{"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/converting-high-dimensional-regression-to","title":"Converting High-Dimensional Regression to High-Dimensional Conditional Density Estimation","arxiv_id":"1704.08095","date":"2017-04-26","proceeding":null,"authors":["Rafael Izbicki","Ann B. Lee"],"abstract":"There is a growing demand for nonparametric conditional density estimators\n(CDEs) in fields such as astronomy and economics. In astronomy, for example,\none can dramatically improve estimates of the parameters that dictate the\nevolution of the Universe by working with full conditional densities instead of\nregression (i.e., conditional mean) estimates. More generally, standard\nregression falls short in any prediction problem where the distribution of the\nresponse is more complex with multi-modality, asymmetry or heteroscedastic\nnoise. Nevertheless, much of the work on high-dimensional inference concerns\nregression and classification only, whereas research on density estimation has\nlagged behind. Here we propose FlexCode, a fully nonparametric approach to\nconditional density estimation that reformulates CDE as a non-parametric\northogonal series problem where the expansion coefficients are estimated by\nregression. By taking such an approach, one can efficiently estimate\nconditional densities and not just expectations in high dimensions by drawing\nupon the success in high-dimensional regression. Depending on the choice of\nregression procedure, our method can adapt to a variety of challenging\nhigh-dimensional settings with different structures in the data (e.g., a large\nnumber of irrelevant components and nonlinear manifold structure) as well as\ndifferent data types (e.g., functional data, mixed data types and sample sets).\nWe study the theoretical and empirical performance of our proposed method, and\nwe compare our approach with traditional conditional density estimators on\nsimulated as well as real-world data, such as photometric galaxy data, Twitter\ndata, and line-of-sight velocities in a galaxy cluster.","url_abs":"http://arxiv.org/abs/1704.08095v1","url_pdf":"http://arxiv.org/pdf/1704.08095v1.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":"converting-high-dimensional-regression-to","repo_url":"https://github.com/rizbicki/FlexCoDE","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":"astronomy","task_name":"Astronomy"},{"task_slug":"density-estimation","task_name":"Density Estimation"},{"task_slug":"high","task_name":"Vocal Bursts Intensity Prediction"},{"task_slug":"regression-1","task_name":"regression"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1704.08095","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}