{"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/statistical-guarantees-for-the-robustness-of","title":"Statistical Guarantees for the Robustness of Bayesian Neural Networks","arxiv_id":"1903.01980","date":"2019-03-05","proceeding":null,"authors":["Luca Cardelli","Marta Kwiatkowska","Luca Laurenti","Nicola Paoletti","Andrea Patane","Matthew Wicker"],"abstract":"We introduce a probabilistic robustness measure for Bayesian Neural Networks\n(BNNs), defined as the probability that, given a test point, there exists a\npoint within a bounded set such that the BNN prediction differs between the\ntwo. Such a measure can be used, for instance, to quantify the probability of\nthe existence of adversarial examples. Building on statistical verification\ntechniques for probabilistic models, we develop a framework that allows us to\nestimate probabilistic robustness for a BNN with statistical guarantees, i.e.,\nwith a priori error and confidence bounds. We provide experimental comparison\nfor several approximate BNN inference techniques on image classification tasks\nassociated to MNIST and a two-class subset of the GTSRB dataset. Our results\nenable quantification of uncertainty of BNN predictions in adversarial\nsettings.","url_abs":"http://arxiv.org/abs/1903.01980v1","url_pdf":"http://arxiv.org/pdf/1903.01980v1.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":"statistical-guarantees-for-the-robustness-of","repo_url":"https://github.com/matthewwicker/StatisticalGuarenteesForBNNs","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"BSD-3-Clause"}}],"tasks":[{"task_slug":"classification","task_name":"General Classification"},{"task_slug":"image-classification","task_name":"Image Classification"},{"task_slug":"image-classification","task_name":"image-classification"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1903.01980","atlas_url":"https://app.syntology.ai/?focus=1903.01980","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1903.01980"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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