{"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/dealing-with-categorical-and-integer-valued","title":"Dealing with Categorical and Integer-valued Variables in Bayesian Optimization with Gaussian Processes","arxiv_id":"1805.03463","date":"2018-05-09","proceeding":null,"authors":["Eduardo C. Garrido-Merchán","Daniel Hernández-Lobato"],"abstract":"Bayesian Optimization (BO) methods are useful for optimizing functions that\nare expen- sive to evaluate, lack an analytical expression and whose\nevaluations can be contaminated by noise. These methods rely on a probabilistic\nmodel of the objective function, typically a Gaussian process (GP), upon which\nan acquisition function is built. The acquisition function guides the\noptimization process and measures the expected utility of performing an\nevaluation of the objective at a new point. GPs assume continous input\nvariables. When this is not the case, for example when some of the input\nvariables take categorical or integer values, one has to introduce extra\napproximations. Consider a suggested input location taking values in the real\nline. Before doing the evaluation of the objective, a common approach is to use\na one hot encoding approximation for categorical variables, or to round to the\nclosest integer, in the case of integer-valued variables. We show that this can\nlead to problems in the optimization process and describe a more principled\napproach to account for input variables that are categorical or integer-valued.\nWe illustrate in both synthetic and a real experiments the utility of our\napproach, which significantly improves the results of standard BO methods using\nGaussian processes on problems with categorical or integer-valued variables.","url_abs":"http://arxiv.org/abs/1805.03463v2","url_pdf":"http://arxiv.org/pdf/1805.03463v2.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":"dealing-with-categorical-and-integer-valued","repo_url":"https://github.com/svedel/greattunes","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"bayesian-optimization","task_name":"Bayesian Optimization"},{"task_slug":"gaussian-processes","task_name":"Gaussian Processes"}],"methods":[{"method_slug":"gaussian-process","method_name":"Gaussian Process"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1805.03463","atlas_url":"https://app.syntology.ai/?focus=1805.03463","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}