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Abstract:
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Gaussian processes (GPs) provide a flexible methodology for modeling complex surfaces. A challenge with GPs is the computational burden with an increasing sample size or number of dimensions. The machine learning community has turned to pseudo-inputs, or inducing points, to obtain an approximation which reduces the computational burden. However, we show the placement of inducing points and their multitude remains an open question, especially in large-scale dynamic response surface modeling tasks. We seek to address this challenge by porting the inducing point idea, which is usually applied globally, over to a more local context in order to obtain accurate and tractable GP approximations for large scale surrogate modeling applications. In this way, our proposed methodology hybridizes inducing point and local approximation approaches for spatial and surrogate modeling applications. Strategies for optimizing the locations of and number of local inducing points are provided, and comparisons are drawn to related methodology. Examples are provided for epidemiological, industrial, and financial applications.
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