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<p>We study Bayesian group-regularized estimation in high-dimensional generalized linear models (GLMs) under a continuous spike-and-slab prior. Our framework covers both canonical and non-canonical link functions and subsumes logistic, Poisson, negative binomial, and Gaussian regression with group sparsity. We obtain the minimax <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10463_2025_964_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\ell _2\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>ℓ</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation> convergence rate for both a maximum a posteriori (MAP) estimator and the full posterior distribution under our prior. Our theoretical results thus justify the use of the posterior mode as a point estimator. The posterior distribution also contracts at the same rate as the MAP estimator, an attractive feature of our approach which is not the case for the group lasso. For computation, we propose expectation-maximization (EM) and Markov chain Monte Carlo (MCMC) algorithms. We illustrate our method through simulations and a real data application on predicting human immunodeficiency virus (HIV) drug resistance from protein sequences.</p>

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Bayesian group regularization in generalized linear models with a continuous spike-and-slab prior

  • 期刊论文

  • 发表日期：

    2025年10月18日

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  • Ray Bai

摘要

We study Bayesian group-regularized estimation in high-dimensional generalized linear models (GLMs) under a continuous spike-and-slab prior. Our framework covers both canonical and non-canonical link functions and subsumes logistic, Poisson, negative binomial, and Gaussian regression with group sparsity. We obtain the minimax \(\ell _2\) ℓ 2 convergence rate for both a maximum a posteriori (MAP) estimator and the full posterior distribution under our prior. Our theoretical results thus justify the use of the posterior mode as a point estimator. The posterior distribution also contracts at the same rate as the MAP estimator, an attractive feature of our approach which is not the case for the group lasso. For computation, we propose expectation-maximization (EM) and Markov chain Monte Carlo (MCMC) algorithms. We illustrate our method through simulations and a real data application on predicting human immunodeficiency virus (HIV) drug resistance from protein sequences.