提出高效生成元模型方法，实现条件不确定性量化加速与精度兼顾
E-QRGMM: Efficient Generative Metamodeling for Covariate-Dependent Uncertainty Quantification
- 用分段三次埃尔米特插值与梯度估计加速量化回归生成建模
- 计算复杂度从O(n^{1/2})降至O(n^{1/5})，保持收敛速度
- 适用于需要高精度条件置信区间的仿真推断场景
基于仿真的推断中，协变量依赖的不确定性量化对高风险决策至关重要，但现有方法如分布外预测和经典自助法在协变量特定条件上表现受限。本文提出高效分位数回归生成元模型（E-QRGMM），通过结合三次埃尔米特插值与梯度估计，加速分位数回归生成元模型（QRGMM）。理论上，E-QRGMM保持原方法的收敛速率，同时将多数分位数水平的网格复杂度从O(n^{1/2})降低至O(n^{1/5})，显著提升计算效率。实验表明，在合成数据和实际数据集上，E-QRGMM在分布准确性与训练速度间取得更优平衡，优于QRGMM及其它先进深度生成模型。此外，该方法支持任意估计量的自助法置信区间构建，为协变量依赖不确定性量化提供实用方案。
原文摘要 · Abstract (English)
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.
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