arXiv subjects

Annie Sauer

Publications and source records attributed to Annie Sauer.

3 recordsLinked to original sources

arXiv2022

Vecchia-approximated Deep Gaussian Processes for Computer Experiments

Deep Gaussian processes (DGPs) upgrade ordinary GPs through functional composition, in which intermediate GP layers warp the original inputs, providing flexibility to model non-stationary dynamics. Two DGP regimes have emerged in recent literature. A "big data" regime, prevalent in machine learning, favors approximate, optimization-based inference for fast, high-fidelity prediction. A "small data" regime, preferred for computer surrogate modeling, deploys posterior integration for enhanced uncertainty quantification (UQ). We aim to bridge this gap by expanding the capabilities of Bayesian DGP posterior inference through the incorporation of the Vecchia approximation, allowing linear computational scaling without compromising accuracy or UQ. We are motivated by surrogate modeling of simulation campaigns with upwards of 100,000 runs - a size too large for previous fully-Bayesian implementations - and demonstrate prediction and UQ superior to that of "big data" competitors. All methods are implemented in the "deepgp" package on CRAN.

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arXiv2022

Triangulation candidates for Bayesian optimization

Bayesian optimization involves "inner optimization" over a new-data acquisition criterion which is non-convex/highly multi-modal, may be non-differentiable, or may otherwise thwart local numerical optimizers. In such cases it is common to replace continuous search with a discrete one over random candidates. Here we propose using candidates based on a Delaunay triangulation of the existing input design. We detail the construction of these "tricands" and demonstrate empirically how they outperform both numerically optimized acquisitions and random candidate-based alternatives, and are well-suited for hybrid schemes, on benchmark synthetic and real simulation experiments.

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arXiv2021

Active Learning for Deep Gaussian Process Surrogates

Deep Gaussian processes (DGPs) are increasingly popular as predictive models in machine learning (ML) for their non-stationary flexibility and ability to cope with abrupt regime changes in training data. Here we explore DGPs as surrogates for computer simulation experiments whose response surfaces exhibit similar characteristics. In particular, we transport a DGP's automatic warping of the input space and full uncertainty quantification (UQ), via a novel elliptical slice sampling (ESS) Bayesian posterior inferential scheme, through to active learning (AL) strategies that distribute runs non-uniformly in the input space -- something an ordinary (stationary) GP could not do. Building up the design sequentially in this way allows smaller training sets, limiting both expensive evaluation of the simulator code and mitigating cubic costs of DGP inference. When training data sizes are kept small through careful acquisition, and with parsimonious layout of latent layers, the framework can be both effective and computationally tractable. Our methods are illustrated on simulation data and two real computer experiments of varying input dimensionality. We provide an open source implementation in the "deepgp" package on CRAN.

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