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

Locally induced Gaussian processes for large-scale simulation experiments