179 citations · 420 across the 27 of their papers we have counts for
6 papers · 1 filter
Learning with Algebraic Invariances, and the Invariant Kernel Trick
Franz J. Király, Andreas Ziehe, Klaus-Robert Müller
When solving data analysis problems it is important to integrate prior knowledge and/or structural invariances. This paper contributes by a novel framework for incorporating algebr…
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…
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…
The Algebraic Approach to Phase Retrieval and Explicit Inversion at the Identifiability Threshold
Franz J Király, Martin Ehler
We study phase retrieval from magnitude measurements of an unknown signal as an algebraic estimation problem. Indeed, phase retrieval from rank-one and more general linear measurem…
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…