On Robust Mean Estimation under Coordinate-level Corruption
Zifan Liu, Jong Ho Park, Theodoros Rekatsinas, Christos Tzamos
Abstract
We study the problem of robust mean estimation and introduce a novel Hamming distance-based measure of distribution shift for coordinate-level corruptions. We show that this measure yields adversary models that capture more realistic corruptions than those used in prior works, and present an information-theoretic analysis of robust mean estimation in these settings. We show that for structured distributions, methods that leverage the structure yield information theoretically more accurate mean estimation. We also focus on practical algorithms for robust mean estimation and study when data cleaning-inspired approaches that first fix corruptions in the input data and then perform robust mean estimation can match the information theoretic bounds of our analysis. We finally demonstrate experimentally that this two-step approach outperforms structure-agnostic robust estimation and provides accurate mean estimation even for high-magnitude corruption.
BibTeX
@InProceedings{pmlr-v139-liu21r,
title = {On Robust Mean Estimation under Coordinate-level Corruption},
author = {Liu, Zifan and Park, Jong Ho and Rekatsinas, Theodoros and Tzamos, Christos},
booktitle = {Proceedings of the 38th International Conference on Machine Learning},
pages = {6914--6924},
year = {2021},
editor = {Meila, Marina and Zhang, Tong},
volume = {139},
series = {Proceedings of Machine Learning Research},
month = {18--24 Jul},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v139/liu21r/liu21r.pdf},
url = {https://proceedings.mlr.press/v139/liu21r.html},
abstract = {We study the problem of robust mean estimation and introduce a novel Hamming distance-based measure of distribution shift for coordinate-level corruptions. We show that this measure yields adversary models that capture more realistic corruptions than those used in prior works, and present an information-theoretic analysis of robust mean estimation in these settings. We show that for structured distributions, methods that leverage the structure yield information theoretically more accurate mean estimation. We also focus on practical algorithms for robust mean estimation and study when data cleaning-inspired approaches that first fix corruptions in the input data and then perform robust mean estimation can match the information theoretic bounds of our analysis. We finally demonstrate experimentally that this two-step approach outperforms structure-agnostic robust estimation and provides accurate mean estimation even for high-magnitude corruption.}
}