72 citations · 250 across the 57 of their papers we have counts for
6 papers · 1 filter
Universality theorems for inscribed polytopes and Delaunay triangulations
Karim A. Adiprasito, Arnau Padrol, Louis Theran
We prove that every primary basic semialgebraic set is homotopy equivalent to the set of inscribed realizations (up to Möbius transformation) of a polytope. If the semialgebraic se…
Algebraic-Combinatorial Methods for Low-Rank Matrix Completion with Application to Athletic Performance Prediction
Duncan A. J. Blythe, Louis Theran, Franz Kiraly
This paper presents novel algorithms which exploit the intrinsic algebraic and combinatorial structure of the matrix completion task for estimating missing en- tries in the general…
Learning with Cross-Kernels and Ideal PCA
Franz J Király, Martin Kreuzer, Louis Theran
We describe how cross-kernel matrices, that is, kernel matrices between the data and a custom chosen set of `feature spanning points' can be used for learning. The main potential o…
Ultrarigid periodic frameworks
Justin Malestein, Louis Theran
We give an algebraic characterization of when a -dimensional periodic framework has no non-trivial, symmetry preserving, motion for any choice of periodicity lattice. Our condit…
Matroid Regression
Franz J Király, Louis Theran
We propose an algebraic combinatorial method for solving large sparse linear systems of equations locally - that is, a method which can compute single evaluations of the signal wit…
Dual-to-kernel learning with ideals
Franz J. Király, Martin Kreuzer, Louis Theran
In this paper, we propose a theory which unifies kernel learning and symbolic algebraic methods. We show that both worlds are inherently dual to each other, and we use this duality…