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Local Privacy and Statistical Minimax Rates
2013
2013 IEEE 54th Annual Symposium on Foundations of Computer Science
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When combined with minimax techniques such as Le Cam's and Fano's methods, these inequalities allow for a precise characterization of statistical rates under local privacy constraints. ...
Working under local differential privacy-a model of privacy in which data remains private even from the statistician or learner-we study the tradeoff between privacy guarantees and the utility of the resulting ...
Army Research Office under grant number W911NF-11-1-0391, and Office of Naval Research MURI grant N00014-11-1-0688. ...
doi:10.1109/focs.2013.53
dblp:conf/focs/DuchiJW13
fatcat:7giskrwqdjc5tpytgf4tdg7oby
Local privacy and statistical minimax rates
2013
2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton)
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When combined with minimax techniques such as Le Cam's and Fano's methods, these inequalities allow for a precise characterization of statistical rates under local privacy constraints. ...
Working under local differential privacy-a model of privacy in which data remains private even from the statistician or learner-we study the tradeoff between privacy guarantees and the utility of the resulting ...
Army Research Office under grant number W911NF-11-1-0391, and Office of Naval Research MURI grant N00014-11-1-0688. ...
doi:10.1109/allerton.2013.6736718
dblp:conf/allerton/DuchiJW13
fatcat:eto4hsyebfcmtng4emvtynhrs4
Local Privacy, Data Processing Inequalities, and Statistical Minimax Rates
[article]
2014
arXiv
pre-print
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When combined with standard minimax techniques, including the Le Cam, Fano, and Assouad methods, these inequalities allow for a precise characterization of statistical rates under local privacy constraints ...
Working under a model of privacy in which data remains private even from the statistician, we study the tradeoff between privacy guarantees and the utility of the resulting statistical estimators. ...
JCD was partially supported by a Facebook Graduate Fellowship and an NDSEG fellowship. Our work was supported ...
arXiv:1302.3203v4
fatcat:tb6nrh3rizcwvhujbwwgbu6dfe
Minimax optimal goodness-of-fit testing for densities and multinomials under a local differential privacy constraint
[article]
2021
arXiv
pre-print
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We establish an upper bound on the separation distance associated with this test, and a matching lower bound on the minimax separation rates of testing under non-interactive privacy in the case that f_ ...
To the best of our knowledge, we provide the first minimax optimal test and associated private transformation under a local differential privacy constraint over Besov balls in the continuous setting, quantifying ...
The main question is whether the minimax rates are affected by the local privacy constraint and to quantify the degradation of the rate in that case. ...
arXiv:2002.04254v3
fatcat:ybdbxqgd2zfm3otr5fh4yn5jda
Minimax-Optimal Privacy-Preserving Sparse PCA in Distributed Systems
2018
International Conference on Artificial Intelligence and Statistics
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DPS-PCA can recover the leading eigenspace of the population covariance at a geometric convergence rate, and simultaneously achieves the optimal minimax statistical error for high-dimensional data. ...
Our algorithm provides fine-tuned control over the tradeoff between estimation accuracy and privacy preservation. ...
Other works such as [9, 42, 44] studied the theoretical tradeoff between the minimax statistical rate and the local privacy level imposed on the initial data. ...
dblp:conf/aistats/GeWWL18
fatcat:bobp3x5u5vcurol6vsdmp3ukpe
Minimax Optimal Procedures for Locally Private Estimation
[article]
2017
arXiv
pre-print
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These inequalities allow for a precise characterization of statistical rates under local privacy constraints and the development of provably (minimax) optimal estimation procedures. ...
Working under a model of privacy in which data remains private even from the statistician, we study the tradeoff between privacy guarantees and the risk of the resulting statistical estimators. ...
Army Research Office under grant number W911NF-11-1-0391, Office of Naval Research MURI grant N00014-11-1-0688, and National Science Foundation (NSF) grants CCF-1553086 and CAREER-1553086. ...
arXiv:1604.02390v2
fatcat:ovynqnrecvd5hagbffzvq7jeuu
Local Privacy and Minimax Bounds: Sharp Rates for Probability Estimation
[article]
2013
arXiv
pre-print
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We give sharp minimax rates of convergence for estimation in these locally private settings, exhibiting fundamental tradeoffs between privacy and convergence rate, as well as providing tools to allow movement ...
along the privacy-statistical efficiency continuum. ...
Army Research Office under grant number W911NF-11-1-0391, and Office of Naval Research MURI grant N00014-11-1-0688. ...
arXiv:1305.6000v1
fatcat:qyija63hunh5vat2aowbsjxvqu
Instance-Optimal Differentially Private Estimation
[article]
2022
arXiv
pre-print
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In this work, we study local minimax convergence estimation rates subject to ϵ-differential privacy. ...
We construct locally minimax differentially private estimators for one-parameter exponential families and estimating the tail rate of a distribution. ...
and Privacy Institute. ...
arXiv:2210.15819v1
fatcat:r2rnqlv4lrdmlm2xq5v2garxce
Blind Attacks on Machine Learners
2016
Neural Information Processing Systems
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For each attack, we analyze minimax rates of convergence and establish lower bounds on the learner's minimax risk, exhibiting limits on a learner's ability to learn under data injection attack even when ...
proportion of malicious data and some family to which the malicious distribution chosen by the attacker belongs. ...
Our work has strong connections to the analysis of minimax lower bounds in local differential privacy. ...
dblp:conf/nips/BeatsonWL16
fatcat:sl6a3l55tfeifcd56gvxyurhjy
Lower Bound of Locally Differentially Private Sparse Covariance Matrix Estimation
2019
Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence
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In this paper, we study the sparse covariance matrix estimation problem in the local differential privacy model, and give a non-trivial lower bound on the non-interactive private minimax risk in the metric ...
as a general method for bounding the private minimax risk of matrix-related estimation problems. ...
Classical Minimax Risk Since all of our lower bounds are in the form of private minimax risk, we first introduce the classical statistical minimax risk before discussing its locally differentially private ...
doi:10.24963/ijcai.2019/665
dblp:conf/ijcai/Wang019
fatcat:tg3ejmshd5bkhfjrvzw4i4napm
Minimax density estimation in the adversarial framework under local differential privacy
[article]
2024
arXiv
pre-print
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To this end, we study minimax rates under local differential privacy over Sobolev spaces. ...
Next, we introduce a new Coordinate block privacy mechanism that guarantees local differential privacy, which, coupled with a projection estimator, achieves the minimax optimal rates. ...
We focus on non interactive local privacy mechanisms satisfying Equation (1). In statistical inference under privacy constraints, we do not have access to the original data. ...
arXiv:2403.18357v1
fatcat:blh6dwcpu5e6jozvtujc35gg2a
On robustness and local differential privacy
[article]
2022
arXiv
pre-print
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the local differential privacy (LDP) constraints. ...
Overall, our work showcases a promising prospect of joint study for robustness and local differential privacy. ...
Acknowledgements We are thankful to the anonymous referees for detailed comments and suggestions, which greatly improved the paper. ...
arXiv:2201.00751v2
fatcat:dok2brzijjdtdog76yigcgbhf4
Preserving Privacy of Continuous High-dimensional Data with Minimax Filters
2015
International Conference on Artificial Intelligence and Statistics
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Preserving privacy of high-dimensional and continuous data such as images or biometric data is a challenging problem. ...
similar or better target task accuracy and lower privacy risk, often significantly lower than previous methods. ...
Related work Utility-privacy trade-offs using the notion of differential privacy have been studied analytically, in particular in the context of the statistical estimation [20, 1, 3] and learnability ...
dblp:conf/aistats/Hamm15
fatcat:jxf6rrladzel3gtmovxaj3icky
The Right Complexity Measure in Locally Private Estimation: It is not the Fisher Information
[article]
2020
arXiv
pre-print
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private estimation and learning problems by developing the local minimax risk. ...
We identify fundamental tradeoffs between statistical utility and privacy under local models of privacy in which data is kept private even from the statistician, providing instance-specific bounds for ...
In work independent of and contemporaneous to our own, Rohde and Steinberger [47] build off of [25] to show that (non-local) minimax rates of convergence under ε-local differential privacy are frequently ...
arXiv:1806.05756v3
fatcat:5myltsf4xvdwzktqwsejrj4kku
Random Differential Privacy
2013
Journal of Privacy and Confidentiality
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We show how to release an RDP histogram and we show that RDP histograms are much more accurate than histograms obtained using ordinary differential privacy. ...
We propose a relaxed privacy definition called {\em random differential privacy} (RDP). ...
We introduce a concept which parallels minimaxity in statistics, and identify the minimax risk for a differentially private histogram. ...
doi:10.29012/jpc.v4i2.621
fatcat:e4snhnf6inhqthcvfqtw5gmr5q
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