Laplace approximation for Bayesian variable selection via Le Cam’s one-step procedure

Tianrui Hou, Yves Atchade
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:3772-3780, 2026.

Abstract

Relevant feature selection in high-dimensional settings is a central challenge in modern scientific research and decision-making. While many existing methods offer strong statistical guarantees, they are often computationally intractable in high-dimensional problems. To address this issue, we introduce a novel Laplace approximation method based on Le Cam’s one-step procedure, termed \textsf{OLAP}. This approach is specifically designed to alleviate computational burdens while maintaining statistical rigor. Under standard high-dimensional assumptions, we establish that \textsf{OLAP} achieves consistent variable selection. Moreover, the method yields a posterior distribution that can be efficiently explored in polynomial time via a simple Gibbs sampling algorithm. We demonstrate the effectiveness of OLAP through applications to logistic and Poisson regression models, using both simulated and real data.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-hou26a, title = { Laplace approximation for Bayesian variable selection via Le Cam’s one-step procedure }, author = {Hou, Tianrui and Atchade, Yves}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {3772--3780}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/hou26a/hou26a.pdf}, url = {https://proceedings.mlr.press/v300/hou26a.html}, abstract = { Relevant feature selection in high-dimensional settings is a central challenge in modern scientific research and decision-making. While many existing methods offer strong statistical guarantees, they are often computationally intractable in high-dimensional problems. To address this issue, we introduce a novel Laplace approximation method based on Le Cam’s one-step procedure, termed \textsf{OLAP}. This approach is specifically designed to alleviate computational burdens while maintaining statistical rigor. Under standard high-dimensional assumptions, we establish that \textsf{OLAP} achieves consistent variable selection. Moreover, the method yields a posterior distribution that can be efficiently explored in polynomial time via a simple Gibbs sampling algorithm. We demonstrate the effectiveness of OLAP through applications to logistic and Poisson regression models, using both simulated and real data. } }
Endnote
%0 Conference Paper %T Laplace approximation for Bayesian variable selection via Le Cam’s one-step procedure %A Tianrui Hou %A Yves Atchade %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-hou26a %I PMLR %P 3772--3780 %U https://proceedings.mlr.press/v300/hou26a.html %V 300 %X Relevant feature selection in high-dimensional settings is a central challenge in modern scientific research and decision-making. While many existing methods offer strong statistical guarantees, they are often computationally intractable in high-dimensional problems. To address this issue, we introduce a novel Laplace approximation method based on Le Cam’s one-step procedure, termed \textsf{OLAP}. This approach is specifically designed to alleviate computational burdens while maintaining statistical rigor. Under standard high-dimensional assumptions, we establish that \textsf{OLAP} achieves consistent variable selection. Moreover, the method yields a posterior distribution that can be efficiently explored in polynomial time via a simple Gibbs sampling algorithm. We demonstrate the effectiveness of OLAP through applications to logistic and Poisson regression models, using both simulated and real data.
APA
Hou, T. & Atchade, Y.. (2026). Laplace approximation for Bayesian variable selection via Le Cam’s one-step procedure . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:3772-3780 Available from https://proceedings.mlr.press/v300/hou26a.html.

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