This thesis concerns the theory of positive-definite completions and its mutually beneficial connections to the statistics of function-valued or continuously-indexed random processes, better known as functional data analysis. In particular, it dwells upon ...
In tensor completion, the goal is to fill in missing entries of a partially known tensor under a low-rank constraint. We propose a new algorithm that performs Riemannian optimization techniques on the manifold of tensors of fixed multilinear rank. More spe ...
Image recovery in optical interferometry is an ill-posed nonlinear inverse problem arising from incomplete power spectrum and bi-spectrum measurements. We formulate a linear version of the problem for the order-3 tensor formed by the tensor product of the ...
Most learning methods with rank or sparsity constraints use convex relaxations, which lead to optimization with the nuclear norm or the`1-norm. However, several important learning applications cannot benet from this approach as they feature these convex no ...
A simple characterisation of topological amenability in terms of bounded cohomology is proved, following Johnson's formulation of amenability. The connection to injective Banach modules is established. ...
