在部分可识别性下,新方法通过控制误排除率选择实验,提升结构分辨力。
Resolution-Aware Experimental Design under Partial Identifiability
- 基于最小化非空结构候选集设计实验,控制误排除风险。
- 在两个地下水流基准测试中,与传统方法产生显著实验选择差异。
- 适用于需高精度分辨结构、容忍小误排除的物理系统实验设计。
实验设计通常以选择最具信息量的实验为目标。但在部分可识别性下,持续存在的干扰不确定性可能导致相同观测具有不同结构含义。本文提出分辨率感知实验设计(RAED),通过最小化受误排除控制的预期非空结构候选集来选择实验。我们证明了跨干扰混淆分离的精确性:一个实验可能在结构信息增益、完整隐变量信息增益、平均分类性能和干扰边际信息性上优于其他,却具有任意差的可靠结构分辨力。尽管如此,RAED在真实复合黑威尔比较下保持期望排序。为使该准则可操作,我们开发了基于学习的评分实现,包含有限样本干扰平均与正尾校准,并刻画了一种罕见尾部样本复杂度障碍。在受限传感条件下,两个地下水流基准测试中出现真正的RAED与期望信息增益(EIG)实验选择分歧,其中WCA表现出最显著且最大的保留分辨率差异。在河流沉积基准中,尾部保护改变了所选物理实验,将硬区域误排除主要替换为显式模糊性。在机制性甲烷氧化基准中,预先设定的5%误排除容忍度也带来了对尾部敏感干扰风险的非平凡有限样本总体保证,所有三个结构族联合置信度达95%。
原文摘要 · Abstract (English)
Experimental design is commonly framed as choosing the experiment expected to provide the most information. Under partial identifiability however, persistent nuisance uncertainty can make the same observation carry different structural meanings. We introduce Resolution-Aware Experimental Design (RAED), which selects an experiment by the smallest expected nonempty structural candidate set achievable subject to false-exclusion control. We prove an exact cross-nuisance aliasing separation: an experiment can be preferred by structural and full-latent information gain, average classification, and nuisance-marginalized informativeness while having arbitrarily poorer valid structural resolution. RAED nevertheless preserves the expected ordering under a genuine composite Blackwell comparison. To make this criterion operational, we develop a learned score-based implementation with finite-sample nuisance-average and positive-tail calibration, and characterize a rare-tail sample-complexity obstruction. Under constrained sensing, two subsurface-flow benchmarks exhibit genuine RAED--expected-information-gain (EIG) experiment-selection disagreements, with the clearest and largest held-out resolution differences in WCA. In a fluvial benchmark, tail protection changes the selected physical experiment and replaces hard-region false exclusions primarily with explicit ambiguity. In a mechanistic methane-oxidation benchmark, a prospectively specified 5\% false-exclusion tolerance also yields a nontrivial finite-sample population guarantee for tail-sensitive nuisance risk, with 95\% joint confidence across all three structural families.
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