The generalization performance of kernel methods is largely determined by the
kernel, but common kernels are stationary thus input-independent and
output-independent, that limits their applications on complicated tasks. In
this paper, we propose a powerful and efficient spectral kernel learning
framework and learned kernels are dependent on both inputs and outputs, by
using non-stationary spectral kernels and flexibly learning the spectral
measure from the data. Further, we derive a data-dependent generalization error
bound based on Rademacher complexity, which estimates the generalization
ability of the learning framework and suggests two regularization terms to
improve performance. Extensive experimental results validate the effectiveness
of the proposed algorithm and confirm our theoretical results.

本文提出了一种基于非平稳谱核并能从数据中灵活学习谱度量的强大高效谱核学习框架，还导出了一个基于 Rademacher 复杂度的数据相关推广误差界，并提出两个正则化项以提高性能。实验结果表明该算法的有效性并验证了作者的理论结果。

自动化谱核学习

Automated Spectral Kernel Learning

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。