论文标题
黑盒模型置信集使用具有高维高斯比较的交叉验证
Black-Box Model Confidence Sets Using Cross-Validation with High-Dimensional Gaussian Comparison
论文作者
论文摘要
我们得出了标准$ V $折叠式验证风险估计的高维高斯比较结果。我们的结果结合了最近基于稳定性的基于稳定性的参数，该论点是交叉验证的低维中心限制定理，以及高维高斯比较框架的独立随机变量之和。这些结果为在模型比较和调谐参数选择的背景下，对跨验证风险的关节采样分布提供了新的见解，其中候选模型和调整参数的数量可能大于拟合样本量。结果，我们的结果为最新的方法论发展提供了理论支持，该方法学开发使用交叉验证构建模型置信度。
We derive high-dimensional Gaussian comparison results for the standard $V$-fold cross-validated risk estimates. Our results combine a recent stability-based argument for the low-dimensional central limit theorem of cross-validation with the high-dimensional Gaussian comparison framework for sums of independent random variables. These results give new insights into the joint sampling distribution of cross-validated risks in the context of model comparison and tuning parameter selection, where the number of candidate models and tuning parameters can be larger than the fitting sample size. As a consequence, our results provide theoretical support for a recent methodological development that constructs model confidence sets using cross-validation.
