Séminaire de mathématiques appliquées

Many sources of our informational landscape can be formalized as a network of intertwined documents and authors. For a long time the textual content of documents and the structure that shows how documents and authors relate to each other have been considered separately. Recently document network embedding has been proposed to learn representations that take both content and structure into account. This space can then be used for downstreams tasks, such as classification or link prediction. In this talk I will give an overview of recent methods that aim at building such embedding spaces.

We consider best approximation problems in a nonlinear subset of a Banach space of functions. The norm is assumed to be a generalization of the L2-norm for which only a weighted Monte Carlo estimate can be computed. We establish error bounds for the empirical best approximation error in this general setting and use these bounds to derive a new, sample efficient algorithm for the model set of low-rank tensors. The viability of this algorithm is demonstrated by recovering quantities of interest for a classical random partial differential equation.

TBA