{"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/positive-definite-estimation-of-large","title":"Positive Definite Estimation of Large Covariance Matrix Using Generalized Nonconvex Penalties","arxiv_id":"1604.04348","date":"2016-04-15","proceeding":null,"authors":["Fei Wen","Yuan Yang","Peilin Liu","Robert C. Qiu"],"abstract":"This work addresses the issue of large covariance matrix estimation in\nhigh-dimensional statistical analysis. Recently, improved iterative algorithms\nwith positive-definite guarantee have been developed. However, these algorithms\ncannot be directly extended to use a nonconvex penalty for sparsity inducing.\nGenerally, a nonconvex penalty has the capability of ameliorating the bias\nproblem of the popular convex lasso penalty, and thus is more advantageous. In\nthis work, we propose a class of positive-definite covariance estimators using\ngeneralized nonconvex penalties. We develop a first-order algorithm based on\nthe alternating direction method framework to solve the nonconvex optimization\nproblem efficiently. The convergence of this algorithm has been proved.\nFurther, the statistical properties of the new estimators have been analyzed\nfor generalized nonconvex penalties. Moreover, extension of this algorithm to\ncovariance estimation from sketched measurements has been considered. The\nperformances of the new estimators have been demonstrated by both a simulation\nstudy and a gene clustering example for tumor tissues. Code for the proposed\nestimators is available at https://github.com/FWen/Nonconvex-PDLCE.git.","url_abs":"http://arxiv.org/abs/1604.04348v3","url_pdf":"http://arxiv.org/pdf/1604.04348v3.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":"positive-definite-estimation-of-large","repo_url":"https://github.com/FWen/Nonconvex-PDLCE","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}