We propose non-stationary spectral kernels for Gaussian process regression.
We propose to model the spectral density of a non-stationary kernel function as
a mixture of input-dependent Gaussian process frequency density surfaces. We
solve the generalised Fourier transform with such a model, and present a family
of non-stationary and non-monotonic kernels that can learn input-dependent and
potentially long-range, non-monotonic covariances between inputs. We derive
efficient inference using model whitening and marginalized posterior, and show
with case studies that these kernels are necessary when modelling even rather
simple time series, image or geospatial data with non-stationary
characteristics.

提出了用于高斯过程回归的非平稳谱核，其谱密度由输入依赖高斯过程频率密度表面的混合物建模，实现了能够学习输入依赖和潜在长程非单调协方差（inputs-dependent and potentially long-range, non-monotonic covariances）的一族非平稳和非单调核函数，并借助模型白化和边缘概率等方法推导出有效的推理方法，证明这些核函数在建模具有非平稳特征的时间序列、图像或地理空间数据时是必要的。