{"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/rectangular-bounding-process-1","title":"Rectangular Bounding Process","arxiv_id":"1903.03906","date":"2019-03-10","proceeding":"NeurIPS 2018 12","authors":["Xuhui Fan","Bin Li","Scott Anthony Sisson"],"abstract":"Stochastic partition models divide a multi-dimensional space into a number of\nrectangular regions, such that the data within each region exhibit certain\ntypes of homogeneity. Due to the nature of their partition strategy, existing\npartition models may create many unnecessary divisions in sparse regions when\ntrying to describe data in dense regions. To avoid this problem we introduce a\nnew parsimonious partition model -- the Rectangular Bounding Process (RBP) --\nto efficiently partition multi-dimensional spaces, by employing a bounding\nstrategy to enclose data points within rectangular bounding boxes. Unlike\nexisting approaches, the RBP possesses several attractive theoretical\nproperties that make it a powerful nonparametric partition prior on a\nhypercube. In particular, the RBP is self-consistent and as such can be\ndirectly extended from a finite hypercube to infinite (unbounded) space. We\napply the RBP to regression trees and relational models as a flexible partition\nprior. The experimental results validate the merit of the RBP {in rich yet\nparsimonious expressiveness} compared to the state-of-the-art methods.","url_abs":"http://arxiv.org/abs/1903.03906v1","url_pdf":"http://arxiv.org/pdf/1903.03906v1.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":"rectangular-bounding-process-1","repo_url":"https://github.com/xuhuifan/RBP","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":"https://app.syntology.ai/?focus=1903.03906","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}