Most low-rank tensor approximations are NP-hard problems. In this paper, we introduce a
novel concept: field-of-experts (FoE) filters guided tensor completion, which aims to integrate …

The geometry of the set of restrictions of rank-one tensors to some of their coordinates is
studied. This gives insight into the problem of rank-one completion of partial tensors …

Completion problems, of recovering points from a set of observed coordinates, are abundant
in applications to image reconstruction, phylogenetics, and data science. We consider a …

Algebraic matroids are combinatorial objects defined by the set of coordinates of an
algebraic variety. These objects are of interest whenever coordinates hold significance: for …

Completion problems, of recovering a point from a set of observed coordinates, are
abundant in applications to image reconstruction, phylogenetics, and data science. We …

In this thesis we apply techniques from algebraic geometry to problems arising from
optimization and statistics. In particular, we consider data that takes the form of a matrix, a …

The set of matrices of given positive semidefinite rank is semialgebraic. In this paper we
study the geometry of this set, and in small cases we describe its boundary. For general …