AIDRC Seminar Series - Emilio Porcu

Title:

Kernel Methods in Probabilistic Learning: Stein Discrepancies on Manifolds)

Abstract:

Reproducing Kernel Hilbert Space methods have become ubiquitous in both statistical learning and machine learning communities. My talk illustrates Stein methods within the planet of Quantisation, being the act of approximating a given probability distribution (think of a picture on the unit square) with a linear combination of Dirac delta functions (a coarse version of the picture). We provide a comparison with quasi Monte Carlo and with MCMC methods in terms of statistical accuracy. The latter being measured in terms of upper bounds for the average worst case error. We also inspect computational scalability of the proposed methods.

We then expose Stein methods on Riemannian manifolds, and we provide a relevant bridge between Stein methods and kernel discrepancies on Sobolev spaces. The impact of these findings on machine learning are then illustrated.

Based on joint works with Mark Girolami, Chris Oates, Alessandro Barpp, and Simon Hubbert

Bio:

Emilio Porcu got his PhD in statistics in 2005. He became a Full professor in 2012, and Chair Professor at Newcastle University and then Trinity College. He is Professor of Statistics at Khalifa University since August 2020.

Emilio's main research interests lie within (a) Statistical Learning, (b) Data Science, and (c) Spatial Statistics. Within Statistical Learning, he has been primarily interested in the foundational aspects of kernel probabilistic methods and kernel discrepancies. Further, he did recent work on kernels on metric graps as well as on product spaces involving graphs.

Emilio has several awards from international societies and universities. He is elected fellow of the International Statistical Institute, as well as Stuart Hunter prize from the Envirometrics society to cite a few.