Neural Information Processing Systems http://nips.cc/

We thank all the reviewers for their supportive and insightful comments. The RMSEs for product SM kernels are shown below.

Neural Information Processing Systems http://nips.cc/

In machine learning, Kernel Ridge Regression (KRR) is central to modern time series analysis and nonparametric regression.

The paper proposes a spectral mixture of laplacian kernel with a levy process prior on the spectral components. This extends on the SM kernel by Wilson, which is a mixture of gaussians with no prior on spectral components. A RJ-MCMC is proposed that can model the number of components and represent the spectral posterior. A large-scale approximation is also implemented (SKI). The idea of Levy prior on the spectral components is very interesting one, but the paper doesn't make it clear what are the benefits with respect to kernel learning.

Automatic forecasting is the task of receiving a time series and returning a forecast for the next time steps without any human intervention. We propose an approach for automatic forecasting based on Gaussian Processes (GPs). So far, the main limits of GPs on this task have been the lack of a criterion for the selection of the kernel and the long times required for training different competing kernels. We design a fixed additive kernel, which contains the components needed to model most time series. During training the unnecessary components are made irrelevant by automatic relevance determination. We assign priors to each hyperparameter. We design the priors by analyzing a separate set of time series through a hierarchical GP. The resulting model performs very well on different types of time series, being competitive or outperforming the state-of-the-art approaches.Thanks to the priors, we reliably estimate the parameters with a single restart; this speedup makes the model efficient to train and suitable for processing a large number of time series.