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Quantum Entropy Scoring for Fast Robust Mean Estimation and Improved Outlier Detection
Yihe Dong · Sam Hopkins · Jerry Li

Tue Dec 10 10:45 AM -- 12:45 PM (PST) @ East Exhibition Hall B + C #228
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 $\mu$ of a distribution on $\mathbb{R}^d$ given $n$ independent samples, an $\epsilon$-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 $\tilde{O}(nd)$ in all parameters, improving on the previous fastest running time $\tilde{O}(\min(nd/\e^6, nd^2))$. 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.

Author Information

Yihe Dong (Microsoft)

Machine learning researcher and engineer interested in geometric deep learning, graph representation learning, and natural language processing.

Sam Hopkins (UC Berkeley)
Jerry Li (Microsoft)

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