论文标题
高斯过程回归的周期性zeta协方差函数
The periodic zeta covariance function for Gaussian process regression
论文作者
论文摘要
我认为Lerch-Hurwitz或周期性的Zeta功能是周期性连续时间固定随机过程的协方差函数。该函数可以使用连续索引$ν$进行参数化，该函数可以以类似于Matérn类的协方差函数的参数$ν$的方式来调节该过程的连续性和不同性属性。这使周期性Zeta成为高斯过程回归的Matérn的幂律频谱季节性成分的好伴侣。它也是圆形Matérn协方差的近亲，同样可以在三个尺寸的球上使用。由于标准库中通常无法使用此特殊功能，因此我详细说明了数值实现。
I consider the Lerch-Hurwitz or periodic zeta function as covariance function of a periodic continuous-time stationary stochastic process. The function can be parametrized with a continuous index $ν$ which regulates the continuity and differentiability properties of the process in a way completely analogous to the parameter $ν$ of the Matérn class of covariance functions. This makes the periodic zeta a good companion to add a power-law prior spectrum seasonal component to a Matérn prior for Gaussian process regression. It is also a close relative of the circular Matérn covariance, and likewise can be used on spheres up to dimension three. Since this special function is not generally available in standard libraries, I explain in detail the numerical implementation.
