{"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/robustness-guarantees-for-bayesian-inference","title":"Robustness Guarantees for Bayesian Inference with Gaussian Processes","arxiv_id":"1809.06452","date":"2018-09-17","proceeding":null,"authors":["Luca Cardelli","Marta Kwiatkowska","Luca Laurenti","Andrea Patane"],"abstract":"Bayesian inference and Gaussian processes are widely used in applications\nranging from robotics and control to biological systems. Many of these\napplications are safety-critical and require a characterization of the\nuncertainty associated with the learning model and formal guarantees on its\npredictions. In this paper we define a robustness measure for Bayesian\ninference against input perturbations, given by the probability that, for a\ntest point and a compact set in the input space containing the test point, the\nprediction of the learning model will remain $\\delta-$close for all the points\nin the set, for $\\delta>0.$ Such measures can be used to provide formal\nguarantees for the absence of adversarial examples. By employing the theory of\nGaussian processes, we derive tight upper bounds on the resulting robustness by\nutilising the Borell-TIS inequality, and propose algorithms for their\ncomputation. We evaluate our techniques on two examples, a GP regression\nproblem and a fully-connected deep neural network, where we rely on weak\nconvergence to GPs to study adversarial examples on the MNIST dataset.","url_abs":"http://arxiv.org/abs/1809.06452v2","url_pdf":"http://arxiv.org/pdf/1809.06452v2.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":"robustness-guarantees-for-bayesian-inference","repo_url":"https://github.com/andreapatane/checkGP","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"GPL-3.0"}}],"tasks":[{"task_slug":"bayesian-inference","task_name":"Bayesian Inference"},{"task_slug":"gaussian-processes","task_name":"Gaussian Processes"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1809.06452","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}