Dr Franz Király
Dr Franz Király

Interests: Compressed Sensing, Discrete Inverse Problems, Algebraic and Combinatorial Methods in Statistics, Time Series and Stationarity, Algebraic Combinatorics and Algebraic Statistics
Personal Webpage at UCL 
Dr Franz Király
Research Topics
My primary interests lie in analyzing data with intrinsic algebraic and combinatorial structure, and developing statistical methods which can find such structure, or make practical use of it. Please have a look on my personal webpage for an overview on my general research interests.
A focus topic of my recent research have been discrete inverse problems. One popular example is the inverse problem of lowrank matrix completion, where a subset of entries of a matrix of low rank is observed, and the task is to reconstruct the original matrix. The problem has algebraic features through lowrank, and combinatorial features through the positions of the observations, and is therefore naturally treated with algebraic combinatorial methods, yielding a detailed analysis of identifiability [arXiv 1211.4116], and methods for actual reconstructions of single entries [arXiv 1302.5337]. A related problem, is combinatorial rigidity, where the positions of objects are to be determined from distance measurements.
Discrete inverse problems of similar flavour also arise when studying optimization problems with algebraic features [arXiv 1108.1483], or compressed sensing from the perspective of discretized representations [arXiv 1302.2767], allowing to construct explicit estimators for nonconvex problems, and problemindependent bounds on the sampling density.
Closely related are source separation and source identification methods which can exploit algebraic structure of the problem, such as tensorial [arXiv 1211.7369], or higher order cumulants [arXiv 1110.4531].
My future research will revolve around the study of inverse problems from the discretized perspective  which is the perspective natural to any digital representation and thus to any practical algorithm  and from the perspective of algebraical and combinatorial structure.