Asymptotic Consistency of Loss-Calibrated Variational Bayes
This work provides theoretical guarantees for variational methods in Bayesian statistics, which is incremental but important for practitioners relying on approximate computations.
The paper proves that loss-calibrated variational Bayes (LCVB) and naive variational Bayesian methods are asymptotically consistent for approximate posteriors and decision rules, addressing the problem of ensuring reliability in Bayesian inference and data-driven decision-making.
This paper establishes the asymptotic consistency of the {\it loss-calibrated variational Bayes} (LCVB) method. LCVB was proposed in~\cite{LaSiGh2011} as a method for approximately computing Bayesian posteriors in a `loss aware' manner. This methodology is also highly relevant in general data-driven decision-making contexts. Here, we not only establish the asymptotic consistency of the calibrated approximate posterior, but also the asymptotic consistency of decision rules. We also establish the asymptotic consistency of decision rules obtained from a `naive' variational Bayesian procedure.