{"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/multivariate-gaussian-and-student-t-process","title":"Multivariate Gaussian and Student$-t$ Process Regression for Multi-output Prediction","arxiv_id":"1703.04455","date":"2017-03-13","proceeding":null,"authors":["Zexun Chen","Bo wang","Alexander N. Gorban"],"abstract":"Gaussian process model for vector-valued function has been shown to be useful\nfor multi-output prediction. The existing method for this model is to\nre-formulate the matrix-variate Gaussian distribution as a multivariate normal\ndistribution. Although it is effective in many cases, re-formulation is not\nalways workable and is difficult to apply to other distributions because not\nall matrix-variate distributions can be transformed to respective multivariate\ndistributions, such as the case for matrix-variate Student$-t$ distribution. In\nthis paper, we propose a unified framework which is used not only to introduce\na novel multivariate Student$-t$ process regression model (MV-TPR) for\nmulti-output prediction, but also to reformulate the multivariate Gaussian\nprocess regression (MV-GPR) that overcomes some limitations of the existing\nmethods. Both MV-GPR and MV-TPR have closed-form expressions for the marginal\nlikelihoods and predictive distributions under this unified framework and thus\ncan adopt the same optimization approaches as used in the conventional GPR. The\nusefulness of the proposed methods is illustrated through several simulated and\nreal data examples. In particular, we verify empirically that MV-TPR has\nsuperiority for the datasets considered, including air quality prediction and\nbike rent prediction. At last, the proposed methods are shown to produce\nprofitable investment strategies in the stock markets.","url_abs":"http://arxiv.org/abs/1703.04455v6","url_pdf":"http://arxiv.org/pdf/1703.04455v6.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":"multivariate-gaussian-and-student-t-process","repo_url":"https://github.com/Magica-Chen/gptp_multi_output","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"gpr","task_name":"GPR"},{"task_slug":"prediction","task_name":"Prediction"},{"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}