Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hida-Mat\'ern Kernel   We present the class of Hida-Mat\'ern kernels, which is the canonical family
of covariance functions over the entire space of stationary Gauss-Markov
Processes. It extends upon Mat\'ern 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.

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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th