{"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/tropical-geometric-tools-for-machine-learning","title":"Tropical Geometric Tools for Machine Learning: the TML package","arxiv_id":"2309.01082","date":"2023-09-03","proceeding":null,"authors":["David Barnhill","Ruriko Yoshida","Georgios Aliatimis","Keiji Miura"],"abstract":"In the last decade, developments in tropical geometry have provided a number of uses directly applicable to problems in statistical learning. The TML package is the first R package which contains a comprehensive set of tools and methods used for basic computations related to tropical convexity, visualization of tropically convex sets, as well as supervised and unsupervised learning models using the tropical metric under the max-plus algebra over the tropical projective torus. Primarily, the TML package employs a Hit and Run Markov chain Monte Carlo sampler in conjunction with the tropical metric as its main tool for statistical inference. In addition to basic computation and various applications of the tropical HAR sampler, we also focus on several supervised and unsupervised methods incorporated in the TML package including tropical principal component analysis, tropical logistic regression and tropical kernel density estimation.","url_abs":"https://arxiv.org/abs/2309.01082v3","url_pdf":"https://arxiv.org/pdf/2309.01082v3.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":"tropical-geometric-tools-for-machine-learning","repo_url":"https://github.com/barnhilldave/tml","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"density-estimation","task_name":"Density Estimation"}],"methods":[{"method_slug":"focus","method_name":"Focus"},{"method_slug":"logistic-regression","method_name":"Logistic Regression"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}