Gaussian processes are rich distributions over functions, with generalization
properties determined by a kernel function. When used for long-range
extrapolation, predictions are particularly sensitive to the choice of kernel
parameters. It is therefore critical to account for kernel uncertainty in our
predictive distributions. We propose a distribution over kernels formed by
modelling a spectral mixture density with a L\'evy process. The resulting
distribution has support for all stationary covariances--including the popular
RBF, periodic, and Mat\'ern kernels--combined with inductive biases which
enable automatic and data efficient learning, long-range extrapolation, and
state of the art predictive performance. The proposed model also presents an
approach to spectral regularization, as the L\'evy process introduces a
sparsity-inducing prior over mixture components, allowing automatic selection
over model order and pruning of extraneous components. We exploit the algebraic
structure of the proposed process for $\mathcal{O}(n)$ training and
$\mathcal{O}(1)$ predictions. We perform extrapolations having reasonable
uncertainty estimates on several benchmarks, show that the proposed model can
recover flexible ground truth covariances and that it is robust to errors in
initialization.

提出一种基于 Levy 过程建模频谱混合密度的内核概率模型，能够自动选择模型阶数、剪枝多余组件、对具备良好不确定性估计的验证数据做长程外推，特别适用于有长程关联的数据集。