{"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/learning-deep-mixtures-of-gaussian-process","title":"Learning Deep Mixtures of Gaussian Process Experts Using Sum-Product Networks","arxiv_id":"1809.04400","date":"2018-09-12","proceeding":null,"authors":["Martin Trapp","Robert Peharz","Carl E. Rasmussen","Franz Pernkopf"],"abstract":"While Gaussian processes (GPs) are the method of choice for regression tasks,\nthey also come with practical difficulties, as inference cost scales cubic in\ntime and quadratic in memory. In this paper, we introduce a natural and\nexpressive way to tackle these problems, by incorporating GPs in sum-product\nnetworks (SPNs), a recently proposed tractable probabilistic model allowing\nexact and efficient inference. In particular, by using GPs as leaves of an SPN\nwe obtain a novel flexible prior over functions, which implicitly represents an\nexponentially large mixture of local GPs. Exact and efficient posterior\ninference in this model can be done in a natural interplay of the inference\nmechanisms in GPs and SPNs. Thereby, each GP is -- similarly as in a mixture of\nexperts approach -- responsible only for a subset of data points, which\neffectively reduces inference cost in a divide and conquer fashion. We show\nthat integrating GPs into the SPN framework leads to a promising probabilistic\nregression model which is: (1) computational and memory efficient, (2) allows\nefficient and exact posterior inference, (3) is flexible enough to mix\ndifferent kernel functions, and (4) naturally accounts for non-stationarities\nin time series. In a variate of experiments, we show that the SPN-GP model can\nlearn input dependent parameters and hyper-parameters and is on par with or\noutperforms the traditional GPs as well as state of the art approximations on\nreal-world data.","url_abs":"http://arxiv.org/abs/1809.04400v1","url_pdf":"http://arxiv.org/pdf/1809.04400v1.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":"learning-deep-mixtures-of-gaussian-process","repo_url":"https://github.com/eugene/spngp","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"gaussian-processes","task_name":"Gaussian Processes"},{"task_slug":"mixture-of-experts","task_name":"Mixture-of-Experts"},{"task_slug":"time-series","task_name":"Time Series Analysis"},{"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}