables are often incorrect, but variational estimates of other useful quantities|including posterior distributions of the hyperparameters|are remarkably accurate. We illustrate how these results guide the use of variational inference for a genome-wide association study with thousands of samples and hundreds of thousands of variables.

Subfields: Genetics, Statistics and Probability

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Citations in the corpus

Variational Inference: A Review for Statisticians (2016, methodology): “For example, VI has been used in genome-wide association studies (Logsdon, Hoffman, and Mezey 2010; Carbonetto and Stephens 2012), regulatory network analysis (Sanguinetti, Lawrence, and Rattray 2006), motif detection (Xing et al. 2004), phylogenetic hidden Markov models (Jojic et al. 2004),…”
Computationally efficient whole-genome regression for quantitative and binary traits (2020, background): “19d and Supplementary Tables 11,12), and SAIGE had slightly deflated Type 1 error rates.”
A variational Bayes approach to variable selection (2017, methodology): “The VB approach is summarized in many places including Bishop (2006); Rue et al. (2009); Ormerod and Wand (2010); Carbonetto and Stephens (2011); Faes et al. (2011); Wand et al. (2011); Murphy (2012); Pham et al. (2013); Luts and Ormerod (2014); Neville et al. (2014); You et al. (2014).”
fastSTRUCTURE: Variational Inference of Population Structure in Large SNP Data Sets (2014, methodology): “…originally used for approximating intractable integrals, have been used for a wide variety of applications in complex networks (Hofman and Wiggins 2008), machine learning (Jordan et al. 1998; Blei et al. 2003), and Bayesian variable selection (Logsdon et al. 2010; Carbonetto and Stephens 2012).”
Mean field variational Bayes for continuous sparse signal shrinkage: Pitfalls and remedies (2014, unknown): “Logsdon, Hoffman and Mezey [21]; Carbonetto and Stephens [8]; Wand and Ormerod [32]).”
Efficient Bayesian mixed model analysis increases association power in large cohorts (2014, methodology): “We apply a fully factored variational approximation 21,22,38 that repeatedly loops through the SNPs, updating the estimated effect size of each SNP with its posterior mean conditional on current estimates of all other SNP effects.”
Bayesian Regression Using a Prior on the Model Fit: The R2-D2 Shrinkage Prior (2016, background): “…selection (George and McCulloch 1993), shotgun stochastic search (Hans, Dobra, and West 2007), variational Bayes (Logsdon, Hoffman, and Mezey 2010; Carbonetto and Stephens 2012; Ray and Szabó 2019), and EM (Ročková and George 2014) all of which have CONTACT Howard D. Bondell…”