{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T02:46:54Z","timestamp":1777949214724,"version":"3.51.4"},"publisher-location":"Singapore","reference-count":40,"publisher":"Springer Nature Singapore","isbn-type":[{"value":"9789819578252","type":"print"},{"value":"9789819578269","type":"electronic"}],"license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026]]},"DOI":"10.1007\/978-981-95-7826-9_16","type":"book-chapter","created":{"date-parts":[[2026,5,3]],"date-time":"2026-05-03T22:18:28Z","timestamp":1777846708000},"page":"299-317","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Risk-Averse Certification of\u00a0Bayesian Neural Networks"],"prefix":"10.1007","author":[{"given":"Xiyue","family":"Zhang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zifan","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yulong","family":"Gao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Licio","family":"Romao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alessandro","family":"Abate","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marta","family":"Kwiatkowska","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,4,1]]},"reference":[{"key":"16_CR1","unstructured":"Adams, S., Patane, A., Lahijanian, M., Laurenti, L.: BNN-DP: robustness certification of bayesian neural networks via dynamic programming. In: International Conference on Machine Learning, ICML 2023. Proceedings of Machine Learning Research, vol. 202, pp. 133\u2013151. PMLR (2023)"},{"key":"16_CR2","doi-asserted-by":"crossref","unstructured":"Alamo, T., Tempo, R., Luque, A.: On the sample complexity of randomized approaches to the analysis and design under uncertainty. In: Proceedings of American Control Conference, pp. 4671\u20134676 (2010)","DOI":"10.1109\/ACC.2010.5531078"},{"issue":"8","key":"16_CR3","doi-asserted-by":"publisher","first-page":"831","DOI":"10.1038\/nbt.3300","volume":"33","author":"A Babak","year":"2015","unstructured":"Babak, A., Delong, A., Weirauch, M.T., Frey, B.J.: Predicting the sequence specificities of dna- and rna-binding proteins by deep learning. Nat. Biotechnol. 33(8), 831\u2013838 (2015). https:\/\/doi.org\/10.1038\/nbt.3300","journal-title":"Nat. Biotechnol."},{"key":"16_CR4","unstructured":"Berrada, L., et al.: Make sure you\u2019re unsure: a framework for verifying probabilistic specifications. In: Proceedings of Annual Conference on Advances in Neural Information Processing Systems, pp. 11136\u201311147 (2021)"},{"key":"16_CR5","unstructured":"Bhat, S.P., LA, P.: Concentration of risk measures: a wasserstein distance approach. In: Advances in Neural Information Processing Systems, vol. 32 (2019)"},{"key":"16_CR6","unstructured":"Blundell, C., Cornebise, J., Kavukcuoglu, K., Wierstra, D.: Weight uncertainty in neural network. In: International Conference on Machine Learning, pp. 1613\u20131622. PMLR (2015)"},{"key":"16_CR7","unstructured":"Bojarski, M., et al.: End to end learning for self-driving cars. arXiv preprint arXiv:1604.07316 (2016)"},{"key":"16_CR8","doi-asserted-by":"crossref","unstructured":"Boskos, D., Cort\u00e9s, J., Mart\u00ednez, S.: High-confidence data-driven ambiguity sets for time-varying linear systems. IEEE Trans. Autom. Control (2023)","DOI":"10.1109\/TAC.2023.3273815"},{"key":"16_CR9","doi-asserted-by":"crossref","unstructured":"Cardelli, L., Kwiatkowska, M., Laurenti, L., Paoletti, N., Patane, A., Wicker, M.: Statistical guarantees for the robustness of Bayesian neural networks. In: Proceedings of International Joint Conferences on Artificial Intelligence (2019)","DOI":"10.24963\/ijcai.2019\/789"},{"key":"16_CR10","doi-asserted-by":"publisher","unstructured":"Chen, Z., Huang, X.: End-to-end learning for lane keeping of self-driving cars. In: IEEE Intelligent Vehicles Symposium (IV), pp. 1856\u20131860 (2017). https:\/\/doi.org\/10.1109\/IVS.2017.7995975","DOI":"10.1109\/IVS.2017.7995975"},{"key":"16_CR11","unstructured":"Chow, Y., Ghavamzadeh, M.: Algorithms for cvar optimization in mdps. In: Advances in Neural Information Processing Systems 27: Annual Conference on Neural Information Processing Systems 2014, pp. 3509\u20133517 (2014)"},{"key":"16_CR12","doi-asserted-by":"publisher","unstructured":"Codevilla, F., M\u00fcller, M., L\u00f3pez, A.M., Koltun, V., Dosovitskiy, A.: End-to-end driving via conditional imitation learning. In: Proceedings of the 2018 IEEE International Conference on Robotics and Automation, pp. 1\u20139. IEEE (2018). https:\/\/doi.org\/10.1109\/ICRA.2018.8460487","DOI":"10.1109\/ICRA.2018.8460487"},{"key":"16_CR13","first-page":"1036","volume":"33","author":"S Curi","year":"2020","unstructured":"Curi, S., Levy, K.Y., Jegelka, S., Krause, A.: Adaptive sampling for stochastic risk-averse learning. Adv. Neural. Inf. Process. Syst. 33, 1036\u20131047 (2020)","journal-title":"Adv. Neural. Inf. Process. Syst."},{"key":"16_CR14","doi-asserted-by":"publisher","unstructured":"Dahl, G.E., Stokes, J.W., Deng, L., Yu, D.: Large-scale malware classification using random projections and neural networks. In: Proceedings of the 38th IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 3422\u20133426. IEEE (2013). https:\/\/doi.org\/10.1109\/ICASSP.2013.6638293","DOI":"10.1109\/ICASSP.2013.6638293"},{"key":"16_CR15","unstructured":"Gal, Y., Ghahramani, Z.: Dropout as a bayesian approximation: representing model uncertainty in deep learning. In: Proceedings of International Conference on Machine Learning, pp. 1050\u20131059. PMLR (2016)"},{"key":"16_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/978-3-319-63387-9_1","volume-title":"Computer Aided Verification","author":"X Huang","year":"2017","unstructured":"Huang, X., Kwiatkowska, M., Wang, S., Wu, M.: Safety verification of deep neural networks. In: Majumdar, R., Kun\u010dak, V. (eds.) CAV 2017. LNCS, vol. 10426, pp. 3\u201329. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-63387-9_1"},{"key":"16_CR17","unstructured":"Kahn, G., Villaflor, A., Pong, V., Abbeel, P., Levine, S.: Uncertainty-aware reinforcement learning for collision avoidance. arXiv preprint arXiv:1702.01182 (2017)"},{"key":"16_CR18","doi-asserted-by":"crossref","unstructured":"Katz, G., Barrett, C., Dill, D.L., Julian, K., Kochenderfer, M.J.: Reluplex: an efficient smt solver for verifying deep neural networks. In: Proceedings of International Conference on Computer Aided Verification, pp. 97\u2013117. Springer (2017)","DOI":"10.1007\/978-3-319-63387-9_5"},{"key":"16_CR19","unstructured":"La, P., Ghavamzadeh, M.: Actor-critic algorithms for risk-sensitive mdps. In: Advances in Neural Information Processing Systems, vol. 26 (2013)"},{"issue":"2","key":"16_CR20","doi-asserted-by":"publisher","first-page":"244","DOI":"10.1016\/j.jval.2020.10.003","volume":"24","author":"DN Lakdawalla","year":"2021","unstructured":"Lakdawalla, D.N., Phelps, C.E.: Health technology assessment with diminishing returns to health: the generalized risk-adjusted cost-effectiveness (grace) approach. Value Health 24(2), 244\u2013249 (2021)","journal-title":"Value Health"},{"key":"16_CR21","first-page":"10171","volume":"34","author":"M Lechner","year":"2021","unstructured":"Lechner, M., Zikelic, D., Chatterjee, K., Henzinger, T.A.: Infinite time horizon safety of bayesian neural networks. Proc. Adv. Neural Inf. Process. Syst. 34, 10171\u201310185 (2021)","journal-title":"Proc. Adv. Neural Inf. Process. Syst."},{"key":"16_CR22","doi-asserted-by":"crossref","unstructured":"Michelmore, R., Wicker, M., Laurenti, L., Cardelli, L., Gal, Y., Kwiatkowska, M.: Uncertainty quantification with statistical guarantees in end-to-end autonomous driving control. In: Proceedings of IEEE International Conference on Robotics and Automation (ICRA), pp. 7344\u20137350. IEEE (2020)","DOI":"10.1109\/ICRA40945.2020.9196844"},{"key":"16_CR23","unstructured":"Neal, R.M.: Bayesian Learning for Neural Networks, vol. 118. Springer Science & Business Media (2012)"},{"issue":"2","key":"16_CR24","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1257\/jep.32.2.91","volume":"32","author":"T O\u2019Donoghue","year":"2018","unstructured":"O\u2019Donoghue, T., Somerville, J.: Modeling risk aversion in economics. J. Econ. Perspect. 32(2), 91\u2013114 (2018)","journal-title":"J. Econ. Perspect."},{"key":"16_CR25","doi-asserted-by":"publisher","first-page":"21","DOI":"10.21314\/JOR.2000.038","volume":"2","author":"RT Rockafellar","year":"2000","unstructured":"Rockafellar, R.T., Uryasev, S., et al.: Optimization of conditional value-at-risk. J. Risk 2, 21\u201342 (2000)","journal-title":"J. Risk"},{"key":"16_CR26","unstructured":"Rushe, D.: Tesla\u2019s autopilot faces us investigation after crashes with emergency vehicles (2021), https:\/\/www.theguardian.com\/technology\/2021\/aug\/16\/teslas-autopilot-us-investigation-crashes-emergency-vehicles"},{"key":"16_CR27","doi-asserted-by":"crossref","unstructured":"Shapiro, A., Dentcheva, D., Ruszczynski, A.: Lectures on stochastic programming: modeling and theory. In: SIAM (2021)","DOI":"10.1137\/1.9781611976595"},{"key":"16_CR28","unstructured":"Shin, E.C.R., Song, D., Moazzezi, R.: Recognizing functions in binaries with neural networks. In: Proceedings of the 24th USENIX Security Symposium, pp. 611\u2013626. USENIX Association (2015)"},{"key":"16_CR29","doi-asserted-by":"crossref","unstructured":"Singh, G., Gehr, T., P\u00fcschel, M., Vechev, M.: An abstract domain for certifying neural networks. In: Proceedings of the ACM on Programming Languages, pp. 1\u201330 (2019)","DOI":"10.1145\/3290354"},{"key":"16_CR30","unstructured":"Tamar, A., Chow, Y., Ghavamzadeh, M., Mannor, S.: Policy gradient for coherent risk measures. In: Proceedings of Annual Conference on Advances in Neural Information Processing Systems, vol. 28 (2015)"},{"key":"16_CR31","unstructured":"Tjeng, V., Xiao, K.Y., Tedrake, R.: Evaluating robustness of neural networks with mixed integer programming. In: Proceedings of International Conference on Learning Representations. OpenReview.net (2019)"},{"key":"16_CR32","doi-asserted-by":"crossref","unstructured":"Vitt, C.A., Dentcheva, D., Xiong, H.: Risk-averse classification. Ann. Oper. Res. 1\u201335 (2019)","DOI":"10.1007\/s10479-019-03344-6"},{"key":"16_CR33","unstructured":"Wang, S., Wang, Z., Yi, X., Zavlanos, M.M., Johansson, K.H., Hirche, S.: Risk-averse learning with non-stationary distributions. arXiv preprint arXiv:2404.02988 (2024)"},{"key":"16_CR34","unstructured":"Wicker, M., Laurenti, L., Patane, A., Kwiatkowska, M.: Probabilistic safety for bayesian neural networks. In: Proceedings of Conference on Uncertainty in Artificial Intelligence, pp. 1198\u20131207. PMLR (2020)"},{"key":"16_CR35","unstructured":"Wicker, M., Laurenti, L., Patane, A., Paoletti, N., Abate, A., Kwiatkowska, M.: Certification of iterative predictions in Bayesian neural networks. In: de Campos, C., Maathuis, M.H. (eds.) Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence. Proceedings of Machine Learning Research, vol. 161, pp. 1713\u20131723. PMLR, 27\u201330 July 2021, https:\/\/proceedings.mlr.press\/v161\/wicker21a.html"},{"key":"16_CR36","doi-asserted-by":"publisher","first-page":"104","DOI":"10.1016\/j.artint.2024.104132","volume":"334","author":"M Wicker","year":"2024","unstructured":"Wicker, M., Laurenti, L., Patane, A., Paoletti, N., Abate, A., Kwiatkowska, M.: Probabilistic reach-avoid for bayesian neural networks. Artif. Intell. 334, 104\u2013132 (2024). https:\/\/doi.org\/10.1016\/j.artint.2024.104132","journal-title":"Artif. Intell."},{"key":"16_CR37","doi-asserted-by":"crossref","unstructured":"Wicker, M., Patane, A., Laurenti, L., Kwiatkowska, M.: Adversarial robustness certification for bayesian neural networks. In: Proceedings of International Symposium on Formal Methods, pp. 3\u201328. Springer (2024)","DOI":"10.1007\/978-3-031-71162-6_1"},{"key":"16_CR38","unstructured":"Xu, K., et al.: Automatic perturbation analysis for scalable certified robustness and beyond. In: Proceedings of Annual Conference on Advances in Neural Information Processing Systems (2020)"},{"key":"16_CR39","first-page":"21860","volume":"34","author":"R Zhai","year":"2021","unstructured":"Zhai, R., Dan, C., Suggala, A., Kolter, J.Z., Ravikumar, P.: Boosted cvar classification. Adv. Neural. Inf. Process. Syst. 34, 21860\u201321871 (2021)","journal-title":"Adv. Neural. Inf. Process. Syst."},{"key":"16_CR40","unstructured":"Zhang, H., Weng, T., Chen, P., Hsieh, C., Daniel, L.: Efficient neural network robustness certification with general activation functions. In: Proceedings of Annual Conference on Advances in Neural Information Processing Systems, pp. 4944\u20134953 (2018)"}],"container-title":["Lecture Notes in Computer Science","Dependable Software Engineering. Theories, Tools, and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-981-95-7826-9_16","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,3]],"date-time":"2026-05-03T22:18:31Z","timestamp":1777846711000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-981-95-7826-9_16"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"ISBN":["9789819578252","9789819578269"],"references-count":40,"URL":"https:\/\/doi.org\/10.1007\/978-981-95-7826-9_16","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026]]},"assertion":[{"value":"1 April 2026","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"SETTA","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Symposium on Dependable Software Engineering: Theories, Tools, and Applications","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Oxford","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"United Kingdom","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2025","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"1 December 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"3 December 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"11","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"setta2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/www.setta2025.uk\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}