{"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/thinning-a-wishart-random-matrix","title":"Thinning a Wishart Random Matrix","arxiv_id":"2502.09957","date":"2025-02-14","proceeding":null,"authors":["Ameer Dharamshi","Anna Neufeld","Lucy L. Gao","Daniela Witten","Jacob Bien"],"abstract":"Recent work has explored data thinning, a generalization of sample splitting that involves decomposing a (possibly matrix-valued) random variable into independent components. In the special case of a $n \\times p$ random matrix with independent and identically distributed $N_p(\\mu, \\Sigma)$ rows, Dharamshi et al. (2024a) provides a comprehensive analysis of the settings in which thinning is or is not possible: briefly, if $\\Sigma$ is unknown, then one can thin provided that $n>1$. However, in some situations a data analyst may not have direct access to the data itself. For example, to preserve individuals' privacy, a data bank may provide only summary statistics such as the sample mean and sample covariance matrix. While the sample mean follows a Gaussian distribution, the sample covariance follows (up to scaling) a Wishart distribution, for which no thinning strategies have yet been proposed. In this note, we fill this gap: we show that it is possible to generate two independent data matrices with independent $N_p(\\mu, \\Sigma)$ rows, based only on the sample mean and sample covariance matrix. These independent data matrices can either be used directly within a train-test paradigm, or can be used to derive independent summary statistics. Furthermore, they can be recombined to yield the original sample mean and sample covariance.","url_abs":"https://arxiv.org/abs/2502.09957v1","url_pdf":"https://arxiv.org/pdf/2502.09957v1.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":"thinning-a-wishart-random-matrix","repo_url":"https://github.com/AmeerD/Wishart","is_official":1,"mentioned_in_paper":0,"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}