{"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/a-latent-variable-approach-to-gaussian","title":"A Latent Variable Approach to Gaussian Process Modeling with Qualitative and Quantitative Factors","arxiv_id":"1806.07504","date":"2018-06-19","proceeding":null,"authors":["Yichi Zhang","Siyu Tao","Wei Chen","Daniel W. Apley"],"abstract":"Computer simulations often involve both qualitative and numerical inputs.\nExisting Gaussian process (GP) methods for handling this mainly assume a\ndifferent response surface for each combination of levels of the qualitative\nfactors and relate them via a multiresponse cross-covariance matrix. We\nintroduce a substantially different approach that maps each qualitative factor\nto an underlying numerical latent variable (LV), with the mapped value for each\nlevel estimated similarly to the correlation parameters. This provides a\nparsimonious GP parameterization that treats qualitative factors the same as\nnumerical variables and views them as effecting the response via similar\nphysical mechanisms. This has strong physical justification, as the effects of\na qualitative factor in any physics-based simulation model must always be due\nto some underlying numerical variables. Even when the underlying variables are\nmany, sufficient dimension reduction arguments imply that their effects can be\nrepresented by a low-dimensional LV. This conjecture is supported by the\nsuperior predictive performance observed across a variety of examples.\nMoreover, the mapped LVs provide substantial insight into the nature and\neffects of the qualitative factors.","url_abs":"http://arxiv.org/abs/1806.07504v2","url_pdf":"http://arxiv.org/pdf/1806.07504v2.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":"a-latent-variable-approach-to-gaussian","repo_url":"https://github.com/PaulsonLab/CAGES","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}},{"paper_slug":"a-latent-variable-approach-to-gaussian","repo_url":"https://github.com/balaranjan/LVGP","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"dimensionality-reduction","task_name":"Dimensionality Reduction"}],"methods":[{"method_slug":"gaussian-process","method_name":"Gaussian Process"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}