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We introduce the Bayesian Nested Group Lasso, a hierarchical model extending the Group Lasso to nested structures. By formulating the penalty as a scale mixture of Gaussians, we derive an efficient MCMC sampling scheme. A simulation study shows that our method reduces posterior variability for irrelevant variables, outperforming the Bayesian Lasso in structured sparsity settings. We discuss potential extensions, including spike-and-slab priors, for exact variable selection.

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Bayesian Nested Group Lasso

  • 会议论文

  • 发表日期：

    2025年

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  • Marco Stefanucci,
  • Pierfrancesco Alaimo Di Loro,
  • Rosario Barone

摘要

We introduce the Bayesian Nested Group Lasso, a hierarchical model extending the Group Lasso to nested structures. By formulating the penalty as a scale mixture of Gaussians, we derive an efficient MCMC sampling scheme. A simulation study shows that our method reduces posterior variability for irrelevant variables, outperforming the Bayesian Lasso in structured sparsity settings. We discuss potential extensions, including spike-and-slab priors, for exact variable selection.