{"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/bayesian-nonparametric-multiway-regression","title":"Bayesian nonparametric multiway regression for clustered binomial data","arxiv_id":"1901.11172","date":"2019-01-31","proceeding":null,"authors":["Eric F. Lock","Dipankar Bandyopadhyay"],"abstract":"We introduce a Bayesian nonparametric regression model for data with multiway\n(tensor) structure, motivated by an application to periodontal disease (PD)\ndata. Our outcome is the number of diseased sites measured over four different\ntooth types for each subject, with subject-specific covariates available as\npredictors. The outcomes are not well-characterized by simple parametric\nmodels, so we use a nonparametric approach with a binomial likelihood wherein\nthe latent probabilities are drawn from a mixture with an arbitrary number of\ncomponents, analogous to a Dirichlet Process (DP). We use a flexible probit\nstick-breaking formulation for the component weights that allows for covariate\ndependence and clustering structure in the outcomes. The parameter space for\nthis model is large and multiway: patients $\\times$ tooth types $\\times$\ncovariates $\\times$ components. We reduce its effective dimensionality, and\naccount for the multiway structure, via low-rank assumptions. We illustrate how\nthis can improve performance, and simplify interpretation, while still\nproviding sufficient flexibility. We describe a general and efficient Gibbs\nsampling algorithm for posterior computation. The resulting fit to the PD data\noutperforms competitors, and is interpretable and well-calibrated. An\ninteractive visual of the predictive model is available at\nhttp://ericfrazerlock.com/toothdata/ToothDisplay.html , and the code is\navailable at https://github.com/lockEF/NonparametricMultiway .","url_abs":"http://arxiv.org/abs/1901.11172v1","url_pdf":"http://arxiv.org/pdf/1901.11172v1.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":"bayesian-nonparametric-multiway-regression","repo_url":"https://github.com/lockEF/NonparametricMultiway","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"},{"task_slug":"regression-1","task_name":"regression"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}