Local Gaussian Process Approximation for Large Computer Experiments

By Robert B. Gramacy, Daniel W. Apley. 2013

433 citations recorded by the source corpus.

We provide a new approach to approximate emulation of large computer experiments. By focusing expressly on desirable properties of the predictive equations, we derive a family of local sequential design schemes that dynamically define the support of a Gaussian process predictor based on a local subset of the data. We further derive expressions for fast sequential updating of all needed quantities as the local designs are built up iteratively. Then we show how independent application of our local design strategy across the elements of a vast predictive grid facilitates a trivially parallel implementation. The end result is a global predictor able to take advantage of modern multicore architectures, providing a nonstationary modeling feature as a bonus. We demonstrate our method on two examples using designs with thousands of data points, and compare to the method of compactly supported covariances. Supplementary materials for this article are available online.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/f4c742a689d6c89df80b9012246bca89b7700583

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Citations in the corpus

Globally Approximate Gaussian Processes for Big Data With Application to Data-Driven Metamaterials Design (2019, methodology): “Locally approximate Gaussian process (LAGP) [28] is perhaps the most widely recognized local method where the subsets are selected either based on their proximity to the query point or to minimize the predictive variance.”
A tutorial on Gaussian process regression: Modelling, exploring, and exploiting functions (2016, background): “For pure exploration, another commonly used acquisition function attempts to minimize the expected variance over the whole input space (Gramacy and Apley, 2014).”
Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets (2014, background): “and replacing the larger conditioning sets on the right hand side of (1) with smaller, carefully chosen, conditioning sets of size at most m, where m k (see, e.g., Vecchia 1988; Stein et al. 2004; Gramacy and Apley 2014; Gramacy et al. 2014).”
When Gaussian Process Meets Big Data: A Review of Scalable GPs (2018, methodology): “Hence, some GP-based active learning methods have been employed to sequentially update the neighborhood set [20], [32], [115], [116].”
A General Framework for Vecchia Approximations of Gaussian Processes (2017, background): “For a given ordering and m , the most common strategy is to simply condition on the m nearest neighbors or locations (NN conditioning), although more elaborate conditioning schemes have been proposed (e.g., Stein et al., 2004; Gramacy and Apley, 2015).”