发表机构
Islamic Azad University, Neyshabur Branch; University of Edinburgh（伊斯兰阿扎大学内沙布尔分校; 爱丁堡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对自适应重要性采样，提出有效提议数量（ENP）指标，可检测标准有效样本量遗漏的提议崩溃与重复，还可用于提议更新的反馈。
AI 中文摘要
基于种群的自适应重要性采样（AIS）方法使用一组提议密度来近似复杂的目标分布，其性能通常通过有效样本量（ESS）及相关基于权重的诊断指标评估，这些指标衡量归一化重要性权重的集中度。然而，大的ESS仅表明归一化样本权重未高度集中，并未描述提议组件在采样空间中的排列方式。在基于种群的AIS中，多个提议组件可能在目标的同一区域生成样本，因此即使不同提议组件的有效数量很小，样本权重也可能表现得平衡良好。本文提出有效提议数量（ENP），这是一种针对基于种群AIS的、感知相似度的提议级诊断指标，ENP将分配给每个提议的总归一化权重与从目标加权样本间相似度计算得到的冗余度度量相结合，估计对近似有贡献的非冗余经验提议的数量。我们确立了其基本有效数量属性，证明ENP可检测标准ESS遗漏的提议崩溃和重复问题，还可将其用作提议更新的针对性反馈信号。
英文摘要
Population-based adaptive importance sampling (AIS) methods use a set of proposal densities to approximate complex target distributions. Their performance is commonly assessed through effective sample size (ESS) and related weight-based diagnostics, which measure the concentration of normalized importance weights. However, a large ESS only indicates that the normalized sample weights are not strongly concentrated; it does not describe how the proposal components are arranged in the sampling space. In population-based AIS, several proposal components may generate samples in the same region of the target, so the sample weights can appear well balanced even though the effective number of distinct proposal components is small. This letter introduces the effective number of proposals (ENP), a similarity-aware proposal-level diagnostic for population-based AIS. ENP combines the total normalized weight assigned to each proposal with a redundancy measure computed from similarities among target-weighted samples, estimating the number of non-redundant empirical proposal contributions to the approximation. We establish basic effective-number properties and show that ENP detects proposal collapse and duplication missed by standard ESS. We also illustrate its use as a targeted feedback signal for proposal rejuvenation.
