{"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-mutually-dependent-hadamard-kernel-for","title":"A Mutually-Dependent Hadamard Kernel for Modelling Latent Variable Couplings","arxiv_id":"1702.08402","date":"2017-02-27","proceeding":null,"authors":["Sami Remes","Markus Heinonen","Samuel Kaski"],"abstract":"We introduce a novel kernel that models input-dependent couplings across\nmultiple latent processes. The pairwise joint kernel measures covariance along\ninputs and across different latent signals in a mutually-dependent fashion. A\nlatent correlation Gaussian process (LCGP) model combines these non-stationary\nlatent components into multiple outputs by an input-dependent mixing matrix.\nProbit classification and support for multiple observation sets are derived by\nVariational Bayesian inference. Results on several datasets indicate that the\nLCGP model can recover the correlations between latent signals while\nsimultaneously achieving state-of-the-art performance. We highlight the latent\ncovariances with an EEG classification dataset where latent brain processes and\ntheir couplings simultaneously emerge from the model.","url_abs":"http://arxiv.org/abs/1702.08402v2","url_pdf":"http://arxiv.org/pdf/1702.08402v2.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-mutually-dependent-hadamard-kernel-for","repo_url":"https://github.com/sremes/wishart-gibbs-kernel","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"bayesian-inference","task_name":"Bayesian Inference"},{"task_slug":"classification-1","task_name":"Classification"},{"task_slug":"eeg-1","task_name":"EEG"},{"task_slug":"eeg","task_name":"Electroencephalogram (EEG)"},{"task_slug":"classification","task_name":"General Classification"}],"methods":[{"method_slug":"gaussian-process","method_name":"Gaussian Process"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}