{"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/variational-inference-based-on-robust","title":"Variational Inference based on Robust Divergences","arxiv_id":"1710.06595","date":"2017-10-18","proceeding":null,"authors":["Futoshi Futami","Issei Sato","Masashi Sugiyama"],"abstract":"Robustness to outliers is a central issue in real-world machine learning\napplications. While replacing a model to a heavy-tailed one (e.g., from\nGaussian to Student-t) is a standard approach for robustification, it can only\nbe applied to simple models. In this paper, based on Zellner's optimization and\nvariational formulation of Bayesian inference, we propose an outlier-robust\npseudo-Bayesian variational method by replacing the Kullback-Leibler divergence\nused for data fitting to a robust divergence such as the beta- and\ngamma-divergences. An advantage of our approach is that superior but complex\nmodels such as deep networks can also be handled. We theoretically prove that,\nfor deep networks with ReLU activation functions, the \\emph{influence function}\nin our proposed method is bounded, while it is unbounded in the ordinary\nvariational inference. This implies that our proposed method is robust to both\nof input and output outliers, while the ordinary variational method is not. We\nexperimentally demonstrate that our robust variational method outperforms\nordinary variational inference in regression and classification with deep\nnetworks.","url_abs":"http://arxiv.org/abs/1710.06595v2","url_pdf":"http://arxiv.org/pdf/1710.06595v2.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":"variational-inference-based-on-robust","repo_url":"https://github.com/futoshi-futami/Robust_VI","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok"}}],"tasks":[{"task_slug":"bayesian-inference","task_name":"Bayesian Inference"},{"task_slug":"variational-inference","task_name":"Variational Inference"}],"methods":[{"method_slug":"relu","method_name":"ReLU"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1710.06595","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}