DOCSLIB.ORG

The Structure of Optimal Private Tests for Simple Hypotheses∗

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
The Structure of Optimal Private Tests for Simple Hypotheses∗ The Structure of Optimal Private Tests for Simple Hypotheses∗ Clément L. Canonne Gautam Kamath Audra McMillan Stanford University Simons Institute for the Theory of Boston University and Northeastern USA Computing University [email protected] USA USA [email protected] [email protected] Adam Smith Jonathan Ullman Boston University Northeastern University USA USA [email protected] [email protected] ABSTRACT of Computing (STOC ’19), June 23–26, 2019, Phoenix, AZ, USA. ACM, New Hypothesis testing plays a central role in statistical inference, and York, NY, USA, 12 pages. https://doi.org/10.1145/3313276.3316336 is used in many settings where privacy concerns are paramount. This work answers a basic question about privately testing simple 1 INTRODUCTION hypotheses: given two distributions P and Q, and a privacy level ε, how many i.i.d. samples are needed to distinguish P from Q subject Hypothesis testing plays a central role in statistical inference, anal- to ε-differential privacy, and what sort of tests have optimal sample ogous to that of decision or promise problems in computability and complexity? Specifically, we characterize this sample complexity complexity theory. A hypothesis testing problem is specified by two up to constant factors in terms of the structure of P and Q and the disjoint sets of probability distributions over the same set, called H H privacy level ε, and show that this sample complexity is achieved by hypotheses, 0 and 1. An algorithm T for this problem, called a a certain randomized and clamped variant of the log-likelihood ratio hypothesis test, is given a sample x from an unknown distribution ¹ º test. Our result is an analogue of the classical Neyman–Pearson P, with the requirement that T x should, with high probability, 2 H 2 H lemma in the setting of private hypothesis testing. We also give output “0” if P 0, and “1” if P 1. There is no requirement H [H an application of our result to the private change-point detection. for distributions outside of 0 1. In computer science, such Our characterization applies more generally to hypothesis tests problems sometimes go by the name distribution property testing. satisfying essentially any notion of algorithmic stability, which Hypothesis testing problems are important in their own right, as is known to imply strong generalization bounds in adaptive data they formalize yes-or-no questions about an underlying population analysis, and thus our results have applications even when privacy based on a randomly drawn sample, such as whether education is not a primary concern. strongly influences life expectancy, or whether a particular med- ical treatment is effective. Successful hypothesis tests with high CCS CONCEPTS degrees of confidence remain the gold standard for publication in top journals in the physical and social sciences. Hypothesis testing • Mathematics of computing → Hypothesis testing and con- problems are also important in the theory of statistics and machine fidence interval computation; • Security and privacy; • The- learning, as many lower bounds for estimation and optimization ory of computation → Design and analysis of algorithms; problems are obtained by reducing from hypothesis testing. KEYWORDS This paper aims to understand the structure and sample complex- ity of optimal hypothesis tests subject to strong privacy guarantees. differential privacy, hypothesis testing Large collections of personal information are now ubiquitous, but ACM Reference Format: their use for effective scientific discovery remains limited bycon- Clément L. Canonne, Gautam Kamath, Audra McMillan, Adam Smith, and Jonathan cerns about privacy. In addition to the well-understood settings of Ullman. 2019. The Structure of Optimal Private Tests for Simple Hypotheses. data collected during scientific studies, such as clinical experiments In Proceedings of the 51st Annual ACM SIGACT Symposium on the Theory and surveys, many other data sources where privacy concerns are ∗In memory of Stephen E. Fienberg (1942–2016). A full version of this paper is available paramount are now being tapped for socially beneficial analysis, as [19]. such as Social Science One [70], which aims to allow access to data collected by Facebook and similar companies. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed We study algorithms that satisfy differential privacy (DP) [32], a for profit or commercial advantage and that copies bear this notice and the full citation restriction on the algorithm that ensures meaningful privacy guar- on the first page. Copyrights for components of this work owned by others than the antees against an adversary with arbitrary side information [47]. author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission Differential privacy has come to be the de facto standard forthe and/or a fee. Request permissions from [email protected]. analysis of private data, used as a measure of privacy for data STOC ’19, June 23–26, 2019, Phoenix, AZ, USA analysis systems at Google [36], Apple [25], and the U.S. Census © 2019 Copyright held by the owner/author(s). Publication rights licensed to ACM. ACM ISBN 978-1-4503-6705-9/19/06...$15.00 Bureau [24]. Differential privacy and related distributional notions https://doi.org/10.1145/3313276.3316336 of algorithmic stability can be crucial for statistical validity even 310 STOC ’19, June 23–26, 2019, Phoenix, AZ, USA Canonne, Kamath, McMillan, Smith, Ullman when confidentiality is not a direct concern, as they provide gener- problems is delicate. We know there are regimes where statisti- alization guarantees in an adaptive setting [29]. cal problems can be solved privately “for free” asymptotically (e.g. Consider an algorithm that takes a set of data points from a set [20, 32, 45, 69]) and others where there is a significant cost, even for X—where each point belongs to some individual—and produces relaxed definitions of privacy (e.g. [15, 35]), and we remain far from some public output. We say the algorithm is differentially private a general characterization of the statistical cost of privacy. Duchi, if no single data point can significantly impact the distribution on Jordan, and Wainwright [26] give a characterization for the special outputs. Formally, we say two data sets x; x 0 2 Xn of the same size case of simple tests by local differentially private algorithms, a more are neighbors if they differ in at most one entry. restricted setting where samples are randomized individually, and Definition 1.1 ([32]). A randomized algorithm T taking inputs in the test makes a decision based on these randomized samples. Our X∗ and returning random outputs in a space with event set S is characterization in the general case is more involved, as it exhibits ε-differentially private if for all n ≥ 1, for all neighboring data sets several distinct regimes for the parameter ε. x; x 0 2 Xn, and for all events S 2 S, P »T ¹xº 2 S¼ ≤ eε P »T ¹x 0º 2 S¼. Our analysis relies on a number of tools of independent interest: For the special case of tests returning output in f0; 1g, the output a characterization of private hypothesis testing in terms of cou- Xn distribution is characterized by the probability of returning “1”. plings between distributions on , and a novel interpretation of Letting д¹xº = P »T ¹xº = 1¼, we can equivalently require that Hellinger distance as the advantage over random guessing of a specific, randomized likelihood ratio test. д¹xº 1 − д¹xº ε max 0 ; 0 ≤ e : д¹x º 1 − д¹x º The Importance of Simple Hypotheses. Many of the hypothe- For algorithms with binary outputs, this definition is essentially ses that arise in application are not simple, but are so-called com- equivalent to all other commonly studied notions of privacy and dis- posite hypotheses. For example, deciding if two features are inde- tributional algorithmic stability (see “Connections to Algorithmic pendent or far from it involves sets H0 and H1 each containing Stability”, below). many distributions. Yet many of those tests can be reduced to sim- Contribution: The Sample Complexity of Private Tests for ple ones. For example, deciding if the mean of a Gaussian is less Simple Hypotheses. We focus on the setting of i.i.d. data and than 0 or greater than 1 can be reduced to testing if the mean is either 0 or 1. Furthermore, simple tests arise in lower bounds for singleton hypotheses H0; H1, which are called simple hypotheses. estimation—the well-known characterization of parametric estima- The algorithm is given a sample of n points x1;:::; xn drawn i.i.d. from one of two distributions, P or Q, and attempts to determine tion in terms of Fisher information is obtained by showing that n n the Fisher information measures variability in the Hellinger dis- which one generated the input. That is, H0 = fP g and H1 = fQ g. We investigate the following question. tance and then employing the Hellinger-based characterization of nonprivate simple tests (e.g. [12, Chap. II.31.2, p.180]). Given two distributions P and Q and a privacy param- Our characterization of private testing implies similar lower eter ε > 0, what is the minimum number of samples P;Q bounds for estimation (along the lines of lower bounds of Duchi (denoted SCε ) needed for an ε-differentially private and Ruan [27] in the local model of differential privacy). test to reliably distinguish P from Q, and what are op- timal private tests? Connection to Algorithmic Stability. For hypothesis tests with These questions are well understood in the classical, nonprivate constant error probabilities, sample complexity bounds for differ- setting.
Load more

Recommended publications
  • Curriculum Vitae
    Curriculum Vitae Prof. Michal Feldman School of Computer Science, Tel-Aviv University Personal Details • Born: Israel, 1976 • Gender: Female • email: [email protected] Education • Ph.D.: Information Management and Systems, University of California at Berkeley, May 2005. Thesis title: Incentives for cooperation in peer-to-peer systems. • B.Sc.: Bar-Ilan University, Computer Science, Summa Cum Laude, June 1999. Academic Positions 2013 - present: Associate Professor, School of Computer Science, Tel-Aviv University, Israel. Associate Professor, School of Business Administration and Center for 2011 - 2013: the Study of Rationality, Hebrew University of Jerusalem, Israel. 2007 - 2011: Senior Lecturer, School of Business Administration and Center for the Study of Rationality, Hebrew University of Jerusalem, Israel. Additional Positions 2011 - 2013: Visiting Researcher (weekly visitor), Microsoft Research New England, Cambridge, MA, USA. 2011 - 2013: Visiting Professor, Harvard School of Engineering and Applied Sciences, Center for Research on Computation and Society, School of Computer Science, Cambridge, MA, USA (Marie Curie IOF program). 2008 - 2011: Senior Researcher (part-time), Microsoft Research in Herzliya, Israel. 2007 - 2013: Member, Center for the Study of Rationality, Hebrew University. 2005 - 2007: Post-Doctoral Fellow (Lady Davis fellowship), Hebrew University, School of Computer Science and Engineering. 2004: Ph.D. Intern, HP Labs, Palo Alto, California, USA. 1 Grants (Funding ID) • European Research Council (ERC) Starting Grant: \Algorithmic Mechanism Design - Beyond Truthfulness": 1.4 million Euro, 2013-2017. • FP7 Marie Curie International Outgoing Fellowship (IOF): \Innovations in Algorithmic Game Theory" (IAGT): 313,473 Euro, 2011-2014. • Israel Science Foundation (ISF) grant. \Equilibria Under Coalitional Covenants in Non-Cooperative Games - Existence, Quality and Computation:" 688,000 NIS (172,000 NIS /year), 2009-2013.
    [Show full text]
  • Limitations and Possibilities of Algorithmic Mechanism Design By
    Incentives, Computation, and Networks: Limitations and Possibilities of Algorithmic Mechanism Design by Yaron Singer A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Computer Science in the Graduate Division of the University of California, Berkeley Committee in charge: Professor Christos Papadimitriou, Chair Professor Shachar Kariv Professor Scott Shenker Spring 2012 Incentives, Computation, and Networks: Limitations and Possibilities of Algorithmic Mechanism Design Copyright 2012 by Yaron Singer 1 Abstract Incentives, Computation, and Networks: Limitations and Possibilities of Algorithmic Mechanism Design by Yaron Singer Doctor of Philosophy in Computer Science University of California, Berkeley Professor Christos Papadimitriou, Chair In the past decade, a theory of manipulation-robust algorithms has been emerging to address the challenges that frequently occur in strategic environments such as the internet. The theory, known as algorithmic mechanism design, builds on the foundations of classical mechanism design from microeconomics and is based on the idea of incentive compatible pro- tocols. Such protocols achieve system-wide objectives through careful design that ensures it is in every agent's best interest to comply with the protocol. As it turns out, however, implementing incentive compatible protocols as advocated in classical mechanism design the- ory often necessitates solving intractable problems. To address this, algorithmic mechanism design focuses on designing
    [Show full text]
  • Satisfiability and Evolution
    2014 IEEE Annual Symposium on Foundations of Computer Science Satisfiability and Evolution Adi Livnat Christos Papadimitriou Aviad Rubinstein Department of Biological Sciences Computer Science Division Computer Science Division Virginia Tech. University of California at Berkeley University of California at Berkeley [email protected] [email protected] [email protected] Gregory Valiant Andrew Wan Computer Science Department Simons Institute Stanford University University of California at Berkeley [email protected] [email protected] Abstract—We show that, if truth assignments on n variables genes are able to efficiently arise in polynomial populations reproduce through recombination so that satisfaction of a par- with recombination. In the standard view of evolution, a ticular Boolean function confers a small evolutionary advan- variant of a particular gene is more likely to spread across tage, then a polynomially large population over polynomially many generations (polynomial in n and the inverse of the initial a population if it makes its own contribution to the overall satisfaction probability) will end up almost surely consisting fitness, independent of the contributions of variants of other exclusively of satisfying truth assignments. We argue that this genes. How can complex, multi-gene traits spread in a theorem sheds light on the problem of the evolution of complex population? This may seem to be especially problematic adaptations. for multi-gene traits whose contribution to fitness does not Keywords-evolution; algorithms; Boolean functions decompose into small additive components associated with each gene variant —traits with the property that even if I. INTRODUCTION one gene variant is different from the one that is needed The TCS community has a long history of applying its for the right combination, there is no benefit, or even a net perspectives and tools to better understand the processes negative benefit.
    [Show full text]
  • A Decade of Lattice Cryptography
    Full text available at: http://dx.doi.org/10.1561/0400000074 A Decade of Lattice Cryptography Chris Peikert Computer Science and Engineering University of Michigan, United States Boston — Delft Full text available at: http://dx.doi.org/10.1561/0400000074 Foundations and Trends R in Theoretical Computer Science Published, sold and distributed by: now Publishers Inc. PO Box 1024 Hanover, MA 02339 United States Tel. +1-781-985-4510 www.nowpublishers.com [email protected] Outside North America: now Publishers Inc. PO Box 179 2600 AD Delft The Netherlands Tel. +31-6-51115274 The preferred citation for this publication is C. Peikert. A Decade of Lattice Cryptography. Foundations and Trends R in Theoretical Computer Science, vol. 10, no. 4, pp. 283–424, 2014. R This Foundations and Trends issue was typeset in LATEX using a class file designed by Neal Parikh. Printed on acid-free paper. ISBN: 978-1-68083-113-9 c 2016 C. Peikert All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, mechanical, photocopying, recording or otherwise, without prior written permission of the publishers. Photocopying. In the USA: This journal is registered at the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923. Authorization to photocopy items for in- ternal or personal use, or the internal or personal use of specific clients, is granted by now Publishers Inc for users registered with the Copyright Clearance Center (CCC). The ‘services’ for users can be found on the internet at: www.copyright.com For those organizations that have been granted a photocopy license, a separate system of payment has been arranged.
    [Show full text]
  • 6.5 X 11.5 Doublelines.P65
    Cambridge University Press 978-0-521-87282-9 - Algorithmic Game Theory Edited by Noam Nisan, Tim Roughgarden, Eva Tardos and Vijay V. Vazirani Copyright Information More information Algorithmic Game Theory Edited by Noam Nisan Hebrew University of Jerusalem Tim Roughgarden Stanford University Eva´ Tardos Cornell University Vijay V. Vazirani Georgia Institute of Technology © Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-87282-9 - Algorithmic Game Theory Edited by Noam Nisan, Tim Roughgarden, Eva Tardos and Vijay V. Vazirani Copyright Information More information cambridge university press Cambridge, New York,Melbourne, Madrid, Cape Town, Singapore, Sao˜ Paulo, Delhi Cambridge University Press 32 Avenue of the Americas, New York, NY 10013-2473, USA www.cambridge.org Information on this title: www.cambridge.org/9780521872829 C Noam Nisan, Tim Roughgarden, Eva´ Tardos, Vijay V. Vazirani 2007 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2007 Printed in the United States of America A catalog record for this book is available from the British Library. Library of Congress Cataloging in Publication Data Algorithmic game theory / edited by Noam Nisan ...[et al.]; foreword by Christos Papadimitriou. p. cm. Includes index. ISBN-13: 978-0-521-87282-9 (hardback) ISBN-10: 0-521-87282-0 (hardback) 1. Game theory. 2. Algorithms. I. Nisan, Noam. II. Title. QA269.A43 2007 519.3–dc22 2007014231 ISBN 978-0-521-87282-9 hardback Cambridge University Press has no responsibility for the persistence or accuracy of URLS for external or third-party Internet Web sites referred to in this publication and does not guarantee that any content on such Web sites is, or will remain, accurate or appropriate.
    [Show full text]
  • Linked Decompositions of Networks and the Power of Choice in Polya Urns
    Linked Decompositions of Networks and the Power of Choice in Polya Urns Henry Lin¤ Christos Amanatidisy Martha Sideriz Richard M. Karpx Christos H. Papadimitriou{ October 12, 2007 Abstract balls total, and each arriving ball is placed in the least loaded A linked decomposition of a graph with n nodes is a set of m bins, drawn independently at random with probability of subgraphs covering the n nodes such that all pairs of proportional to load. Our analysis shows that in our new subgraphs intersect; we seek linked decompositions such process, with high probability the bin loads become roughly p 2+² that all subgraphs have about n vertices, logarithmic balanced some time before O(n ) further balls have arrived diameter, and each vertex of the graph belongs to either and stay roughly balanced, regardless of how the initial O(n) one or two subgraphs. A linked decomposition enables balls were distributed, where ² > 0 can be arbitrarily small, many control and management functions to be implemented provided m is large enough. locally, such as resource sharing, maintenance of distributed directory structures, deadlock-free routing, failure recovery 1 Introduction and load balancing, without requiring any node to maintain Throwing balls into bins uniformly at random is well- information about the state of the network outside the known to produce relatively well-balanced occupancies subgraphs to which it belongs. Linked decompositions also with high probability. In contrast, when each new ball is enable e±cient routing schemes with small routing tables, added to a bin selected with probability proportional to which we describe in Section 5.
    [Show full text]
  • Sharing Non-Anonymous Costs of Multiple Resources Optimally
    Sharing Non-Anonymous Costs of Multiple Resources Optimally Max Klimm∗ Daniel Schmand† July 18, 2018 Abstract In cost sharing games, the existence and efficiency of pure Nash equi- libria fundamentally depends on the method that is used to share the resources’ costs. We consider a general class of resource allocation prob- lems in which a set of resources is used by a heterogeneous set of selfish users. The cost of a resource is a (non-decreasing) function of the set of its users. Under the assumption that the costs of the resources are shared by uniform cost sharing protocols, i.e., protocols that use only lo- cal information of the resource’s cost structure and its users to determine the cost shares, we exactly quantify the inefficiency of the resulting pure Nash equilibria. Specifically, we show tight bounds on prices of stabil- ity and anarchy for games with only submodular and only supermodular cost functions, respectively, and an asymptotically tight bound for games with arbitrary set-functions. While all our upper bounds are attained for the well-known Shapley cost sharing protocol, our lower bounds hold for arbitrary uniform cost sharing protocols and are even valid for games with anonymous costs, i.e., games in which the cost of each resource only depends on the cardinality of the set of its users. 1 Introduction Resource allocation problems are omnipresent in many areas of economics, com- puter science, and operations research with many applications, e.g., in routing, network design, and scheduling. Roughly speaking, when solving these prob- arXiv:1412.4456v2 [cs.GT] 4 Feb 2015 lems the central question is how to allocate a given set of resources to a set of potential users so as to optimize a given social welfare function.
    [Show full text]
  • Pairwise Independence and Derandomization
    Pairwise Independence and Derandomization Pairwise Independence and Derandomization Michael Luby Digital Fountain Fremont, CA, USA Avi Wigderson Institute for Advanced Study Princeton, NJ, USA [email protected] Boston – Delft Foundations and TrendsR in Theoretical Computer Science Published, sold and distributed by: now Publishers Inc. PO Box 1024 Hanover, MA 02339 USA Tel. +1-781-985-4510 www.nowpublishers.com [email protected] Outside North America: now Publishers Inc. PO Box 179 2600 AD Delft The Netherlands Tel. +31-6-51115274 A Cataloging-in-Publication record is available from the Library of Congress The preferred citation for this publication is M. Luby and A. Wigderson, Pairwise R Independence and Derandomization, Foundation and Trends in Theoretical Com- puter Science, vol 1, no 4, pp 237–301, 2005 Printed on acid-free paper ISBN: 1-933019-22-0 c 2006 M. Luby and A. Wigderson All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, mechanical, photocopying, recording or otherwise, without prior written permission of the publishers. Photocopying. In the USA: This journal is registered at the Copyright Clearance Cen- ter, Inc., 222 Rosewood Drive, Danvers, MA 01923. Authorization to photocopy items for internal or personal use, or the internal or personal use of specific clients, is granted by now Publishers Inc for users registered with the Copyright Clearance Center (CCC). The ‘services’ for users can be found on the internet at: www.copyright.com For those organizations that have been granted a photocopy license, a separate system of payment has been arranged.
    [Show full text]
  • Identifying the Roles of Race-Based Choice and Chance in High School Friendship Network Formation
    Identifying the roles of race-based choice and chance in high school friendship network formation Sergio Currarinia, Matthew O. Jacksonb,c,1, and Paolo Pind aDipartimento di Scienze Economiche, Università Ca′ Foscari di Venezia, and School for Advanced Studies in Venice, 30123 Venice, Italy; bDepartment of Economics, Stanford University, Stanford, CA 94305; cSanta Fe Institute, Santa Fe, NM 87501; and dDipartimento di Economia Politica, Università degli Studi di Siena, 53100 Siena, Italy Edited* by Christos Papadimitriou, University of California, Berkeley, CA, and approved January 13, 2010 (received for review October 12, 2009) Homophily, the tendency of people to associate with others similar preferences of the individual by careful observation of the choices to themselves, is observed in many social networks, ranging from that they make based on the opportunities that they have. We adapt friendships to marriages to business relationships, and is based on a these techniques for the analysis of social behavior and friendship variety of characteristics, including race, age, gender, religion, and formation. Here we infer students’ preferences by observing how the education. We present a technique for distinguishing two primary number of friendships they have changes with the racial composition sources of homophily: biases in the preferences of individuals over of their school. We employ the friendship formation model (3), here the types of their friends and biases in the chances that people meet extended to allow for differentbiases across race in both preferences individuals of other types. We use this technique to analyze racial and opportunities. Using a parameterized version of this model, we patterns in friendship networks in a set of American high schools are able to distinguish between the two primary sources of homo- from the Add Health dataset.
    [Show full text]
  • Preliminary Program (Ver
    Preliminary Program (ver. 12) 39th International Colloquium on Automata, Languages and Programming University of Warwick, July 9 – 13, 2012 39th ICALP 2012, University of Warwick Monday 9 July 2012 Invited Talk 08.45 – 09.00 Opening and Welcome Stefano Leonardi 09.00 – 10.00 On Multiple Keyword Sponsored Search Auctions with Budgets 10.00 – 10.30 COFFEE BREAK Track A1 Inge Li Gørtz, Viswanath Nagarajan and Rishi Saket 10.30 – 10.50 Stochastic Vehicle Routing with Recourse Nicole Megow, Martin Skutella, Jose Verschae and Andreas 10.55 – 11.15 Wiese The Power of Recourse for Online MST and TSP Yossi Azar and Iftah Gamzu 11.20 – 11.40 Efficient Submodular Function Maximization under Linear Packing Constraints Alberto Marchetti-Spaccamela, Cyriel Rutten, Suzanne van der 11.45 – 12.05 Ster and Andreas Wiese Assigning Sporadic Tasks to Unrelated Parallel Machines Siddharth Barman, Shuchi Chawla, David Malec and Seeun 12.10 – 12.30 Umboh Secretary Problems with Convex Costs Track C1 Ning Chen, Xiaotie Deng, Hongyang Zhang and Jie Zhang 10.30 – 10.50 Incentive Ratios of Fisher Markets Ilias Diakonikolas, Christos Papadimitriou, George 10.55 – 11.15 Pierrakos and Yaron Singer Efficiency-Revenue Trade-offs in Auctions Khaled Elbassioni 11.20 – 11.40 A QPTAS for -Envy-Free Profit-Maximizing Pricing on Line Graphs Elias Koutsoupias and Katia Papakonstantinopoulou 11.45 – 12.05 Contention Issues in Congestion Games Fedor Fomin, Petr Golovach, Jesper Nederlof and Michał 12.10 – 12.30 Pilipczuk Minimizing Rosenthal Potential in Multicast Games Page
    [Show full text]
  • Christos-Alexandros (Alex) Psomas
    CHRISTOS-ALEXANDROS (ALEX) PSOMAS Address: Gates-Hillman Center, Office #9116, Pittsburgh PA, USA 15213 Phone: (+1)5105178185 Email: [email protected] Website: http://www.cs.cmu.edu/∼cpsomas/ EMPLOYMENT Carnegie Mellon University, Pittsburgh PA, USA Post Doctoral Fellow hosted by Ariel Procaccia. 2017-present Microsoft Research, Redmond WA, USA Research Internship under the supervision of Nikhil R. Devanur. Summer 2015 International Computer Science Institute (ICSI), Berkeley CA, USA Research Internship under the supervision of Eric J. Friedman. Summers 2013 and 2014 National Center for Scientific Research ( NCSR ) "Demokritos", Athens, Greece Research Internship under the supervision of Sergios Petridis. March, 2011 - July, 2011 EDUCATION University of California, Berkeley, USA 2012-2017 Ph.D. in Computer Science Thesis: Algorithmic Mechanism Design in Dynamic Environments Advisor: Christos H. Papadimitriou University of Athens, Greece 2011-2012 M.Sc. in Logic, Algorithms and Computation GPA: 8.62/10 Thesis: Strategyproof Allocation of Multidimensional Tasks on Clusters Athens University of Economics and Business, Greece 2007-2011 B.S. in Computer Science GPA: 9.18/10 ( ranked 1st in a class of more than 200 students ) TEACHING EXPERIENCE Carnegie Mellon University, USA Instructor for the course Truth, Justice, and Algorithms. Fall 2018 Course website: http://www.cs.cmu.edu/∼15896/ University of California, Berkeley, USA Instructor for the course Discrete Mathematics and Probability Theory. Summer 2016 Course website: https://inst.eecs.berkeley.edu/∼cs70/su16/ Teaching assistant for the course Discrete Mathematics and Probability Theory. Spring 2016 CS Scholars Tutor for the course Discrete Mathematics and Probability Theory. Spring 2016 Teaching assistant for the course Efficient Algorithms and Intractable Problems.
    [Show full text]
  • The Algorithmic Foundations of Differential Privacy
    Full text available at: http://dx.doi.org/10.1561/0400000042 The Algorithmic Foundations of Differential Privacy Cynthia Dwork Microsoft Research, USA [email protected] Aaron Roth University of Pennsylvania, USA [email protected] Boston — Delft Full text available at: http://dx.doi.org/10.1561/0400000042 Foundations and TrendsR in Theoretical Computer Science Published, sold and distributed by: now Publishers Inc. PO Box 1024 Hanover, MA 02339 United States Tel. +1-781-985-4510 www.nowpublishers.com [email protected] Outside North America: now Publishers Inc. PO Box 179 2600 AD Delft The Netherlands Tel. +31-6-51115274 The preferred citation for this publication is C. Dwork and A. Roth. The Algorithmic Foundations of Differential Privacy. Foundations and TrendsR in Theoretical Computer Science, vol. 9, nos. 3–4, pp. 211–407, 2013. R This Foundations and Trends issue was typeset in LATEX using a class file designed by Neal Parikh. Printed on acid-free paper. ISBN: 978-1-60198-819-5 c 2014 C. Dwork and A. Roth All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, mechanical, photocopying, recording or otherwise, without prior written permission of the publishers. Photocopying. In the USA: This journal is registered at the Copyright Clearance Cen- ter, Inc., 222 Rosewood Drive, Danvers, MA 01923. Authorization to photocopy items for internal or personal use, or the internal or personal use of specific clients, is granted by now Publishers Inc for users registered with the Copyright Clearance Center (CCC).
    [Show full text]