E-QRGMM: Efficient Generative Metamodeling for Covariate-Dependent Uncertainty Quantification

TL;DR

E-QRGMM is a new framework that enhances generative metamodeling for covariate-dependent uncertainty quantification by improving computational efficiency and accuracy, enabling practical confidence interval construction in simulation-based inference.

Contribution

It introduces a novel interpolation and gradient estimation technique that preserves convergence rates while reducing computational complexity in covariate-dependent uncertainty quantification.

Findings

E-QRGMM reduces grid complexity from $O(n^{1/2})$ to $O(n^{1/5})$ for most quantile levels.

E-QRGMM outperforms existing methods in accuracy and speed on synthetic and real datasets.

The framework enables bootstrap-based confidence interval construction for arbitrary estimands.

Abstract

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.