{"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/projective-inference-in-high-dimensional","title":"Projective Inference in High-dimensional Problems: Prediction and Feature Selection","arxiv_id":"1810.02406","date":"2018-10-04","proceeding":null,"authors":["Juho Piironen","Markus Paasiniemi","Aki Vehtari"],"abstract":"This paper discusses predictive inference and feature selection for\ngeneralized linear models with scarce but high-dimensional data. We argue that\nin many cases one can benefit from a decision theoretically justified two-stage\napproach: first, construct a possibly non-sparse model that predicts well, and\nthen find a minimal subset of features that characterize the predictions. The\nmodel built in the first step is referred to as the \\emph{reference model} and\nthe operation during the latter step as predictive \\emph{projection}. The key\ncharacteristic of this approach is that it finds an excellent tradeoff between\nsparsity and predictive accuracy, and the gain comes from utilizing all\navailable information including prior and that coming from the left out\nfeatures. We review several methods that follow this principle and provide\nnovel methodological contributions. We present a new projection technique that\nunifies two existing techniques and is both accurate and fast to compute. We\nalso propose a way of evaluating the feature selection process using fast\nleave-one-out cross-validation that allows for easy and intuitive model size\nselection. Furthermore, we prove a theorem that helps to understand the\nconditions under which the projective approach could be beneficial. The\nbenefits are illustrated via several simulated and real world examples.","url_abs":"http://arxiv.org/abs/1810.02406v1","url_pdf":"http://arxiv.org/pdf/1810.02406v1.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":"projective-inference-in-high-dimensional","repo_url":"https://github.com/stan-dev/projpred","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"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":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}