{"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/scalable-fitting-methods-for-multivariate","title":"Scalable Fitting Methods for Multivariate Gaussian Additive Models with Covariate-dependent Covariance Matrices","arxiv_id":"2504.03368","date":"2025-04-04","proceeding":null,"authors":["Vincenzo Gioia","Matteo Fasiolo","Ruggero Bellio","Simon N. Wood"],"abstract":"We propose efficient computational methods to fit multivariate Gaussian additive models, where the mean vector and the covariance matrix are allowed to vary with covariates, in an empirical Bayes framework. To guarantee the positive-definiteness of the covariance matrix, we model the elements of an unconstrained parametrisation matrix, focussing particularly on the modified Cholesky decomposition and the matrix logarithm. A key computational challenge arises from the fact that, for the model class considered here, the number of parameters increases quadratically with the dimension of the response vector. Hence, here we discuss how to achieve fast computation and low memory footprint in moderately high dimensions, by exploiting parsimonious model structures, sparse derivative systems and by employing block-oriented computational methods. Methods for building and fitting multivariate Gaussian additive models are provided by the SCM R package, available at https://github.com/VinGioia90/SCM, while the code for reproducing the results in this paper is available at https://github.com/VinGioia90/SACM.","url_abs":"https://arxiv.org/abs/2504.03368v1","url_pdf":"https://arxiv.org/pdf/2504.03368v1.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":"scalable-fitting-methods-for-multivariate","repo_url":"https://github.com/vingioia90/sacm","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null},{"paper_slug":"scalable-fitting-methods-for-multivariate","repo_url":"https://github.com/vingioia90/scm","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"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}