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

**Authors:** Tianrui Hou, Liwei Wang, Yves Atchadé  
**arXiv:** [2407.20580](https://arxiv.org/abs/2407.20580)  
**Date:** 2024-07-30  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2407.20580v1/

## Key points

- Authors address the challenge of variable selection in high-dimensional spaces
- Existing approaches struggle with computational demands in high dimensionality
- Proposed novel Laplace approximation method, Le Cam's one-step procedure (OLAP), to manage computational burden effectively
- OLAP is statistically consistent under classical high-dimensional assumptions
- Posterior distribution generated by OLAP can be explored in polynomial time using Gibbs sampling algorithm
- Authors contribute to mixing time analysis of Markov chains, enhancing understanding of computational complexities in statistical inference
- Application of OLAP to logistic and Poisson regression models with simulated and real data examples demonstrates efficient and accurate variable selection in complex high-dimensional datasets

## Summary

In their paper titled "Laplace approximation for Bayesian variable selection via Le Cam's one-step procedure," authors Tianrui Hou, Liwei Wang, and Yves Atchadé address the challenge of variable selection in high-dimensional spaces. This is a common issue in contemporary scientific research and decision-making processes. Existing approaches with strong statistical guarantees often struggle to handle the computational demands associated with high dimensionality. To overcome this limitation, the authors propose a novel Laplace approximation method known as Le Cam's one-step procedure (OLAP), specifically designed to effectively manage the computational burden. Through their research, the authors demonstrate that OLAP serves as a statistically consistent variable selection procedure under certain classical high-dimensional assumptions. Moreover, they establish that this approach generates a posterior distribution that can be explored in polynomial time using a straightforward Gibbs sampling algorithm. In addition to these findings, the authors make significant contributions to the mixing time analysis of Markov chains, enhancing our understanding of computational complexities in statistical inference. To illustrate the effectiveness of their proposed method, the authors apply it to logistic and Poisson regression models using both simulated and real data examples. By doing so, they showcase how OLAP can facilitate efficient and accurate variable selection in complex high-dimensional datasets. Overall, this study provides valuable insights into addressing the challenges of variable selection in modern scientific exploration through innovative computational techniques and rigorous statistical analysis.