Linear Combinations of Kernels

[willtebbutt]

There are a variety of interesting optimisations that can be performed on kernels of the form

k(x, z) = w_1 * k_1(x, z) + w_2 * k_2(x, z) + ... + w_L k_L(x, z)

A naive recursive implementation in terms of the current Sum and Scaled kernels hides opportunities for parallelism in the computation of each term, and the summation over terms.

Notable examples of kernels with this form include:

• The stationary spectral mixture kernel [1]
• Non-stationary spectral mixture kernels and generalisations of [1]: [2] [3]

[1] - Wilson, Andrew, and Ryan Adams. "Gaussian process kernels for pattern discovery and extrapolation." International Conference on Machine Learning. 2013.
[2] - Remes, Sami, Markus Heinonen, and Samuel Kaski. "Non-stationary spectral kernels." Advances in Neural Information Processing Systems. 2017
[3] - Samo, Yves-Laurent Kom, and Stephen Roberts. "Generalized spectral kernels." arXiv preprint arXiv:1506.02236 (2015).