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

FOCS, pp. 184-195, 2020.

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Abstract:

Let $V$ be any vector space of multivariate degree-$d$ homogeneous polynomials with co-dimension at most $k$, and $S$ be the set of points where all polynomials in $V$ {\em nearly} vanish. We establish a qualitatively optimal upper bound on the size of $\epsilon$-covers for $S$, in the $\ell_2$-norm. Roughly speaking, we show that there...More

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