AI 中文总结
针对似然评估成本高、预算有限的场景，提出基于采样的自适应主动学习（SALE）的高斯过程框架，通过序贯设计准则分配评估，在多类基准和实例中降低总变差误差，表现优于多个基线。
AI 中文摘要
当似然评估成本高昂且预算有限时，贝叶斯推断会面临困难。我们提出采样自适应主动学习（SALE），这是一种用于代理贝叶斯推断的高斯过程（GP）框架。SALE利用归一化GP样本路径诱导的期望后验（EP）作为通用序贯设计准则：它定义了后验引导的搜索区域并对不确定性减少（UR）进行加权。一种状态依赖规则在用于定位的贝叶斯优化（BO）和用于校准的UR之间分配评估。对于BO，退火目标在EP和汤普森采样之间插值，同时正则化查询律以应对代理路径扰动。对于UR，我们引入了理想的EP加权规则和计算可行的代理。在贝叶斯GP框架下，我们通过扰动和贝叶斯后悔界刻画了退火目标的稳定性-偏差权衡，推导了理想EP加权UR的显式依赖预算的总变差期望控制，并为所实现的代理建立了总变差期望速率。在分析基准和模拟似然上，SALE在所有考虑的设置中降低了总变差误差，同时避免了多个外部基线下出现的严重失败。计量经济学和天体物理学实例证明了其实用价值。
英文摘要
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.
Comments74 pages, 11 figures, 1 table; comments are welcome
