{"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/laplace-approximation-for-logistic-gaussian","title":"Laplace approximation for logistic Gaussian process density estimation and regression","arxiv_id":"1211.0174","date":"2012-11-01","proceeding":null,"authors":["Jaakko Riihimäki","Aki Vehtari"],"abstract":"Logistic Gaussian process (LGP) priors provide a flexible alternative for\nmodelling unknown densities. The smoothness properties of the density estimates\ncan be controlled through the prior covariance structure of the LGP, but the\nchallenge is the analytically intractable inference. In this paper, we present\napproximate Bayesian inference for LGP density estimation in a grid using\nLaplace's method to integrate over the non-Gaussian posterior distribution of\nlatent function values and to determine the covariance function parameters with\ntype-II maximum a posteriori (MAP) estimation. We demonstrate that Laplace's\nmethod with MAP is sufficiently fast for practical interactive visualisation of\n1D and 2D densities. Our experiments with simulated and real 1D data sets show\nthat the estimation accuracy is close to a Markov chain Monte Carlo\napproximation and state-of-the-art hierarchical infinite Gaussian mixture\nmodels. We also construct a reduced-rank approximation to speed up the\ncomputations for dense 2D grids, and demonstrate density regression with the\nproposed Laplace approach.","url_abs":"http://arxiv.org/abs/1211.0174v3","url_pdf":"http://arxiv.org/pdf/1211.0174v3.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":"laplace-approximation-for-logistic-gaussian","repo_url":"https://github.com/Tan-Furukawa/badzupa","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"bayesian-inference","task_name":"Bayesian Inference"},{"task_slug":"density-estimation","task_name":"Density Estimation"},{"task_slug":"regression-1","task_name":"regression"}],"methods":[{"method_slug":"gaussian-process","method_name":"Gaussian Process"},{"method_slug":"speed","method_name":"SPEED"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}