{"ID":2828285,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.13992","arxiv_id":"2512.13992","title":"Bayesian Global-Local Regularization","abstract":"We propose a unified framework for global-local regularization that bridges the gap between classical techniques -- such as ridge regression and the nonnegative garotte -- and modern Bayesian hierarchical modeling. By estimating local regularization strengths via marginal likelihood under order constraints, our approach generalizes Stein's positive-part estimator and provides a principled mechanism for adaptive shrinkage in high-dimensional settings. We establish that this isotonic empirical Bayes estimator achieves near-minimax risk (up to logarithmic factors) over sparse ordered model classes, constituting a significant advance in high-dimensional statistical inference. Applications to orthogonal polynomial regression demonstrate the methodology's flexibility, while our theoretical results clarify the connections between empirical Bayes, shape-constrained estimation, and degrees-of-freedom adjustments.","short_abstract":"We propose a unified framework for global-local regularization that bridges the gap between classical techniques -- such as ridge regression and the nonnegative garotte -- and modern Bayesian hierarchical modeling. By estimating local regularization strengths via marginal likelihood under order constraints, our approac...","url_abs":"https://arxiv.org/abs/2512.13992","url_pdf":"https://arxiv.org/pdf/2512.13992v1","authors":"[\"Jyotishka Datta\",\"Nick Polson\",\"Vadim Sokolov\"]","published":"2025-12-16T01:11:17Z","proceeding":"stat.ME","tasks":"[\"stat.ME\",\"math.ST\"]","methods":"[]","has_code":false}