Covariate-dependent uncertainty quantification in simulation-based inference is crucial for high-stakes decision-making but remains challenging due to the limitations of existing methods such as conformal prediction and classical bootstrap, which struggle with covariate-specific conditioning. We propose Efficient Quantile-Regression-Based Generative Metamodeling (E-QRGMM), a novel framework that accelerates the quantile-regression-based generative metamodeling (QRGMM) approach by integrating cubic Hermite interpolation with gradient estimation. Theoretically, we show that E-QRGMM preserves the convergence rate of the original QRGMM while reducing grid complexity from $O(n^{1/2})$ to $O(n^{1/5})$ for the majority of quantile levels, thereby substantially improving computational efficiency. Empirically, E-QRGMM achieves a superior trade-off between distributional accuracy and training speed compared to both QRGMM and other advanced deep generative models on synthetic and practical datasets. Moreover, by enabling bootstrap-based construction of confidence intervals for arbitrary estimands of interest, E-QRGMM provides a practical solution for covariate-dependent uncertainty quantification.

翻译：基于仿真的推理中，协变量依赖的不确定性量化对于高风险决策至关重要，但由于现有方法（如保形预测和经典自助法）在处理协变量特定条件时存在局限，该问题仍具挑战。我们提出高效分位数回归生成式元建模（E-QRGMM），该新颖框架通过将三次埃尔米特插值与梯度估计相结合，加速了基于分位数回归的生成式元建模（QRGMM）方法。理论上，我们证明E-QRGMM保持了原始QRGMM的收敛速率，同时将大多数分位数水平下的网格复杂度从$O(n^{1/2})$降低至$O(n^{1/5})$，从而显著提升了计算效率。实证上，在合成与实际数据集上，相较于QRGMM及其他先进深度生成模型，E-QRGMM在分布准确性与训练速度之间实现了更优的权衡。此外，通过支持基于自助法构建任意目标估计量的置信区间，E-QRGMM为协变量依赖的不确定性量化提供了一种实用解决方案。