{"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/structured-and-efficient-variational-deep","title":"Structured and Efficient Variational Deep Learning with Matrix Gaussian Posteriors","arxiv_id":"1603.04733","date":"2016-03-15","proceeding":null,"authors":["Christos Louizos","Max Welling"],"abstract":"We introduce a variational Bayesian neural network where the parameters are\ngoverned via a probability distribution on random matrices. Specifically, we\nemploy a matrix variate Gaussian \\cite{gupta1999matrix} parameter posterior\ndistribution where we explicitly model the covariance among the input and\noutput dimensions of each layer. Furthermore, with approximate covariance\nmatrices we can achieve a more efficient way to represent those correlations\nthat is also cheaper than fully factorized parameter posteriors. We further\nshow that with the \"local reprarametrization trick\"\n\\cite{kingma2015variational} on this posterior distribution we arrive at a\nGaussian Process \\cite{rasmussen2006gaussian} interpretation of the hidden\nunits in each layer and we, similarly with \\cite{gal2015dropout}, provide\nconnections with deep Gaussian processes. We continue in taking advantage of\nthis duality and incorporate \"pseudo-data\" \\cite{snelson2005sparse} in our\nmodel, which in turn allows for more efficient sampling while maintaining the\nproperties of the original model. The validity of the proposed approach is\nverified through extensive experiments.","url_abs":"http://arxiv.org/abs/1603.04733v5","url_pdf":"http://arxiv.org/pdf/1603.04733v5.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":"structured-and-efficient-variational-deep","repo_url":"https://github.com/AMLab-Amsterdam/SEVDL_MGP","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"structured-and-efficient-variational-deep","repo_url":"https://github.com/beauCoker/bayesian_neural_networks","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"deep-learning","task_name":"Deep Learning"},{"task_slug":"gaussian-processes","task_name":"Gaussian Processes"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1603.04733","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}