An efficient sampling algorithm with adaptations for Bayesian variable selection.

Area of Science:

• Statistics
• Computational Statistics
• Machine Learning

Background:

• Indicator Model Selection (IMS) is a key technique in Bayesian variable selection, utilizing pseudo-priors.
• Existing IMS methods like Gibbs Variable Selection (GVS) and Kuo-Mallick (KM) can suffer from slow mixing due to fixed parameter choices.
• The efficiency of IMS methods is sensitive to the parameters of proposal distributions and pseudo-priors.

Purpose of the Study:

• To develop a novel adaptive algorithm for IMS that dynamically adjusts parameters during analysis.
• To enhance the mixing efficiency and overall performance of Bayesian variable selection algorithms.
• To provide theoretical guarantees for the proposed adaptive IMS algorithm.

Main Methods:

• An adaptive algorithm is proposed that adjusts IMS parameters on-the-fly.
• The algorithm's convergence is theoretically proven.
• Experimental evaluations compare the adaptive algorithm against conventional IMS methods.

Main Results:

• The adaptive algorithm successfully improves the mixing of IMS methods.
• Parameters obtained "on the fly" lead to more appropriate proposal distributions and pseudo-priors.
• Experimental results demonstrate superior efficiency compared to existing GVS and KM methods.

Conclusions:

• The proposed adaptive algorithm offers a significant improvement for Bayesian variable selection using IMS.
• Dynamic parameter adaptation is crucial for efficient sampling in IMS.
• This work provides a more robust and efficient tool for variable selection in complex models.