Ομιλία του κ. Omiros Papaspiliopoulos (ICREA research professor, based at UPF) , στο Σεμινάριο του Τομέα Μαθηματικών της ΣΕΜΦΕ, την Τετάρτη 17 Μαΐου στις 12:30, στην Αίθουσα Σεμιναρίων του τομέα Μαθηματικών (2ος όροφος, κτίριο Ε).
Title: Markov chain Monte Carlo sampling for machine learning and inverse problems.
Abstract: I will give a synthetic overview of the challenges, objectives and the state-of-the-art for prediction and uncertainty quantification using Markov chain Monte Carlo in Bayesian inverse problems and in machine learning. I will first show how some standard problems in inverse problems and machine learning can be formulated as problems of simulating from high (or even infinite) dimensional change of Gaussian measure. I will then show how Monte Carlo simulation algorithms can be constructed by discretising the Langevin stochastic differential equation and highlight the two most popular algorithms, the so-called preconditioned Metropolis-adjsuted Langevin algorithm (pMALA) and the preconditioned Crank-Nicolson Langevin (pcNL) algorithm. I will then refer to some recent work jointly with Michalis Titsias (Computer Science, AUEB) that has produced algorithms that achieve enormous efficiency gains relative to the state-of-the-art and demonstrate their success in high-dimensional regression and classification problems