LADE Seminar
Jean Barbier (ICTP)
Title: Fundamental limits in structured principal component analysis and how to reach them
Abstract
How does structure and statistical dependencies in the noise impact inference? This talk will answer this question in the context of the estimation of low-rank matrices corrupted by structured noise, namely noise matrices with generic spectrum, and thus dependencies among its entries. We show that the Approximate Message Passing (AMP) algorithm currently proposed in the literature for Bayesian estimation is sub-optimal. We explain the reason for this sub-optimality and as a consequence we deduce an optimal Bayesian AMP algorithm with a rigorous state evolution matching our prediction for the minimum mean-square error. Based on a joint work with Francesco Camilli, Marco Mondelli and Manuel Saenz: https://www.pnas.org/doi/abs/10.1073/pnas.2302028120?doi=10.1073/pnas.2302028120
Area Science Park - RIT
Research Institute
The Institute of Research and Innovation Technology (RIT) at Area Science Park carries out cutting-edge research and provides services and consulting to public and private-sector users through its three laboratories equipped with state-of-the-art technology.