Papers › Quantum Entropy Scoring for Fast Robust Mean Estimation and Improved Outlier Detection

Quantum Entropy Scoring for Fast Robust Mean Estimation and Improved Outlier Detection

26 Jun 2019NeurIPS 2019 12arXiv:1906.11366archive 2025-07-28

Yihe Dong, Samuel B. Hopkins, Jerry Li

We study two problems in high-dimensional robust statistics: \emph{robust mean estimation} and \emph{outlier detection}. In robust mean estimation the goal is to estimate the mean μ of a distribution on ℝᵈ given n independent samples, an ε-fraction of which have been corrupted by a malicious adversary. In outlier detection the goal is to assign an \emph{outlier score} to each element of a data set such that elements more likely to be outliers are assigned higher scores. Our algorithms for both problems are based on a new outlier scoring method we call QUE-scoring based on \emph{quantum entropy regularization}. For robust mean estimation, this yields the first algorithm with optimal error rates and nearly-linear running time O(nd) in all parameters, improving on the previous fastest running time O(min(nd/ε⁶, nd²)). For outlier detection, we evaluate the performance of QUE-scoring via extensive experiments on synthetic and real data, and demonstrate that it often performs better than previously proposed algorithms. Code for these experiments is available at https://github.com/twistedcubic/que-outlier-detection .

Code

Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.

Code Syntology ran Syntology

Not run by Syntology. Nothing on this page verifies that the listed code works.

Tasks

Results from the paper archive 2025-07-28

No leaderboard rows for this paper in the archive.

Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections