发表机构
Université du Québec à Trois-Rivières; Département de mathématiques et d’informatique（魁北克三河市大学; 数学与计算机科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对组污染结构化结果的因果推断，提出可观测商、无损约化与精确随机化推断方法，在RxRx1等实验中验证了商检验的低I类错误率与高功效。
AI 中文摘要
诸如显微镜图像之类的结构化潜在结果，可能在经过未知的、单元特定的变换后被记录下来。如果该变换可依赖于处理、协变量或内在结果，那么原始坐标分析可能会将生物学效应与采集几何结构相混合。我们研究无约束观测模型 X = Γ·Y(A)，并刻画其可观测信息：当目标在群轨道上恒定时，该目标可被均匀精确恢复；而Borel极大不变量则保留所有可测量的不变目标。随后，我们区分可观测性与统计无损性。商忠实重构定理表明，当给定处理、协变量和商的原始观测的条件分布具有无参数版本时，商约化足以实现完整的变换实验。紧群上的条件Haar污染是Blackwell等价的特例；在主模型中并未施加该条件。我们还区分独立的位点特定乘积作用与共享对角作用，并说明逐分量规范化为何会丢弃相对跨位点信息。在明确的度量与核正则性条件下，近似污染定理对商律Wasserstein误差及总体最大均值差异的诱导扰动进行了界定。对于有限支撑多通道晶格图像，我们在整数平移和四分之一旋转下构造了极大不变量，将其特征高斯核与完整配对交换检验相结合，并保留了原始模拟及RxRx1 HUVEC研究。在尖锐原假设下，商检验在0.052的模拟重复中被拒绝；在单元效应强度下，其功效为0.992。主要RxRx1对比的枚举配对交换检验p值为0.0078。
英文摘要
Structured potential outcomes such as microscopy images may be recorded after an unknown, unit-specific transformation. If that transformation can depend on treatment, covariates or the intrinsic outcome, raw-coordinate analyses may mix biological effects with acquisition geometry. We study the unrestricted observation model X = Γ . Y(A) and characterize its observable information: a target is uniformly recoverable exactly when it is constant on group orbits, while a Borel maximal invariant retains every measurable invariant target. We then distinguish observability from statistical losslessness. A quotient-faithful reconstruction theorem shows that quotient reduction is sufficient for the full transformed experiment exactly when the conditional law of the raw observation given treatment, covariates and the quotient has a parameter-free version. Conditional Haar contamination on a compact group yields Blackwell equivalence as a special case; it is not imposed in the main model. We also separate independent site-specific product actions from shared diagonal actions and show why componentwise canonicalization can discard relative cross-site information. Under explicit metric and kernel regularity, an approximate-contamination theorem bounds quotient-law Wasserstein error and the induced perturbation of population maximum mean discrepancy. For finite-support multichannel lattice images, we construct a maximal invariant under integer translations and quarter turns, combine its characteristic Gaussian kernel with a complete paired-swap test, and retain the original simulations and RxRx1 HUVEC study. Under the sharp null, the quotient test rejected in 0.052 of simulation replicates; at unit effect strength its power was 0.992. The primary RxRx1 contrast had an enumerated paired-swap p-value of 0.0078.
