Small Covers for Near-Zero Sets of Polynomials and Learning Latent Variable Models

@article{Diakonikolas2020SmallCF,
  title={Small Covers for Near-Zero Sets of Polynomials and Learning Latent Variable Models},
  author={Ilias Diakonikolas and D. Kane},
  journal={2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS)},
  year={2020},
  pages={184-195}
}
  • Ilias Diakonikolas, D. Kane
  • Published 2020
  • Computer Science, Mathematics
  • 2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS)
  • Let <tex>$V$</tex> be any vector space of multivariate degree-<tex>$d$</tex> homogeneous polynomials with co-dimension at most <tex>$k$</tex>, and <tex>$S$</tex> be the set of points where all polynomials in <tex>$V$</tex> nearly vanish. We establish a qualitatively optimal upper bound on the size of <tex>$\epsilon$</tex>-covers for <tex>$S$</tex>, in the <tex>$\ell_{2}$</tex>-norm. Roughly speaking, we show that there exists an <tex>$\epsilon$</tex>-cover for <tex>$S$</tex> of cardinality <tex… CONTINUE READING

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