Free Lunches and Subsampling Monte Carlo in Bayesian Computation

Learn about the challenges and limitations of MCMC algorithms for large datasets in this mathematics research seminar. Explore why subsampling approaches, while successful for optimization problems in machine learning, face fundamental limitations for Bayesian computation. Examine a "no-free-lunch" theorem that demonstrates the inherent constraints of subsampling methods, understand its proof mechanics, and discover how these results apply to real statistical problems. Investigate special cases that can circumvent these limitations, including extensions to non-reversible chains and complex posteriors. Based on collaborative research with multiple contributors, this technical presentation delves into the theoretical foundations and practical implications of subsampling Monte Carlo methods for computationally expensive posterior distributions.