{"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/graphspme-markov-precision-matrix-estimation","title":"GraphSPME: Markov Precision Matrix Estimation and Asymptotic Stein-Type Shrinkage","arxiv_id":"2205.07584","date":"2022-05-16","proceeding":null,"authors":["Berent Ånund Strømnes Lunde","Feda Curic","Sondre Sortland"],"abstract":"GraphSPME is an open source Python, R and C++ header-only package implement-ing non-parametric sparse precision matrix estimation along with asymptotic Stein-type shrinkage estimation of the covariance matrix. The user defines a potential neighbourhood structure and provides data that potentially are p >> n. This paper introduces a novel approach for finding the optimal order (that data allows to estimate) of a potential Markov property. The algorithm is implemented in the package, alleviating the problem of users making Markov assumptions and implementing corresponding complex higher-order neighbourhood structures. Estimation is made accurate and stable by simultaneously utilising both Markov properties and Stein-type shrinkage. Asymptotic results on Stein-type shrinkage ensure that non-singular well conditioned matrices are obtained in an automatic manner. Final symmetry conversion creates symmetric positive definite estimates. Furthermore, the estimation routine is made efficient and scalable to very high-dimensional problems (~10^7) by utilising the sparse nature of the precision matrix under Markov assumptions. Implementation wise, the sparsity is exploited by employing the sparsity possibilities made available by the Eigen C++ linear-algebra library. The package and examples are available at https://github.com/equinor/GraphSPME","url_abs":"https://arxiv.org/abs/2205.07584v1","url_pdf":"https://arxiv.org/pdf/2205.07584v1.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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"graphspme-markov-precision-matrix-estimation","repo_url":"https://github.com/equinor/graphspme","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}