The Algorithmic Foundations of Differential Privacy

The Algorithmic Foundations of Differential Privacy PDF Author: Cynthia Dwork
Publisher:
ISBN: 9781601988188
Category : Computers
Languages : en
Pages : 286

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Book Description
The problem of privacy-preserving data analysis has a long history spanning multiple disciplines. As electronic data about individuals becomes increasingly detailed, and as technology enables ever more powerful collection and curation of these data, the need increases for a robust, meaningful, and mathematically rigorous definition of privacy, together with a computationally rich class of algorithms that satisfy this definition. Differential Privacy is such a definition. The Algorithmic Foundations of Differential Privacy starts out by motivating and discussing the meaning of differential privacy, and proceeds to explore the fundamental techniques for achieving differential privacy, and the application of these techniques in creative combinations, using the query-release problem as an ongoing example. A key point is that, by rethinking the computational goal, one can often obtain far better results than would be achieved by methodically replacing each step of a non-private computation with a differentially private implementation. Despite some powerful computational results, there are still fundamental limitations. Virtually all the algorithms discussed herein maintain differential privacy against adversaries of arbitrary computational power -- certain algorithms are computationally intensive, others are efficient. Computational complexity for the adversary and the algorithm are both discussed. The monograph then turns from fundamentals to applications other than query-release, discussing differentially private methods for mechanism design and machine learning. The vast majority of the literature on differentially private algorithms considers a single, static, database that is subject to many analyses. Differential privacy in other models, including distributed databases and computations on data streams, is discussed. The Algorithmic Foundations of Differential Privacy is meant as a thorough introduction to the problems and techniques of differential privacy, and is an invaluable reference for anyone with an interest in the topic.

The Algorithmic Foundations of Differential Privacy

The Algorithmic Foundations of Differential Privacy PDF Author: Cynthia Dwork
Publisher:
ISBN: 9781601988188
Category : Computers
Languages : en
Pages : 286

Get Book Here

Book Description
The problem of privacy-preserving data analysis has a long history spanning multiple disciplines. As electronic data about individuals becomes increasingly detailed, and as technology enables ever more powerful collection and curation of these data, the need increases for a robust, meaningful, and mathematically rigorous definition of privacy, together with a computationally rich class of algorithms that satisfy this definition. Differential Privacy is such a definition. The Algorithmic Foundations of Differential Privacy starts out by motivating and discussing the meaning of differential privacy, and proceeds to explore the fundamental techniques for achieving differential privacy, and the application of these techniques in creative combinations, using the query-release problem as an ongoing example. A key point is that, by rethinking the computational goal, one can often obtain far better results than would be achieved by methodically replacing each step of a non-private computation with a differentially private implementation. Despite some powerful computational results, there are still fundamental limitations. Virtually all the algorithms discussed herein maintain differential privacy against adversaries of arbitrary computational power -- certain algorithms are computationally intensive, others are efficient. Computational complexity for the adversary and the algorithm are both discussed. The monograph then turns from fundamentals to applications other than query-release, discussing differentially private methods for mechanism design and machine learning. The vast majority of the literature on differentially private algorithms considers a single, static, database that is subject to many analyses. Differential privacy in other models, including distributed databases and computations on data streams, is discussed. The Algorithmic Foundations of Differential Privacy is meant as a thorough introduction to the problems and techniques of differential privacy, and is an invaluable reference for anyone with an interest in the topic.

Algorithmic Results in List Decoding

Algorithmic Results in List Decoding PDF Author: Venkatesan Guruswami
Publisher: Now Publishers Inc
ISBN: 1601980043
Category : Computers
Languages : en
Pages : 110

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Book Description
Algorithmic Results in List Decoding introduces and motivates the problem of list decoding, and discusses the central algorithmic results of the subject, culminating with the recent results on achieving "list decoding capacity." The main technical focus is on giving a complete presentation of the recent algebraic results achieving list decoding capacity, while pointers or brief descriptions are provided for other works on list decoding. Algorithmic Results in List Decoding is intended for scholars and graduate students in the fields of theoretical computer science and information theory. The author concludes by posing some interesting open questions and suggests directions for future work.

Coding for Interactive Communication

Coding for Interactive Communication PDF Author: Ran Gelles
Publisher:
ISBN: 9781680833461
Category : Computers
Languages : en
Pages : 182

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Book Description
This monograph provides the reader with a comprehensive view on the foundations of coding for interactive communication. It reviews the basic features of coding schemes in the interactive setting, and surveys the main techniques used in designing such schemes.

Arithmetic Circuits

Arithmetic Circuits PDF Author: Amir Shpilka
Publisher: Now Publishers Inc
ISBN: 1601984006
Category : Computers
Languages : en
Pages : 193

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Book Description
A large class of problems in symbolic computation can be expressed as the task of computing some polynomials; and arithmetic circuits form the most standard model for studying the complexity of such computations. This algebraic model of computation attracted a large amount of research in the last five decades, partially due to its simplicity and elegance. Being a more structured model than Boolean circuits, one could hope that the fundamental problems of theoretical computer science, such as separating P from NP, will be easier to solve for arithmetic circuits. However, in spite of the appearing simplicity and the vast amount of mathematical tools available, no major breakthrough has been seen. In fact, all the fundamental questions are still open for this model as well. Nevertheless, there has been a lot of progress in the area and beautiful results have been found, some in the last few years. As examples we mention the connection between polynomial identity testing and lower bounds of Kabanets and Impagliazzo, the lower bounds of Raz for multilinear formulas, and two new approaches for proving lower bounds: Geometric Complexity Theory and Elusive Functions. The goal of this monograph is to survey the field of arithmetic circuit complexity, focusing mainly on what we find to be the most interesting and accessible research directions. We aim to cover the main results and techniques, with an emphasis on works from the last two decades. In particular, we discuss the recent lower bounds for multilinear circuits and formulas, the advances in the question of deterministically checking polynomial identities, and the results regarding reconstruction of arithmetic circuits. We do, however, also cover part of the classical works on arithmetic circuits. In order to keep this monograph at a reasonable length, we do not give full proofs of most theorems, but rather try to convey the main ideas behind each proof and demonstrate it, where possible, by proving some special cases.

PCK50

PCK50 PDF Author: Dina Q. Goldin
Publisher: Association for Computing Machinery (ACM)
ISBN:
Category : Computers
Languages : en
Pages : 122

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Book Description


Average-Case Complexity

Average-Case Complexity PDF Author: Andrej Bogdanov
Publisher: Now Publishers Inc
ISBN: 1933019492
Category : Computers
Languages : en
Pages : 1

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Book Description
Average-Case Complexity is a thorough survey of the average-case complexity of problems in NP. The study of the average-case complexity of intractable problems began in the 1970s, motivated by two distinct applications: the developments of the foundations of cryptography and the search for methods to "cope" with the intractability of NP-hard problems. This survey looks at both, and generally examines the current state of knowledge on average-case complexity. Average-Case Complexity is intended for scholars and graduate students in the field of theoretical computer science. The reader will also discover a number of results, insights, and proof techniques whose usefulness goes beyond the study of average-case complexity.

Semialgebraic Proofs and Efficient Algorithm Design

Semialgebraic Proofs and Efficient Algorithm Design PDF Author: Noah Fleming
Publisher:
ISBN: 9781680836363
Category : Computers
Languages : en
Pages : 234

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Book Description
The book provides the advanced reader with a deep insight into the exciting line of research, namely, proof that a solution exists has enabled an algorithm to find that solution itself with applications in many areas of computer science. It will inspire readers in deploying the techniques in their own further research.

Automatic Sequences

Automatic Sequences PDF Author: Jean-Paul Allouche
Publisher: Cambridge University Press
ISBN: 9780521823326
Category : Computers
Languages : en
Pages : 592

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Book Description
Uniting dozens of seemingly disparate results from different fields, this book combines concepts from mathematics and computer science to present the first integrated treatment of sequences generated by 'finite automata'. The authors apply the theory to the study of automatic sequences and their generalizations, such as Sturmian words and k-regular sequences. And further, they provide applications to number theory (particularly to formal power series and transcendence in finite characteristic), physics, computer graphics, and music. Starting from first principles wherever feasible, basic results from combinatorics on words, numeration systems, and models of computation are discussed. Thus this book is suitable for graduate students or advanced undergraduates, as well as for mature researchers wishing to know more about this fascinating subject. Results are presented from first principles wherever feasible, and the book is supplemented by a collection of 460 exercises, 85 open problems, and over 1600 citations to the literature.

Elements of Finite Model Theory

Elements of Finite Model Theory PDF Author: Leonid Libkin
Publisher: Springer Science & Business Media
ISBN: 3662070030
Category : Mathematics
Languages : en
Pages : 320

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Book Description
Emphasizes the computer science aspects of the subject. Details applications in databases, complexity theory, and formal languages, as well as other branches of computer science.

On the Power of Small-Depth Computation

On the Power of Small-Depth Computation PDF Author: Emanuele Viola
Publisher: Now Publishers Inc
ISBN: 160198300X
Category : Computers
Languages : en
Pages : 84

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Book Description
In this work we discuss selected topics on small-depth computation, presenting a few unpublished proofs along the way. The four sections contain: (1) A unified treatment of the challenge of exhibiting explicit functions that have small correlation with low-degree polynomials over {0, 1}.(2) An unpublished proof that small bounded-depth circuits (AC0) have exponentially small correlation with the parity function. The proof is due to Klivans and Vadhan; it builds upon and simplifies previous ones. (3) Valiant's simulation of log-depth linear-size circuits of fan-in 2 by sub-exponential size circuits of depth 3 and unbounded fan-in. To our knowledge, a proof of this result has never appeared in full. (4) Applebaum, Ishai, and Kushilevitz's cryptography in bounded depth.