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Lipics-Vol192-Forc2021-Complete.Pdf (17 2nd Symposium on Foundations of Responsible Computing FORC 2021, June 9–11, 2021, Virtual Conference Edited by Katrina Ligett Swati Gupta L I P I c s – Vo l . 192 – FORC 2021 www.dagstuhl.de/lipics Editors Katrina Ligett Hebrew University of Jerusalem, Israel [email protected] Swati Gupta Georgia Institute of Technology, Atlanta, Georgia, United States [email protected] ACM Classifcation 2012 Security and privacy → Privacy-preserving protocols; Theory of computation → Machine learning theory; Theory of computation → Design and analysis of algorithms; Mathematics of computing → Probability and statistics; Social and professional topics → Computing / technology policy; Computing methodologies → Supervised learning; Security and privacy; Applied computing → Law; Applied computing → Voting / election technologies; Computing methodologies → Machine learning; Computing methodologies → Ranking ISBN 978-3-95977-187-0 Published online and open access by Schloss Dagstuhl – Leibniz-Zentrum für Informatik GmbH, Dagstuhl Publishing, Saarbrücken/Wadern, Germany. Online available at https://www.dagstuhl.de/dagpub/978-3-95977-187-0. Publication date June, 2021 Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografe; detailed bibliographic data are available in the Internet at https://portal.dnb.de. License This work is licensed under a Creative Commons Attribution 4.0 International license (CC-BY 4.0): https://creativecommons.org/licenses/by/4.0/legalcode. In brief, this license authorizes each and everybody to share (to copy, distribute and transmit) the work under the following conditions, without impairing or restricting the authors’ moral rights: Attribution: The work must be attributed to its authors. The copyright is retained by the corresponding authors. Digital Object Identifer: 10.4230/LIPIcs.FORC.2021.0 ISBN 978-3-95977-187-0 ISSN 1868-8969 https://www.dagstuhl.de/lipics 0:iii LIPIcs – Leibniz International Proceedings in Informatics LIPIcs is a series of high-quality conference proceedings across all felds in informatics. LIPIcs volumes are published according to the principle of Open Access, i.e., they are available online and free of charge. Editorial Board Luca Aceto (Chair, Gran Sasso Science Institute and Reykjavik University) Christel Baier (TU Dresden) Mikolaj Bojanczyk (University of Warsaw) Roberto Di Cosmo (INRIA and University Paris Diderot) Javier Esparza (TU München) Meena Mahajan (Institute of Mathematical Sciences) Anca Muscholl (University Bordeaux) Luke Ong (University of Oxford) Catuscia Palamidessi (INRIA) Thomas Schwentick (TU Dortmund) Raimund Seidel (Saarland University and Schloss Dagstuhl – Leibniz-Zentrum für Informatik) ISSN 1868-8969 https://www.dagstuhl.de/lipics FO R C 2 0 2 1 Contents Preface Katrina Ligett and Swati Gupta ................................................. 0:vii Regular Papers Privately Answering Counting Queries with Generalized Gaussian Mechanisms Arun Ganesh and Jiazheng Zhao . 1:1–1:18 An Algorithmic Framework for Fairness Elicitation Christopher Jung, Michael Kearns, Seth Neel, Aaron Roth, Logan Stapleton, and Zhiwei Steven Wu . 2:1–2:19 On the Computational Tractability of a Geographic Clustering Problem Arising in Redistricting Vincent Cohen-Addad, Philip N. Klein, Dániel Marx, Archer Wheeler, and Christopher Wolfram . 3:1–3:18 A Possibility in Algorithmic Fairness: Can Calibration and Equal Error Rates Be Reconciled? Claire Lazar Reich and Suhas Vijaykumar . 4:1–4:21 Census TopDown: The Impacts of Diferential Privacy on Redistricting Aloni Cohen, Moon Duchin, JN Matthews, and Bhushan Suwal . 5:1–5:22 Lexicographically Fair Learning: Algorithms and Generalization Emily Diana, Wesley Gill, Ira Globus-Harris, Michael Kearns, Aaron Roth, and Saeed Sharif-Malvajerdi . 6:1–6:23 Causal Intersectionality and Fair Ranking Ke Yang, Joshua R. Loftus, and Julia Stoyanovich . 7:1–7:20 2nd Symposium on Foundations of Responsible Computing (FORC 2021). Editors: Katrina Ligett and Swati Gupta Leibniz International Proceedings in Informatics Schloss Dagstuhl – Leibniz-Zentrum für Informatik, Dagstuhl Publishing, Germany Preface The Symposium on Foundations of Responsible Computing (FORC), now in its second year, is a forum for mathematically rigorous research in computation and society writ large. The Symposium aims to catalyze the formation of a community supportive of the application of theoretical computer science, statistics, economics, and other relevant analytical felds to problems of pressing and anticipated societal concern. Twenty-four papers were selected to appear at FORC 2021, held virtually due to the COVID-19 pandemic, on June 9–11, 2021. The 24 papers were selected by the program committee, with the help of additional expert reviewers, out of 52 submissions. FORC 2021 ofered two submission tracks: archival-option (giving authors of selected papers the option to appear in this proceedings volume) and non-archival (in order to accommodate a variety of publication cultures, and to ofer a venue to showcase FORC-relevant work that will appear or has recently appeared in another venue). Seven archival-option and 17 non-archival submissions were selected for the program. Thank you to the entire program committee and to the external reviewers for their hard work during the review process amid the challenging conditions of the pandemic. It has been an honor and a pleasure to work together with you to shape the program of this young conference. Finally, we would like to thank our generous sponsors: the Simons Collaboration on the Theory of Algorithmic Fairness and the Harvard Center of Mathematical Sciences and Applications (CSMA) for partial conference support. Katrina Ligett, Jerusalem Swati Gupta, Atlanta, Georgia April 19, 2021 2nd Symposium on Foundations of Responsible Computing (FORC 2021). Editors: Katrina Ligett and Swati Gupta Leibniz International Proceedings in Informatics Schloss Dagstuhl – Leibniz-Zentrum für Informatik, Dagstuhl Publishing, Germany Privately Answering Counting Queries with Generalized Gaussian Mechanisms Arun Ganesh ! Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, CA, USA Jiazheng Zhao ! Computer Science Department, Stanford University, CA, USA Abstract We give the frst closed-form privacy guarantees for the Generalized Gaussian mechanism (the p mechanism that adds noise x to a vector with probability proportional to exp(−(||x||p/σ) ) for some σ, p), in the setting of answering k counting (i.e. sensitivity-1) queries about a database with (ϵ, δ)-diferential privacy (in particular, with low ℓ∞-error). Just using Generalized Gaussian noise, we obtain a mechanism such that if the true answers to the queries are the vector d, the mechanism outputs answers d˜ with the ℓ∞-error guarantee: ! pk log log k log(1/δ) E ||d˜− d|| = O . ∞ ϵ This matches the error bound of [18], but using a much simpler mechanism. By composing this mechanism with the sparse vector mechanism (generalizing a technique of [18]), we obtain √ √ a mechanism improving the k log log k dependence on k to k log log log k, Our main technical contribution is showing that certain powers of Generalized Gaussians, which follow a Generalized Gamma distribution, are sub-gamma. p In subsequent work, the optimal ℓ∞-error bound of O( k log(1/δ)/ϵ) has been achieved by [4] and [9] independently. However, the Generalized Gaussian mechanism has some qualitative advant- ages over the mechanisms used in these papers which may make it of interest to both practitioners and theoreticians, both in the setting of answering counting queries and more generally. 2012 ACM Subject Classifcation Security and privacy → Privacy-preserving protocols Keywords and phrases Diferential privacy, counting queries, Generalized Gaussians Digital Object Identifer 10.4230/LIPIcs.FORC.2021.1 Related Version Previous Version: https://arxiv.org/abs/2010.01457 Funding Arun Ganesh: Supported in part by NSF Award CCF-1535989. Acknowledgements The inspiration for this project was a suggestion by Kunal Talwar that Gen- eralized Gaussians could achieve the same asymptotic worst-case errors for query response as the mechanism of Steinke and Ullman. In particular, he suggested a proof sketch of a statement similar to Lemma 14 which was the basis for our proof that lemma. We are also thankful to the anonymous reviewers for multiple helpful suggestions on improving the paper. 1 Introduction A fundamental question in data analysis is to, given a database, release answers to k numerical queries about a database d, balancing the goals of preserving the privacy of the individuals whose data comprises the database and preserving the utility of the answers to the queries. A standard formal guarantee for privacy is (ϵ, δ)-diferential privacy [6, 5]. A mechanism M that takes database d as input and outputs (a distribution over) answers d˜ to the queries is (ϵ, δ)-diferentially private if for any two databases d, d′ which difer by only one individual and for any set of outcomes S, we have: © Arun Ganesh and Jiazheng Zhao; licensed under Creative Commons License CC-BY 4.0 2nd Symposium on Foundations of Responsible Computing (FORC 2021). Editors: Katrina Ligett and Swati Gupta; Article No. 1; pp. 1:1–1:18 Leibniz International Proceedings in Informatics Schloss Dagstuhl – Leibniz-Zentrum für Informatik, Dagstuhl Publishing, Germany 1:2 Privately Answering Counting Queries with Generalized Gaussian
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