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The development of tools and techniques for certifying fairness of this software or describing its biases is, therefore, critical. In this paper, we propose a perfectly parallel static analysis for certifying fairness of feed-forward neural networks used for classification of tabular data. When certification succeeds, our approach provides definite guarantees, otherwise, it describes and quantifies the biased input space regions. We design the analysis to be sound, in practice also exact, and configurable in terms of scalability and precision, thereby enabling pay-as-you-go certification. We implement our approach in an open-source tool called Libra and demonstrate its effectiveness on neural networks trained on popular datasets.<\/jats:p>","DOI":"10.1145\/3428253","type":"journal-article","created":{"date-parts":[[2020,11,24]],"date-time":"2020-11-24T23:36:06Z","timestamp":1606260966000},"page":"1-30","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":51,"title":["Perfectly parallel fairness certification of neural networks"],"prefix":"10.1145","volume":"4","author":[{"given":"Caterina","family":"Urban","sequence":"first","affiliation":[{"name":"Inria, France \/ ENS, France \/ CNRS, France \/ PSL University, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maria","family":"Christakis","sequence":"additional","affiliation":[{"name":"MPI-SWS, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Valentin","family":"W\u00fcstholz","sequence":"additional","affiliation":[{"name":"ConsenSys, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fuyuan","family":"Zhang","sequence":"additional","affiliation":[{"name":"MPI-SWS, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2020,11,13]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-63387-9_9"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/3133904"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/3287560.3287588"},{"key":"e_1_2_2_4_1","volume-title":"Wagner","author":"Athalye Anish","year":"2018","unstructured":"Anish Athalye , Nicholas Carlini , and David A . 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In ICML. 807 - 814 . Vinod Nair and Geofrey E. Hinton. 2010. Rectified Linear Units Improve Restricted Boltzmann Machines. In ICML. 807-814.","journal-title":"ICML."},{"key":"e_1_2_2_60_1","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2015.7298640"},{"key":"e_1_2_2_61_1","doi-asserted-by":"crossref","unstructured":"Ziad Obermeyer Brian Powers Christine Vogeli and Sendhil Mullainathan. 2019. Dissecting Racial Bias in an Algorithm Used to Manage the Health of Populations. Science 366 ( 2019 ) 447-453. Issue 6464.  Ziad Obermeyer Brian Powers Christine Vogeli and Sendhil Mullainathan. 2019. Dissecting Racial Bias in an Algorithm Used to Manage the Health of Populations. Science 366 ( 2019 ) 447-453. Issue 6464.","DOI":"10.1126\/science.aax2342"},{"key":"e_1_2_2_62_1","volume-title":"Goodfellow","author":"Odena Augustus","year":"2019","unstructured":"Augustus Odena , Catherine Olsson , David Andersen , and Ian J . Goodfellow . 2019 . 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Yuchi Tian, Kexin Pei, Suman Jana, and Baishakhi Ray. 2018. DeepTest: Automated Testing of Deep-Neural-Network-Driven Autonomous Cars. In ICSE. ACM, 303-314.","journal-title":"Automated Testing of Deep-Neural-Network-Driven Autonomous Cars. In ICSE. ACM"},{"key":"e_1_2_2_73_1","first-page":"401","article-title":"FairTest","author":"Tram\u00e8r Florian","year":"2017","unstructured":"Florian Tram\u00e8r , Vaggelis Atlidakis , Roxana Geambasu , Daniel J. Hsu , Jean-Pierre Hubaux , Mathias Humbert , Ari Juels , and Huang Lin . 2017 . FairTest : Discovering Unwarranted Associations in Data-Driven Applications. In EuroS&P. IEEE , 401 - 416 . Florian Tram\u00e8r, Vaggelis Atlidakis, Roxana Geambasu, Daniel J. Hsu, Jean-Pierre Hubaux, Mathias Humbert, Ari Juels, and Huang Lin. 2017. FairTest: Discovering Unwarranted Associations in Data-Driven Applications. In EuroS&P. IEEE, 401-416.","journal-title":"Discovering Unwarranted Associations in Data-Driven Applications. In EuroS&P. IEEE"},{"key":"e_1_2_2_74_1","first-page":"18","article-title":"Verification of Deep Convolutional Neural Networks Using ImageStars","author":"Tran Hoang-Dung","year":"2020","unstructured":"Hoang-Dung Tran , Stanley Bak , Weiming Xiang , and Taylor T. Johnson . 2020 . Verification of Deep Convolutional Neural Networks Using ImageStars . In CAV. 18 - 42 . Hoang-Dung Tran, Stanley Bak, Weiming Xiang, and Taylor T. Johnson. 2020. Verification of Deep Convolutional Neural Networks Using ImageStars. In CAV. 18-42.","journal-title":"CAV."},{"key":"e_1_2_2_75_1","first-page":"98","article-title":"Automated Directed Fairness Testing","author":"Udeshi Sakshi","year":"2018","unstructured":"Sakshi Udeshi , Pryanshu Arora , and Sudipta Chattopadhyay . 2018 . Automated Directed Fairness Testing . In ASE. ACM , 98 - 108 . Sakshi Udeshi, Pryanshu Arora, and Sudipta Chattopadhyay. 2018. Automated Directed Fairness Testing. In ASE. ACM, 98-108.","journal-title":"ASE. ACM"},{"key":"e_1_2_2_76_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-89884-1_24"},{"key":"e_1_2_2_77_1","first-page":"1599","article-title":"Formal Security Analysis of Neural Networks Using Symbolic Intervals. In Security","author":"Wang Shiqi","year":"2018","unstructured":"Shiqi Wang , Kexin Pei , Justin Whitehouse , Junfeng Yang , and Suman Jana . 2018 . Formal Security Analysis of Neural Networks Using Symbolic Intervals. In Security . USENIX , 1599 - 1614 . Shiqi Wang, Kexin Pei, Justin Whitehouse, Junfeng Yang, and Suman Jana. 2018. Formal Security Analysis of Neural Networks Using Symbolic Intervals. In Security. USENIX, 1599-1614.","journal-title":"USENIX"},{"key":"e_1_2_2_78_1","unstructured":"Mikhail Yurochkin Amanda Bower and Yuekai Sun. 2020. Training Individually Fair ML Models with Sensitive Subspace Robustness. In ICLR.  Mikhail Yurochkin Amanda Bower and Yuekai Sun. 2020. Training Individually Fair ML Models with Sensitive Subspace Robustness. In ICLR."},{"key":"e_1_2_2_79_1","volume-title":"Sankalan Pal Chowdhury, and Maria Christakis","author":"Zhang Fuyuan","year":"2020","unstructured":"Fuyuan Zhang , Sankalan Pal Chowdhury, and Maria Christakis . 2020 . DeepSearch: A Simple and Efective Blackbox Attack for Deep Neural Networks. In ESEC\/FSE. ACM. To appear. Fuyuan Zhang, Sankalan Pal Chowdhury, and Maria Christakis. 2020. DeepSearch: A Simple and Efective Blackbox Attack for Deep Neural Networks. In ESEC\/FSE. ACM. To appear."},{"key":"e_1_2_2_80_1","first-page":"132","article-title":"DeepRoad","author":"Zhang Mengshi","year":"2018","unstructured":"Mengshi Zhang , Yuqun Zhang , Lingming Zhang , Cong Liu , and Sarfraz Khurshid . 2018 . DeepRoad : GAN-Based Metamorphic Testing and Input Validation Framework for Autonomous Driving Systems. In ASE. ACM , 132 - 142 . Mengshi Zhang, Yuqun Zhang, Lingming Zhang, Cong Liu, and Sarfraz Khurshid. 2018. DeepRoad: GAN-Based Metamorphic Testing and Input Validation Framework for Autonomous Driving Systems. In ASE. ACM, 132-142.","journal-title":"In ASE. 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