Learning Guarantees for Approximate Vanishing Ideal Computations

  • Elias Wirth (TU Berlin)
E1 05 (Leibniz-Saal)


The approximate vanishing ideal of a set of points $X\subseteq \R^n$ is the set of polynomials that approximately evaluate to $0$ over all points $\textbf{x} \in X$ and admits an efficient representation by a finite set of polynomials called generators. The constructed generators capture polynomial structures in data and give rise to a feature map that can, for example, be used in combination with a linear classifier for supervised learning. Generator-constructing algorithms are widely studied, but their computational complexities remain expensive and the methods lack learning guarantees. We introduce a generator-constructing algorithm that admits several learning guarantees and whose computational complexity is linear in the number of samples.

Mirke Olschewski

MPI for Mathematics in the Sciences Contact via Mail

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