Mini-Workshop: Stochastic Processes and Probabilistic Models in Machine Learning

The study of complex phenomena through the analysis of data often requires us to make assumptions about the underlying dynamics. In modern applications, for many systems of interest we are facing the challenge of doing so when very little is known about their mechanistic description. Even when a mechanistic description is available, simulating such systems is so computationally expensive that we cannot use it effectively. While probabilistic models based on Gaussian Processes (GPs) offer attractive tools to tackle these challenges in a principled way and to allow for a sound quantification of uncertainty, carrying out inference for these models poses huge computational challenges that arguably hinder their wide adoption. Recent contributions, however, make it possible to massively improve scalability of GPs and to exploit parallel and distributed computing, so that GPs are now in the position to compete with Deep Neural Networks on various problems where the latter are usually the preferred choice. This lecture aims to expose students to the fundamentals of modern GP research. In particular, the lecture will touch upon these points: (i) the basics of GPs; (ii) the challenges in employing GPs for large scale learning problems; (iii) recent advances in GP research to allow for scalable and accurate quantification of uncertainty; (iv) interesting applications of GPs; (v) current and future directions.