On automatic differentiation for the Matérn covariance

01/01/2022

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by   Oana Marin, et al.

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To target challenges in differentiable optimization we analyze and propose strategies for derivatives of the Matérn kernel with respect to the smoothness parameter. This problem is of high interest in Gaussian processes modelling due to the lack of robust derivatives of the modified Bessel function of second kind with respect to order. In the current work we focus on newly identified series expansions for the modified Bessel function of second kind valid for complex orders. Using these expansions we obtain highly accurate results using the complex step method. Furthermore, we show that the evaluations using the recommended expansions are also more efficient than finite differences.