Majorization-minimization from a hierarchical Bayesian perspective

A while ago, I got involved in an interesting collaboration with Alexandre Gramfort, Joseph Salmon & Yousra Bekhti from the Télécom ParisTech. We drew a connection between majorization-minimization methods for sparse non-convex regression and a particular kind of hierarchical Bayesian modeling. Furthermore, we demonstrate how it can be used to quantify the inherent uncertainty and ambiguity of ill-posed regression problems such as EEG/MEG source reconstruction. The paper can be found on arXiv, big thanks to all the co-authors! [Update: It has been published in Inverse Problems.]