Adaptive Bayesian Predictive Inference

Explore adaptive Bayesian predictive inference in this 50-minute colloquium talk by Veronika Rockovà, presented at the Colloque des sciences mathématiques du Québec (CSMQ). Delve into the examination of sparsity priors from a predictive inference perspective, focusing on estimating predictive distributions of high-dimensional Gaussian observations with known variance but unknown sparse mean under Kullback-Leibler loss. Discover why LASSO (Laplace) priors fail to achieve rate-optimal performance, and learn how Spike-and-Slab frameworks can attain rate-minimax performance with proper parameter tuning. Investigate the discrepancy between prior calibration for prediction and estimation purposes. Uncover groundbreaking findings on hierarchical Spike-and-Slab priors, which achieve adaptive rate-minimax performance for both estimation and predictive inference without prior knowledge of sparsity levels. Gain insights into the first rate-adaptive result in predictive density estimation for sparse setups, highlighting the benefits of fully Bayesian inference in mathematical sciences.