arXiv subjects

Deyu Ming

Publications and source records attributed to Deyu Ming.

6 recordsLinked to original sources

arXiv2026

Generalized and Scalable Deep Gaussian Process Emulation

Gaussian process (GP) emulators have become essential tools for approximating complex simulators, significantly reducing computational demands in optimization, sensitivity analysis, and model calibration. While traditional GP emulators effectively model continuous and Gaussian-distributed simulator outputs with homogeneous variability, they typically struggle with discrete, heteroskedastic Gaussian, or non-Gaussian data, limiting their applicability to increasingly common stochastic simulators. In this work, we introduce a scalable Generalized Deep Gaussian Process (GDGP) emulation framework designed to accommodate simulators with heteroskedastic Gaussian outputs and a wide range of non-Gaussian response distributions, including Poisson, negative binomial, and categorical distributions. The GDGP framework leverages the expressiveness of DGPs and extends them to latent GP structures, enabling it to capture the complex, non-stationary behavior inherent in many simulators while also modeling non-Gaussian simulator outputs. We make GDGP scalable by incorporating the Vecchia approximation for settings with a large number of input locations, while also developing efficient inference procedures for handling large numbers of replicates. In particular, we present methodological developments that further enhance the computation of the approach for heteroskedastic Gaussian responses. We demonstrate through a series of synthetic and empirical examples that these extensions deliver the practical application of GDGP emulators and a unified methodology capable of addressing diverse modeling challenges. The proposed GDGP framework is implemented in the open-source R package dgpsi.

stat.CO↗

arXiv2025

Integrative Analysis and Imputation of Multiple Data Streams via Deep Gaussian Processes

Healthcare data, particularly in critical care settings, presents three key challenges for analysis. First, physiological measurements come from different sources but are inherently related. Yet, traditional methods often treat each measurement type independently, losing valuable information about their relationships. Second, clinical measurements are collected at irregular intervals, and these sampling times can carry clinical meaning. Finally, the prevalence of missing values. Whilst several imputation methods exist to tackle this common problem, they often fail to address the temporal nature of the data or provide estimates of uncertainty in their predictions. We propose using deep Gaussian process emulation with stochastic imputation, a methodology initially conceived to deal with computationally expensive models and uncertainty quantification, to solve the problem of handling missing values that naturally occur in critical care data. This method leverages longitudinal and cross-sectional information and provides uncertainty estimation for the imputed values. Our evaluation of a clinical dataset shows that the proposed method performs better than conventional methods, such as multiple imputations with chained equations (MICE), last-known value imputation, and individually fitted Gaussian Processes (GPs).

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arXiv2025

Deep Gaussian Process Emulation with gradient Information and Sequential Design for Simulators with Sharp Variations

Deep Gaussian Processes (DGPs) compose GP layers to warp inputs, enabling improved emulation of computer models with nonstationary input-output behavior compared with ordinary GPs. In contrast to GPs, the predictive uncertainty for DGP gradients remains relatively underexplored. Quantifying DGP gradient uncertainty can support gradient-based tasks in complex, nonstationary settings where ordinary GPs may struggle. While GP gradient posteriors are analytically tractable, extending such constructions to DGPs is challenging due to their hierarchical composition. In this paper, we propose an efficient approximation to the gradient distribution of a two-layer DGP emulator. Using the chain rule with local linearization, we derive closed-form expressions for the gradient mean and covariance, enabling fast gradient evaluation with uncertainty quantification (UQ). Empirically, our approach delivers promising performance while uniquely providing UQ of gradients. We then use the gradient uncertainties to guide sequential design for models with sharp variations: we define sharp variation regions as those where the gradient norm exceeds a threshold. We subsequently introduce an entropy-based acquisition rule that selects new samples in locations where the classification of points as inside versus outside the sharp-variation region is most uncertain. Experiments on synthetic benchmarks and a real-world application show that the resulting sequential design more accurately emulates functions with sharp variations than existing design methods.

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arXiv2023

Linked Deep Gaussian Process Emulation for Model Networks

Modern scientific problems are often multi-disciplinary and require integration of computer models from different disciplines, each with distinct functional complexities, programming environments, and computation times. Linked Gaussian process (LGP) emulation tackles this challenge through a divide-and-conquer strategy that integrates Gaussian process emulators of the individual computer models in a network. However, the required stationarity of the component Gaussian process emulators within the LGP framework limits its applicability in many real-world applications. In this work, we conceptualize a network of computer models as a deep Gaussian process with partial exposure of its hidden layers. We develop a method for inference for these partially exposed deep networks that retains a key strength of the LGP framework, whereby each model can be emulated separately using a DGP and then linked together. We show in both synthetic and empirical examples that our linked deep Gaussian process emulators exhibit significantly better predictive performance than standard LGP emulators in terms of accuracy and uncertainty quantification. They also outperform single DGPs fitted to the network as a whole because they are able to integrate information from the partially exposed hidden layers. Our methods are implemented in an R package $\texttt{dgpsi}$ that is freely available on CRAN.

stat.ML↗

arXiv2022

Deep Gaussian Process Emulation using Stochastic Imputation

Deep Gaussian processes (DGPs) provide a rich class of models that can better represent functions with varying regimes or sharp changes, compared to conventional GPs. In this work, we propose a novel inference method for DGPs for computer model emulation. By stochastically imputing the latent layers, our approach transforms a DGP into a linked GP: a novel emulator developed for systems of linked computer models. This transformation permits an efficient DGP training procedure that only involves optimizations of conventional GPs. In addition, predictions from DGP emulators can be made in a fast and analytically tractable manner by naturally utilizing the closed form predictive means and variances of linked GP emulators. We demonstrate the method in a series of synthetic examples and empirical applications, and show that it is a competitive candidate for DGP surrogate inference, combining efficiency that is comparable to doubly stochastic variational inference and uncertainty quantification that is comparable to the fully-Bayesian approach. A $\texttt{Python}$ package $\texttt{dgpsi}$ implementing the method is also produced and available at https://github.com/mingdeyu/DGP.

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arXiv2021

Linked Gaussian Process Emulation for Systems of Computer Models using Matérn Kernels and Adaptive Design

The state-of-the-art linked Gaussian process offers a way to build analytical emulators for systems of computer models. We generalize the closed form expressions for the linked Gaussian process under the squared exponential kernel to a class of Matérn kernels, that are essential in advanced applications. An iterative procedure to construct linked Gaussian processes as surrogate models for any feed-forward systems of computer models is presented and illustrated on a feed-back coupled satellite system. We also introduce an adaptive design algorithm that could increase the approximation accuracy of linked Gaussian process surrogates with reduced computational costs on running expensive computer systems, by allocating runs and refining emulators of individual sub-models based on their heterogeneous functional complexity.

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