More than ever before, we have access to massive datasets in almost every area of science and engineering. These datasets provide unprecedented opportunities to automatically discover rich statistical structure, from which we can derive new scientific discoveries.

Gaussian processes are rich distributions over functions, which can learn interpretable structure through covariance kernels. In this talk, I introduce a Gaussian process framework which is capable of learning expressive kernel functions on large datasets. I show how this framework can be extended to develop probabilistic deep learning models for characterizing uncertainty. I consider applications in epidemiology, change point modelling, counterfactuals, human learning, astronomy, inpainting. I will also present recent software packages implementing this work, and very recent results we have obtained for autonomous vehicles.