Locally induced Gaussian processes for large-scale simulation experiments

TL;DR

This paper introduces a local inducing point approach for Gaussian processes, improving scalability and accuracy in large-scale simulation experiments by combining global and local approximation strategies.

Contribution

It proposes a hybrid local-global inducing point method for Gaussian processes, addressing pathologies and computational challenges in large-scale dynamic surface modeling.

Findings

Enhanced accuracy and efficiency over traditional global inducing points

Effective in large-scale satellite drag interpolation tasks

Outperforms existing methods in benchmark tests

Abstract

Gaussian processes (GPs) serve as flexible surrogates for complex surfaces, but buckle under the cubic cost of matrix decompositions with big training data sizes. Geospatial and machine learning communities suggest pseudo-inputs, or inducing points, as one strategy to obtain an approximation easing that computational burden. However, we show how placement of inducing points and their multitude can be thwarted by pathologies, especially in large-scale dynamic response surface modeling tasks. As remedy, we suggest porting the inducing point idea, which is usually applied globally, over to a more local context where selection is both easier and faster. In this way, our proposed methodology hybridizes global inducing point and data subset-based local GP approximation. A cascade of strategies for planning the selection of local inducing points is provided, and comparisons are drawn to related methodology with emphasis on computer surrogate modeling applications. We show that local inducing points extend their global and data-subset component parts on the accuracy--computational efficiency frontier. Illustrative examples are provided on benchmark data and a large-scale real-simulation satellite drag interpolation problem.