论文标题
关于Matérn协方差的自动差异化
On automatic differentiation for the Matérn covariance
论文作者
论文摘要
为了在可区分优化中引起挑战，我们分析并提出了Matérn内核衍生物相对于平滑度参数的策略。由于缺乏第二种修改后的贝塞尔功能相对于顺序，因此对高斯工艺建模引起了极大的兴趣。在当前的工作中，我们着重于新确定的串联扩展，用于对复杂订单有效的第二种贝塞尔功能。使用这些扩展，我们使用复杂的步骤方法获得了高度准确的结果。此外，我们表明使用推荐扩展的评估也比有限差异更有效。
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.
