{"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/on-the-spectrum-of-random-features-maps-of","title":"On the Spectrum of Random Features Maps of High Dimensional Data","arxiv_id":"1805.11916","date":"2018-05-30","proceeding":"ICML 2018 7","authors":["Zhenyu Liao","Romain Couillet"],"abstract":"Random feature maps are ubiquitous in modern statistical machine learning,\nwhere they generalize random projections by means of powerful, yet often\ndifficult to analyze nonlinear operators. In this paper, we leverage the\n\"concentration\" phenomenon induced by random matrix theory to perform a\nspectral analysis on the Gram matrix of these random feature maps, here for\nGaussian mixture models of simultaneously large dimension and size. Our results\nare instrumental to a deeper understanding on the interplay of the nonlinearity\nand the statistics of the data, thereby allowing for a better tuning of random\nfeature-based techniques.","url_abs":"http://arxiv.org/abs/1805.11916v2","url_pdf":"http://arxiv.org/pdf/1805.11916v2.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":"on-the-spectrum-of-random-features-maps-of","repo_url":"https://github.com/Zhenyu-LIAO/RMT4RFM","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"machine-learning","task_name":"BIG-bench Machine Learning"},{"task_slug":"high","task_name":"Vocal Bursts Intensity Prediction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1805.11916","atlas_url":"https://app.syntology.ai/?focus=1805.11916","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}