Open Access
June 2020 A global-local approach for detecting hotspots in multiple-response regression
Hélène Ruffieux, Anthony C. Davison, Jörg Hager, Jamie Inshaw, Benjamin P. Fairfax, Sylvia Richardson, Leonardo Bottolo
Ann. Appl. Stat. 14(2): 905-928 (June 2020). DOI: 10.1214/20-AOAS1332


We tackle modelling and inference for variable selection in regression problems with many predictors and many responses. We focus on detecting hotspots, that is, predictors associated with several responses. Such a task is critical in statistical genetics, as hotspot genetic variants shape the architecture of the genome by controlling the expression of many genes and may initiate decisive functional mechanisms underlying disease endpoints. Existing hierarchical regression approaches designed to model hotspots suffer from two limitations: their discrimination of hotspots is sensitive to the choice of top-level scale parameters for the propensity of predictors to be hotspots, and they do not scale to large predictor and response vectors, for example, of dimensions $10^{3}$–$10^{5}$ in genetic applications. We address these shortcomings by introducing a flexible hierarchical regression framework that is tailored to the detection of hotspots and scalable to the above dimensions. Our proposal implements a fully Bayesian model for hotspots based on the horseshoe shrinkage prior. Its global-local formulation shrinks noise globally and, hence, accommodates the highly sparse nature of genetic analyses while being robust to individual signals, thus leaving the effects of hotspots unshrunk. Inference is carried out using a fast variational algorithm coupled with a novel simulated annealing procedure that allows efficient exploration of multimodal distributions.


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Hélène Ruffieux. Anthony C. Davison. Jörg Hager. Jamie Inshaw. Benjamin P. Fairfax. Sylvia Richardson. Leonardo Bottolo. "A global-local approach for detecting hotspots in multiple-response regression." Ann. Appl. Stat. 14 (2) 905 - 928, June 2020.


Received: 1 October 2018; Revised: 1 February 2020; Published: June 2020
First available in Project Euclid: 29 June 2020

zbMATH: 07239889
MathSciNet: MR4117834
Digital Object Identifier: 10.1214/20-AOAS1332

Keywords: Annealed variational inference , hierarchical model , horseshoe prior , molecular quantitative trait locus analyses , multiplicity control , normal scale mixture , regulation hotspot , shrinkage , statistical genetics , Variable selection

Rights: Copyright © 2020 Institute of Mathematical Statistics

Vol.14 • No. 2 • June 2020
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