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Tricking the Hashing Trick: A Tight Lower Bound on the Robustness of CountSketch to Adaptive Inputs. (arXiv:2207.00956v2 [cs.DS] UPDATED)
Aug. 30, 2022, 1:11 a.m. | Edith Cohen, Jelani Nelson, Tamás Sarlós, Uri Stemmer
cs.LG updates on arXiv.org arxiv.org
CountSketch and Feature Hashing (the "hashing trick") are popular randomized
dimensionality reduction methods that support recovery of $\ell_2$-heavy
hitters (keys $i$ where $v_i^2 > \epsilon \|\boldsymbol{v}\|_2^2$) and
approximate inner products. When the inputs are {\em not adaptive} (do not
depend on prior outputs), classic estimators applied to a sketch of size
$O(\ell/\epsilon)$ are accurate for a number of queries that is exponential in
$\ell$. When inputs are adaptive, however, an adversarial input can be
constructed after $O(\ell)$ queries with the …
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