Drawing meaningful conclusions on the way complex real life phenomena work and being able to predict the behavior of systems of interest require developing accurate and highly interpretable mathematical models whose parameters need to be estimated from observations. In modern applications, however, we are often challenged with the lack of such models, and even when these are available they are too computational demanding to be suitable for standard parameter optimization/inference methods.
This tutorial will introduce probabilistic models based on Gaussian processes as attractive tools to tackle these challenges in a principled way and to allow for a sound quantification of uncertainty. The tutorial will formally define Gaussian processes starting from the formulation of Bayesian linear models with infinite basis functions, and draw connections with non-probabilistic kernel machines and deep neural networks.
Carrying out inference for Gaussian processes poses huge computational challenges that arguably hinder their wide adoption. In recent years, however, have been a considerable amount of novel contributions that are allowing Gaussian processes to be applied to problems at an unprecedented scale and to new areas where uncertainty quantification is of fundamental importance. This tutorial will expose attendees to such recent advances, trends and challenges in Gaussian process modeling and inference, and stimulate the debate about the role of Gaussian process models in solving complex modern machine-learning tasks where deep neural networks are currently the preferred choice.

Generative models of images have made an extraordinary amount of progress over the past five years, moving from vaguely plausible images of handwritten digit to nearly-photorealistic pictures of imaginary people. This tutorial will cover the key line of work, generative adversarial networks and their variants. We will discuss the original algorithm, theoretical issues with its foundations, and various approaches to resolving them, including the Wasserstein GAN and recent kernel-based improvements.