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arXiv · 1910.03305

Computational complexity of learning algebraic varieties

Oliver Gäfvert
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Abstract

We analyze the complexity of fitting a variety, coming from a class of varieties, to a configuration of points in $\Bbb C^n$. The complexity measure, called the algebraic complexity, computes the Euclidean Distance Degree (EDdegree) of a certain variety called the hypothesis variety as the number of points in the configuration increases. For the problem of fitting an $(n-1)$-sphere to a configuration of $m$ points in $\Bbb C^n$, we give a closed formula of the algebraic complexity of the hypothesis variety as $m$ grows for the case of $n=1$. For the case $n>1$ we conjecture a generalization of this formula supported by numerical experiments.

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Oliver Gäfvert. 2019-10-08. Computational complexity of learning algebraic varieties. https://doi.org/10.1016/j.aam.2020.102100

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