Séminaire IMAGE : Quentin Bertrand (MILA), « Hyperparameter selection for high dimensional sparse learning: application to neuro-imaging »

Speaker:

Quentin Bertrand (https://qb3.github.io/)

Abstract:
Due to non-invasiveness and excellent time resolution, magneto- and electroencephalography (M/EEG) have emerged as tools of choice to monitor brain activity. Reconstructing brain signals from M/EEG measurements is a high dimensional ill-posed inverse problem. Typical estimators of brain signals involve challenging optimization problems, composed of the sum of a data-fidelity term, and a sparsity promoting term. Because of their notoriously hard to tune regularization hyperparameters, sparsity-based estimators are currently not massively used by neuroscientists.

During this talk I will talk about two aspects of the brain source reconstruction problem:
– State of the art solvers for the source localization problem include coordinate descent, which is notoriously hard to accelerate in practice. I will introduce an effective way to speed it up in theory and practice.
– Then I will focus on the hyperparameter selection and investigate hyperparameter optimization. It requires tackling bilevel optimization with nonsmooth inner problems. Such problems are canonically solved using zeros order techniques, such as grid-search or random-search. I will present a more efficient technique to solve these challenging bilevel optimization problems using first-order methods.