A1354
Title: Scalable Bayesian variable selection without MCMC
Authors: Argyro Damoulaki - Athens University Economic Business (Greece) [presenting]
Ioannis Ntzoufras - AUEB (Greece)
Abstract: Bayesian model evaluation and variable selection pose significant challenges in high-dimensional settings, where the number of candidate models grows exponentially with the number of covariates $p$. Standard approaches rely on Bayes factors to compute posterior model and inclusion probabilities, requiring the evaluation of up to $2^p$ marginal likelihoods. In practice, this is typically addressed via searching the model space using MCMC methods, which can become computationally prohibitive and difficult to scale. A scalable alternative to Bayesian variable selection is proposed that avoids computationally intensive sampling techniques. The approach is based on an efficient screening procedure that reduces the model space by exploiting sharp lower and upper bounds on posterior inclusion probabilities. The method is implemented under the usual g-prior setup, but it may be extended for any case where the marginal likelihood is available (by asymptotic or exact methods). Under this setup, the proposed method enables fast identification of promising variables while discarding irrelevant ones early in the process. The resulting procedure is computationally efficient and well-suited for high-dimensional problems, while remaining robust in challenging scenarios such as strong collinearity among predictors. This makes it a practical tool for scalable Bayesian inference in modern data settings.
