Statistics seminar - Dr Khue-Dung Dang - University of Western Australia

A seminar by Dr Khue-Dung Dang from University of Western Australia

Title: Variational approximate penalised credible regions for Bayesian grouped regression

Abstract: Most existing Bayesian methods for high-dimensional regression either incur high computational costs from long Markov chain Monte Carlo runs or yield ambiguous variable selection results due to non-sparse solution output. In this talk, I will present a fast and accurate grouped penalised credible region approach for variable selection and prediction in Bayesian high-dimensional linear regression. The method uses a grouped global-local shrinkage prior to achieve high estimation accuracy, and posterior summaries are approximated using coordinate ascent variational inference. Sparse post-processed estimates are then obtained via a penalised credible region framework, which can be formulated as a convex optimisation problem and solved efficiently. The resulting post-processed estimators can be proved to be both parameter-consistent and variable selection consistent in high-dimensional settings. Through extensive simulations and a real data application, I will demonstrate that the proposed method outperforms state-of-the-art methods in grouped variable selection, prediction accuracy, and computation time across a range of models, including ANOVA and nonparametric varying coefficient models.

https://arxiv.org/abs/2601.16585

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