{"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/robust-estimation-and-generative-adversarial","title":"Robust Estimation and Generative Adversarial Nets","arxiv_id":"1810.02030","date":"2018-10-04","proceeding":null,"authors":["Chao Gao","jiyi LIU","Yuan YAO","Weizhi Zhu"],"abstract":"Robust estimation under Huber's $\\epsilon$-contamination model has become an\nimportant topic in statistics and theoretical computer science. Statistically\noptimal procedures such as Tukey's median and other estimators based on depth\nfunctions are impractical because of their computational intractability. In\nthis paper, we establish an intriguing connection between $f$-GANs and various\ndepth functions through the lens of $f$-Learning. Similar to the derivation of\n$f$-GANs, we show that these depth functions that lead to statistically optimal\nrobust estimators can all be viewed as variational lower bounds of the total\nvariation distance in the framework of $f$-Learning. This connection opens the\ndoor of computing robust estimators using tools developed for training GANs. In\nparticular, we show in both theory and experiments that some appropriate\nstructures of discriminator networks with hidden layers in GANs lead to\nstatistically optimal robust location estimators for both Gaussian distribution\nand general elliptical distributions where first moment may not exist.","url_abs":"http://arxiv.org/abs/1810.02030v3","url_pdf":"http://arxiv.org/pdf/1810.02030v3.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":"robust-estimation-and-generative-adversarial","repo_url":"https://github.com/yao-lab/Robust-GAN-Center","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"robust-estimation-and-generative-adversarial","repo_url":"https://github.com/zhuwzh/Robust-GAN-Center","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1810.02030","atlas_url":"https://app.syntology.ai/?focus=1810.02030","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}