{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/quantum-entropy-scoring-for-fast-robust-mean","title":"Quantum Entropy Scoring for Fast Robust Mean Estimation and Improved Outlier Detection","arxiv_id":"1906.11366","date":"2019-06-26","proceeding":"NeurIPS 2019 12","authors":["Yihe Dong","Samuel B. Hopkins","Jerry Li"],"abstract":"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 $\\varepsilon$-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 $\\widetilde{O}(nd)$ in all parameters, improving on the previous fastest running time $\\widetilde{O}(\\min(nd/\\varepsilon^6, nd^2))$. 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. Code for these experiments is available at https://github.com/twistedcubic/que-outlier-detection .","url_abs":"https://arxiv.org/abs/1906.11366v1","url_pdf":"https://arxiv.org/pdf/1906.11366v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"quantum-entropy-scoring-for-fast-robust-mean","repo_url":"https://github.com/twistedcubic/que-outlier-detection","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"outlier-detection","task_name":"Outlier Detection"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1906.11366","atlas_url":"https://app.syntology.ai/?focus=1906.11366","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}