Abstract

Gaussian processes (GPs) are Bayesian nonparametric generative models for time series and are particularly well suited for continuous-time nonlinear regression tasks. The talk will start with a brief introduction to GPs so as to illustrate their advantages and challenges as well as to motivate their use in a variety of tasks involving missing or irregularly-sampled data. We will then interpret the GP model from a (Fourier) spectral analysis perspective and motivate the construction of covariance functions based on the GPs frequency representation; we will also show how GPs can be used for Spectral Estimation. Then, we will present recent advances using optimal transport (a distance between probability distributions) to define a distance between GPs and explore alternative, cost-efficient, training strategies for GP. Throughout the talk, we will show illustrative and real world examples.

Bio: Felipe is an Associate Professor at the Initiative for Data and Artificial Intelligence, Universidad de Chile, and the Director of the Initiative for Data and Artificial Intelligence at the same institution. He holds Researcher positions at the Center for Mathematical Modeling and the Advanced Center for Electrical and Electronic Engineering. Prior to joining Universidad de Chile, Felipe was a postdoc at the Machine Learning Group, University of Cambridge, during 2015 and he received a PhD in Signal Processing from Imperial College London in 2014. Felipe’s research interests lie in the interface between Machine Learning and Statistical Signal Processing, including approximate inference, Bayesian nonparametrics, spectral estimation, optimal transport and Gaussian processes.