{"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/bayesian-approximate-kernel-regression-with","title":"Bayesian Approximate Kernel Regression with Variable Selection","arxiv_id":"1508.01217","date":"2015-08-05","proceeding":null,"authors":["Lorin Crawford","Kris C. Wood","Xiang Zhou","Sayan Mukherjee"],"abstract":"Nonlinear kernel regression models are often used in statistics and machine\nlearning because they are more accurate than linear models. Variable selection\nfor kernel regression models is a challenge partly because, unlike the linear\nregression setting, there is no clear concept of an effect size for regression\ncoefficients. In this paper, we propose a novel framework that provides an\neffect size analog of each explanatory variable for Bayesian kernel regression\nmodels when the kernel is shift-invariant --- for example, the Gaussian kernel.\nWe use function analytic properties of shift-invariant reproducing kernel\nHilbert spaces (RKHS) to define a linear vector space that: (i) captures\nnonlinear structure, and (ii) can be projected onto the original explanatory\nvariables. The projection onto the original explanatory variables serves as an\nanalog of effect sizes. The specific function analytic property we use is that\nshift-invariant kernel functions can be approximated via random Fourier bases.\nBased on the random Fourier expansion we propose a computationally efficient\nclass of Bayesian approximate kernel regression (BAKR) models for both\nnonlinear regression and binary classification for which one can compute an\nanalog of effect sizes. We illustrate the utility of BAKR by examining two\nimportant problems in statistical genetics: genomic selection (i.e. phenotypic\nprediction) and association mapping (i.e. inference of significant variants or\nloci). State-of-the-art methods for genomic selection and association mapping\nare based on kernel regression and linear models, respectively. BAKR is the\nfirst method that is competitive in both settings.","url_abs":"http://arxiv.org/abs/1508.01217v4","url_pdf":"http://arxiv.org/pdf/1508.01217v4.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":"bayesian-approximate-kernel-regression-with","repo_url":"https://github.com/lorinanthony/BAKR","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"binary-classification","task_name":"Binary Classification"},{"task_slug":"variable-selection","task_name":"Variable Selection"},{"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}