{"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/uniform-inference-in-high-dimensional","title":"Uniform Inference in High-Dimensional Gaussian Graphical Models","arxiv_id":"1808.10532","date":"2018-08-30","proceeding":null,"authors":["Sven Klaassen","Jannis Kück","Martin Spindler","Victor Chernozhukov"],"abstract":"Graphical models have become a very popular tool for representing\ndependencies within a large set of variables and are key for representing\ncausal structures. We provide results for uniform inference on high-dimensional\ngraphical models with the number of target parameters $d$ being possible much\nlarger than sample size. This is in particular important when certain features\nor structures of a causal model should be recovered. Our results highlight how\nin high-dimensional settings graphical models can be estimated and recovered\nwith modern machine learning methods in complex data sets. To construct\nsimultaneous confidence regions on many target parameters, sufficiently fast\nestimation rates of the nuisance functions are crucial. In this context, we\nestablish uniform estimation rates and sparsity guarantees of the square-root\nestimator in a random design under approximate sparsity conditions that might\nbe of independent interest for related problems in high-dimensions. We also\ndemonstrate in a comprehensive simulation study that our procedure has good\nsmall sample properties.","url_abs":"http://arxiv.org/abs/1808.10532v2","url_pdf":"http://arxiv.org/pdf/1808.10532v2.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":"uniform-inference-in-high-dimensional","repo_url":"https://github.com/SvenKlaassen/GGMtest","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"high","task_name":"Vocal Bursts Intensity Prediction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}