Abstract: Machine learning algorithms learn models that automatically infer data representations and generalise into new data. Gaussian processes are Bayesian kernel-based models with a key advantage of being able to efficiently learn kernel functions from data. All kernel functions can be decomposed into sinusoidal components, which provide a highly expressive basis for learning arbitrary representations. In this talk I will discuss how we can exploit spectral kernel learning for large-scale multi-task learning. We also generalise spectral learning into learning non-stationary kernels with input-specific behavior