部分可识别性下的分辨率感知实验设计

中文摘要 AI 辅助

实验设计通常被定义为选择有望提供最多信息的实验。然而在部分可识别性下，持续存在的干扰不确定性会使得同一观测结果具有不同的结构含义。我们提出了分辨率感知实验设计（Resolution-Aware Experimental Design, RAED），该方法在假排除控制的约束下，通过最小化可实现的非空结构候选集的期望来选择实验。我们证明了一种精确的跨干扰混叠分离：一个实验可同时被结构信息增益、全潜变量信息增益、平均分类性能以及干扰边缘化信息增益所偏好，但其有效结构分辨率却可能任意差。不过，RAED在真正的复合布莱克韦尔比较下仍能保持期望的排序。为使该准则可操作，我们开发了一种基于学习的评分实现，具有有限样本干扰平均和正尾校准，并刻画了一种稀有的尾样本复杂度阻碍。在受限感知下，两个地下流基准显示出RAED与期望信息增益（Expected Information Gain, EIG）的实验选择分歧，其中WCA的保留分辨率差异最明显且最大。在一个河流基准中，尾保护改变了所选物理实验，并主要用显式模糊取代了硬区域假排除。在一个机制性甲烷氧化基准中，预先指定的5%假排除容忍度还为尾敏感干扰风险提供了非平凡的有限样本总体保证，在所有三个结构族上具有95%的联合置信度。

英文摘要

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.

发表机构

• National Technical University of Athens（雅典国立技术大学）

机构由 AI 辅助整理，请以论文原文为准。