🤖 AI Summary
This work addresses the challenge of performing efficient and accurate Bayesian inference when likelihood evaluations are computationally expensive and budgets are limited. The authors propose the Sampling-adaptive Active Learning (SALE) framework, which employs a Gaussian process surrogate model and introduces expected posterior as a unified acquisition criterion to dynamically allocate evaluation resources between Bayesian optimization and uncertainty reduction. SALE integrates a state-dependent sampling strategy, an annealed objective function to balance bias and stability, and a tractable rule for quantifying uncertainty reduction. Experimental results demonstrate that SALE significantly reduces total variation error across multiple benchmark and synthetic tasks, avoids failure modes observed in existing methods, and exhibits strong empirical performance in real-world applications from econometrics and astrophysics.
📝 Abstract
Bayesian inference is difficult when likelihood evaluations are expensive and budgets are limited. We propose sampling-based adaptive active learning (SALE), a Gaussian-process (GP) framework for surrogate-based Bayesian inference. SALE uses the expected posterior (EP) induced by normalised GP sample paths as a common sequential-design measure: it defines a posterior-guided search region and weights uncertainty reduction (UR). A state-dependent rule allocates evaluations between Bayesian optimisation (BO) for localisation and UR for calibration. For BO, an annealed objective interpolates between the EP and Thompson sampling while regularising the query law against surrogate-path perturbations. For UR, we introduce an ideal EP-weighted rule and a computationally feasible proxy. Under a Bayesian GP framework, we characterise the annealed objective's stability--bias trade-off through perturbation and Bayesian regret bounds, derive explicit budget-dependent expected total-variation control for the ideal EP-weighted UR, and establish an expected total-variation rate for the implemented proxy. Across analytic benchmarks and simulated likelihoods, SALE reduces total-variation error across all considered settings while avoiding severe failures seen under several external baselines. Econometric and astrophysical examples demonstrate its practical value.