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Abstract:
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The use of Gaussian processes (GPs) in the emulation of complex computer simulations has seen wide application in the literature. As simulations have grown increasingly complex with more inputs, there is a need for better function estimation. In the context of computer simulations, it is often the case that the partial derivatives of a function can be obtained relatively cheaply. It is known that the use of partial derivative information can dramatically improve function estimation, especially in high dimensional settings. However, the use of partial derivative information comes at the cost of high numerical instability. This paper investigates an approach to mitigate this instability by exploiting the possibility that some partial derivatives may introduce enough error due to numerical instability to significantly degrade predictive accuracy. We utilize techniques from variable selection to select the partial derivatives which provide balance between numerical error and nominal error. Specifically, sparsity constraints are used to select partial derivatives. Experimental results indicate this procedure can dramatically reduce numerical error in interpolation.
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