连接外在与内在变量重要性
Bridging extrinsic and intrinsic variable importance
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中文总结 AI 辅助
本文建立了VIMP与MPLOCO的渐近等价条件，推广到一般损失函数并形式化分组MPLOCO，经模拟和HIV-1数据分析验证了二者的一致性，明确了内在与外在变量重要性的关系。
中文摘要 AI 辅助
变量重要性可描述总体中的内在预测信息，或拟合预测规则的外在重要性，量化变量重要性估计的不确定性对解释至关重要。估计内在变量重要性的方法（下称VIMP）与微样本留一协变量过程（MPLOCO）分别针对内在与外在重要性，且提供标准误计算方法。两种方法共享比较有无特征时预测性能的结构，但二者关系未被正式刻画。本文建立了两种视角一致的条件：在平方误差损失下，若拟合的全模型与简化模型学习器足够快地收敛到其 oracle 对应项，则MPLOCO与VIMP渐近等价；本文提供进一步条件将该结果推广到一般损失函数，并形式化了针对潜在重叠特征组的分组MPLOCO。通过模拟发现，当拟合学习器与数据生成机制匹配良好时，VIMP与MPLOCO一致性最高；在高维分组模拟中，两种方法均识别出含信号的组；在HIV-1 VRC01中和敏感性分析中，两种方法均将三个相同的生物学相关特征组列为最高排名。这些结果明确了内在与外在重要性何时可被类似解释，何时可提供互补信息。
英文摘要
Variable importance may describe either intrinsic predictive information in a population or extrinsic importance for a fitted prediction rule. Quantifying the uncertainty in variable importance estimates is critical for interpretation. Methods for estimating intrinsic variable importance (we will refer to these as VIMP) and the minipatch leave-one-covariate-out procedure (MPLOCO) target intrinsic and extrinsic importance, respectively, and provide methods for computing standard errors. These two approaches have a shared structure, comparing prediction performance with and without features, but the relationship between them has not been formally characterized. We establish conditions under which the two perspectives align. Under squared-error loss, if the fitted full and reduced learners converge to their oracle counterparts sufficiently fast, then MPLOCO is asymptotically equivalent to VIMP. We provide further conditions extending this result to general loss functions and formalize grouped MPLOCO for potentially overlapping feature groups. Through simulations, we show that VIMP and MPLOCO agree most closely when the fitted learner is well aligned with the data-generating mechanism. In a high-dimensional grouped simulation, both procedures identified the signal-containing groups. In an analysis of HIV-1 VRC01 neutralization sensitivity, both methods placed the same three biologically relevant feature groups among their highest-ranked groups. These results clarify when intrinsic and extrinsic importance can be interpreted similarly and when they provide complementary information.
