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

• URL: http://arxiv.org/abs/2601.19256v1
• Date: Tue, 27 Jan 2026 06:39:24 GMT
• Title: E-QRGMM: Efficient Generative Metamodeling for Covariate-Dependent Uncertainty Quantification
• Authors: Zhiyang Liang, Qingkai Zhang,
• Abstract summary: Efficient Quantile-Regression-Based Generative Metamodeling (E-QRGMM) is a novel framework that accelerates the quantile-regression-based generative metamodeling (QRGMM)<n>We show that E-QRGMM preserves the convergence rate of the original QRGMM while reducing grid complexity from $O(n1/2)$ to $O(n1/5)$ for the majority of quantile levels.<n>E-QRGMM achieves a superior trade-off between distributional accuracy and training speed compared to both QRGMM and other advanced deep generative
• Score: 0.5371337604556311
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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.

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