Hida-Matérn核
Hida-Matérn Kernel
摘要：
我们提出了一类Hida-Matérn核，这是在整个平稳Gauss-Markov过程空间上的协方差函数的规范族。它扩展到Matérn内核，允许灵活的建设先验过程中的振荡组件。任何平稳内核，包括广泛使用的平方指数和频谱混合内核，要么直接在这一类或适当的渐近极限，证明了这类的一般性。利用它的马尔可夫性质，我们展示了如何表示这样的过程，状态空间模型只使用内核及其衍生物。反过来，这使我们能够更有效地执行高斯过程推理，并避免通常的计算负担。我们还展示了如何利用状态空间表示的特殊性质，除了进一步降低计算复杂性，还可以提高数值稳定性。
英文摘要：
We present the class of Hida-Matérn kernels, which is the canonical family of covariance functions over the entire space of stationary Gauss-Markov Processes. It extends upon Matérn kernels, by allowing for flexible construction of priors over processes with oscillatory components. Any stationary kernel, including the widely used squared-exponential and spectral mixture kernels, are either directly within this class or are appropriate asymptotic limits, demonstrating the generality of this class. Taking advantage of its Markovian nature we show how to represent such processes as state space models using only the kernel and its derivatives. In turn this allows us to perform Gaussian Process inference more efficiently and side step the usual computational burdens. We also show how exploiting special properties of the state space representation enables improved numerical stability in addition to further reductions of computational complexity.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
