TY - JOUR
T1 - On the Robustness of CountSketch to Adaptive Inputs
AU - Cohen, Edith
AU - Lyu, Xin
AU - Nelson, Jelani
AU - Sarlós, Tamás
AU - Shechner, Moshe
AU - Stemmer, Uri
N1 - Publisher Copyright:
Copyright © 2022 by the author(s)
PY - 2022
Y1 - 2022
N2 - The last decade saw impressive progress towards understanding the performance of algorithms in adaptive settings, where subsequent inputs may depend on the output from prior inputs. Adaptive settings arise in processes with feedback or with adversarial attacks. Existing designs of robust algorithms are generic wrappers of non-robust counterparts and leave open the possibility of better tailored designs. The lowers bounds (attacks) are similarly worst-case and their significance to practical setting is unclear. Aiming to understand these questions, we study the robustness of CountSketch, a popular dimensionality reduction technique that maps vectors to a lower dimension using randomized linear measurements. The sketch supports recovering l2-heavy hitters of a vector (entries with (Eqaution presented)). We show that the classic estimator is not robust, and can be attacked with a number of queries of the order of the sketch size. We propose a robust estimator (for a slightly modified sketch) that allows for quadratic number of queries in the _sketch size, which is an improvement factor of √k (for k heavy hitters) over prior "blackbox" approaches.
AB - The last decade saw impressive progress towards understanding the performance of algorithms in adaptive settings, where subsequent inputs may depend on the output from prior inputs. Adaptive settings arise in processes with feedback or with adversarial attacks. Existing designs of robust algorithms are generic wrappers of non-robust counterparts and leave open the possibility of better tailored designs. The lowers bounds (attacks) are similarly worst-case and their significance to practical setting is unclear. Aiming to understand these questions, we study the robustness of CountSketch, a popular dimensionality reduction technique that maps vectors to a lower dimension using randomized linear measurements. The sketch supports recovering l2-heavy hitters of a vector (entries with (Eqaution presented)). We show that the classic estimator is not robust, and can be attacked with a number of queries of the order of the sketch size. We propose a robust estimator (for a slightly modified sketch) that allows for quadratic number of queries in the _sketch size, which is an improvement factor of √k (for k heavy hitters) over prior "blackbox" approaches.
UR - http://www.scopus.com/inward/record.url?scp=85163064158&partnerID=8YFLogxK
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AN - SCOPUS:85163064158
SN - 2640-3498
VL - 162
SP - 4112
EP - 4140
JO - Proceedings of Machine Learning Research
JF - Proceedings of Machine Learning Research
T2 - 39th International Conference on Machine Learning, ICML 2022
Y2 - 17 July 2022 through 23 July 2022
ER -