{"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/calibrated-simplex-mapping-classification","title":"Calibrated simplex-mapping classification","arxiv_id":"2103.02926","date":"2021-03-04","proceeding":null,"authors":["Raoul Heese","Jochen Schmid","Michał Walczak","Michael Bortz"],"abstract":"We propose a novel methodology for general multi-class classification in arbitrary feature spaces, which results in a potentially well-calibrated classifier. Calibrated classifiers are important in many applications because, in addition to the prediction of mere class labels, they also yield a confidence level for each of their predictions. In essence, the training of our classifier proceeds in two steps. In a first step, the training data is represented in a latent space whose geometry is induced by a regular $(n-1)$-dimensional simplex, $n$ being the number of classes. We design this representation in such a way that it well reflects the feature space distances of the datapoints to their own- and foreign-class neighbors. In a second step, the latent space representation of the training data is extended to the whole feature space by fitting a regression model to the transformed data. With this latent-space representation, our calibrated classifier is readily defined. We rigorously establish its core theoretical properties and benchmark its prediction and calibration properties by means of various synthetic and real-world data sets from different application domains.","url_abs":"https://arxiv.org/abs/2103.02926v2","url_pdf":"https://arxiv.org/pdf/2103.02926v2.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":"calibrated-simplex-mapping-classification","repo_url":"https://github.com/raoulheese/casimac","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"classification-1","task_name":"Classification"},{"task_slug":"classification","task_name":"General Classification"},{"task_slug":"multi-class-classification","task_name":"Multi-class Classification"},{"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}