E-QRGMM: Efficient Generative Metamodeling for Covariate-Dependent Uncertainty Quantification
This provides a practical solution for high-stakes decision-making in fields requiring simulation-based inference, though it is incremental as it builds on prior QRGMM methods.
The paper tackled the challenge of covariate-dependent uncertainty quantification in simulation-based inference by proposing E-QRGMM, which accelerates quantile-regression-based generative metamodeling using cubic Hermite interpolation and gradient estimation, achieving a grid complexity reduction from O(n^{1/2}) to O(n^{1/5}) and superior trade-offs in accuracy and speed.
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.