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Title: Joint estimation of multiple penalized graphs using zoom-in/out penalties to map functional brain connectivity Authors:  Eugen Pircalabelu - Université catholique de Louvain (Belgium) [presenting]
Gerda Claeskens - KU Leuven (Belgium)
Lourens Waldorp - University of Amsterdam (Netherlands)
Abstract: A new method is proposed to simultaneously estimate graphical models from data obtained at $K$ different coarseness scales. Starting from a predefined scale $k^{*}\leq K$, the method offers the possibility to zoom in or out over scales on particular edges. The estimated graphs over the different scales have similar structures, although their sparsity level depends on the scale at which estimation takes place. The graphs are jointly estimated at all coarseness scales and the method makes it possible to evaluate the evolution of the graphs from the coarsest to the finest scale or vice-versa. The method is motivated by fMRI datasets that do not all contain measurements on the same set of brain regions. For certain datasets, some of the regions have been split in smaller subregions and the purpose is to estimate sparse graphical models. We accomplish this by pooling information from all subjects in order to estimate a common undirected and directed graph at each coarseness scale, accounting for time dependencies and multiple coarseness scales and by jointly estimating the graphs at all coarseness scales. Empirical and theoretical evaluations illustrate the usefulness of the method and show the method's performance in practice.