提出新指标ENP，解决重要性采样中提案冗余问题
Beyond Effective Sample Size: Effective Number of Proposals for Adaptive Importance Sampling
- 用相似性感知的冗余度衡量提案分布，改进传统评估方式
- ENP能发现ESS忽略的提案重复与退化现象
- 适合需要优化采样效率的贝叶斯推断与强化学习场景
基于种群的自适应重要性采样（AIS）方法使用一组提案密度来逼近复杂目标分布。其性能通常通过有效样本量（ESS）及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程度。然而，高ESS仅说明归一化权重不高度集中，并不能反映提案组件在采样空间中的分布情况。在基于种群的AIS中，多个提案可能在目标分布的同一区域生成样本，导致样本权重看似平衡，但实际有效提案数量却很少。本文提出有效提案数（ENP），一种面向提案级别的相似性感知诊断指标。ENP结合每个提案的总归一化权重与目标加权样本间的相似性计算出的冗余度，估计对近似结果有非冗余贡献的经验提案数量。我们建立了基本的有效数性质，并证明ENP可检测标准ESS遗漏的提案崩溃与重复问题。同时，我们展示了其作为提案再生的定向反馈信号的应用。
原文摘要 · Abstract (English)
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.
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