{"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/high-dimensional-semiparametric-latent","title":"High Dimensional Semiparametric Latent Graphical Model for Mixed Data","arxiv_id":"1404.7236","date":"2014-04-29","proceeding":null,"authors":["Jianqing Fan","Han Liu","Yang Ning","Hui Zou"],"abstract":"Graphical models are commonly used tools for modeling multivariate random\nvariables. While there exist many convenient multivariate distributions such as\nGaussian distribution for continuous data, mixed data with the presence of\ndiscrete variables or a combination of both continuous and discrete variables\nposes new challenges in statistical modeling. In this paper, we propose a\nsemiparametric model named latent Gaussian copula model for binary and mixed\ndata. The observed binary data are assumed to be obtained by dichotomizing a\nlatent variable satisfying the Gaussian copula distribution or the\nnonparanormal distribution. The latent Gaussian model with the assumption that\nthe latent variables are multivariate Gaussian is a special case of the\nproposed model. A novel rank-based approach is proposed for both latent graph\nestimation and latent principal component analysis. Theoretically, the proposed\nmethods achieve the same rates of convergence for both precision matrix\nestimation and eigenvector estimation, as if the latent variables were\nobserved. Under similar conditions, the consistency of graph structure recovery\nand feature selection for leading eigenvectors is established. The performance\nof the proposed methods is numerically assessed through simulation studies, and\nthe usage of our methods is illustrated by a genetic dataset.","url_abs":"http://arxiv.org/abs/1404.7236v1","url_pdf":"http://arxiv.org/pdf/1404.7236v1.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":"high-dimensional-semiparametric-latent","repo_url":"https://github.com/mingzehuang/latentcor","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"GPL-3.0"}}],"tasks":[{"task_slug":"high","task_name":"Vocal Bursts Intensity Prediction"},{"task_slug":"feature-selection","task_name":"feature selection"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1404.7236","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}