{"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/learning-directed-acyclic-graphs-with","title":"Learning Directed Acyclic Graphs with Penalized Neighbourhood Regression","arxiv_id":"1511.08963","date":"2015-11-29","proceeding":null,"authors":["Bryon Aragam","Arash A. Amini","Qing Zhou"],"abstract":"We study a family of regularized score-based estimators for learning the\nstructure of a directed acyclic graph (DAG) for a multivariate normal\ndistribution from high-dimensional data with $p\\gg n$. Our main results\nestablish support recovery guarantees and deviation bounds for a family of\npenalized least-squares estimators under concave regularization without\nassuming prior knowledge of a variable ordering. These results apply to a\nvariety of practical situations that allow for arbitrary nondegenerate\ncovariance structures as well as many popular regularizers including the MCP,\nSCAD, $\\ell_{0}$ and $\\ell_{1}$. The proof relies on interpreting a DAG as a\nrecursive linear structural equation model, which reduces the estimation\nproblem to a series of neighbourhood regressions. We provide a novel\nstatistical analysis of these neighbourhood problems, establishing uniform\ncontrol over the superexponential family of neighbourhoods associated with a\nGaussian distribution. We then apply these results to study the statistical\nproperties of score-based DAG estimators, learning causal DAGs, and inferring\nconditional independence relations via graphical models. Our results\nyield---for the first time---finite-sample guarantees for structure learning of\nGaussian DAGs in high-dimensions via score-based estimation.","url_abs":"http://arxiv.org/abs/1511.08963v3","url_pdf":"http://arxiv.org/pdf/1511.08963v3.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":"learning-directed-acyclic-graphs-with","repo_url":"https://github.com/itsrainingdata/sparsebn","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"regression-1","task_name":"regression"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1511.08963","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}