{"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/universal-inference-meets-random-projections","title":"Universal Inference Meets Random Projections: A Scalable Test for Log-concavity","arxiv_id":"2111.09254","date":"2021-11-17","proceeding":null,"authors":["Robin Dunn","Aditya Gangrade","Larry Wasserman","Aaditya Ramdas"],"abstract":"Shape constraints yield flexible middle grounds between fully nonparametric and fully parametric approaches to modeling distributions of data. The specific assumption of log-concavity is motivated by applications across economics, survival modeling, and reliability theory. However, there do not currently exist valid tests for whether the underlying density of given data is log-concave. The recent universal inference methodology provides a valid test. The universal test relies on maximum likelihood estimation (MLE), and efficient methods already exist for finding the log-concave MLE. This yields the first test of log-concavity that is provably valid in finite samples in any dimension, for which we also establish asymptotic consistency results. Empirically, we find that a random projections approach that converts the d-dimensional testing problem into many one-dimensional problems can yield high power, leading to a simple procedure that is statistically and computationally efficient.","url_abs":"https://arxiv.org/abs/2111.09254v4","url_pdf":"https://arxiv.org/pdf/2111.09254v4.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":"universal-inference-meets-random-projections","repo_url":"https://github.com/robinmdunn/logconcaveuniv","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"universal-inference-meets-random-projections","repo_url":"https://github.com/robinmdunn/universal_inference_logconcave","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":null,"task_name":"valid"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}