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Locally differentially private estimation of nonlinear functionals of discrete distributions [article]

Cristina Butucea, Yann Issartel
2021 arXiv   pre-print
,x_n ∈ [K] are supposed i.i.d. and distributed according to an unknown discrete distribution p = (p_1,...,p_K). Only α-locally differentially private (LDP) samples z_1,...  ...  We study the problem of estimating non-linear functionals of discrete distributions in the context of local differential privacy. The initial data x_1,...  ...  Optimality of the results We give lower bounds over all estimators and all α-locally differentially private mechanisms.  ... 
arXiv:2107.03940v1 fatcat:ggwqf2g4nzh5td5vwnozakkkgu

Compressive Sensing Approaches for Sparse Distribution Estimation Under Local Privacy [article]

Zhongzheng Xiong, Jialin Sun, Xiaojun Mao, Jian Wang, Shan Ying, Zengfeng Huang
2022 arXiv   pre-print
In this paper, we consider the problem of discrete distribution estimation under local differential privacy constraints.  ...  Distribution estimation is one of the most fundamental estimation problems, which is widely studied in both non-private and private settings.  ...  CONCLUSION In this paper, we study sparse distribution estimation in the local differential privacy model.  ... 
arXiv:2012.02081v2 fatcat:2oev6kz7q5cgbisvlfpnf44fli

Lower Bound of Locally Differentially Private Sparse Covariance Matrix Estimation

Di Wang, Jinhui Xu
2019 Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence  
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.  ...  The goal of sparse covariance matrix estimation is to estimate the unknown matrix Σ based on samples { 1 , ⋯ , }, and the locally private version is to determine a locally differentially private estimator  ... 
doi:10.24963/ijcai.2019/665 dblp:conf/ijcai/Wang019 fatcat:tg3ejmshd5bkhfjrvzw4i4napm

A Comprehensive Survey on Local Differential Privacy

Xingxing Xiong, Shubo Liu, Dan Li, Zhaohui Cai, Xiaoguang Niu
2020 Security and Communication Networks  
., frequency estimation and mean estimation) and complex statistical estimation (e.g., multivariate distribution estimation and private estimation over complex data) under LDP.  ...  Local differential privacy (LDP) is a state-of-the-art privacy preservation technique that allows to perform big data analysis (e.g., statistical estimation, statistical learning, and data mining) while  ...  Some studies focused on the investigation of locally differentially private distribution estimation on the original data.  ... 
doi:10.1155/2020/8829523 fatcat:xjk3vgyambb5xioc2q5hyr2hua

Local privacy and statistical minimax rates

John C. Duchi, Michael I. Jordan, Martin J. Wainwright
2013 2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton)  
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  ...  statistical estimators.  ...  differentially private (2) distributions Q.  ... 
doi:10.1109/allerton.2013.6736718 dblp:conf/allerton/DuchiJW13 fatcat:eto4hsyebfcmtng4emvtynhrs4

Local Privacy and Statistical Minimax Rates

John C. Duchi, Michael I. Jordan, Martin J. Wainwright
2013 2013 IEEE 54th Annual Symposium on Foundations of Computer Science  
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  ...  statistical estimators.  ...  differentially private (2) distributions Q.  ... 
doi:10.1109/focs.2013.53 dblp:conf/focs/DuchiJW13 fatcat:7giskrwqdjc5tpytgf4tdg7oby

Deconvoluting Kernel Density Estimation and Regression for Locally Differentially Private Data [article]

Farhad Farokhi
2020 arXiv   pre-print
This approach also allows us to adapt the results from non-parameteric regression with errors-in-variables to develop regression models based on locally differentially private data.  ...  However, locally differential data can twist the probability density of the data because of the additive noise used to ensure privacy.  ...  However, most of the existing work on probability distributions estimation based on locally differential private data focuses on categorical data [19] [20] [21] [22] [23] .  ... 
arXiv:2008.12466v2 fatcat:znwscsliinbs3auyese3xr7dkq

Deconvoluting kernel density estimation and regression for locally differentially private data

Farhad Farokhi
2020 Scientific Reports  
This approach also allows us to adapt the results from non-parametric regression with errors-in-variables to develop regression models based on locally differentially private data.  ...  However, locally differential data can twist the probability density of the data because of the additive noise used to ensure privacy.  ...  However, most of the existing work on probability distributions estimation based on locally differential private data focuses on categorical data [19] [20] [21] [22] [23] .  ... 
doi:10.1038/s41598-020-78323-0 pmid:33288799 fatcat:7l74ykwnzzg5hmrcdg4hywwzim

Mutual Information Optimally Local Private Discrete Distribution Estimation [article]

Shaowei Wang, Liusheng Huang, Pengzhan Wang, Yiwen Nie, Hongli Xu, Wei Yang, Xiang-Yang Li, Chunming Qiao
2016 arXiv   pre-print
Consider statistical learning (e.g. discrete distribution estimation) with local ϵ-differential privacy, which preserves each data provider's privacy locally, we aim to optimize statistical data utility  ...  After analysing the limitations of existing local private mechanisms from mutual information perspective, we propose an efficient implementation of the k-subset mechanism for discrete distribution estimation  ...  Each provider randomizes x i via a local ǫ-differential private mechanism Q to obtain a private view z i , then publishes z i to the aggregator, who infers a estimation of the truly distribution θ from  ... 
arXiv:1607.08025v1 fatcat:6euqmewcdrcrjgn6uz5zw36lmy

Public wage differentials and the treatment of occupational differences

Dale Belman, John S. Heywood
2003 Journal of policy analysis and management  
This finding is contrasted with that for the local sector in which the differing distribution of common occupations largely explains the pattern of the differential.  ...  This finding is contrasted with that for the local sector in which the differing distribution of common occupations largely explains the pattern of the differential.  ...  For example, estimates of the federal government differential are made using federal and private employees but exclude state and local employees.  ... 
doi:10.1002/pam.10183 fatcat:5quhkd24n5c57hda5fomgjf63q

Locally Differentially Private Minimum Finding

Kazuto FUKUCHI, Chia-Mu YU, Jun SAKUMA
2022 IEICE transactions on information and systems  
We investigate a problem of finding the minimum, in which each user has a real value, and we want to estimate the minimum of these values under the local differential privacy constraint.  ...  Instead of considering the worst case, we aim to construct a private mechanism whose error rate is adaptive to the easiness of estimation of the minimum.  ...  We will prove that no locally differentially private mechanism consistently estimates the minimum under the worst-case users' data distribution.  ... 
doi:10.1587/transinf.2021edp7187 fatcat:w2nwqf722vc4dawhvjnoffrx3e

Differentially Private High Dimensional Sparse Covariance Matrix Estimation [article]

Di Wang, Jinhui Xu
2019 arXiv   pre-print
Our approach can be easily extended to local differential privacy. Experiments on the synthetic datasets show consistent results with our theoretical claims.  ...  In this paper, we study the problem of estimating the covariance matrix under differential privacy, where the underlying covariance matrix is assumed to be sparse and of high dimensions.  ...  Distribution estimation under local differential privacy has been studied in [13, 11] . However, both of them study only the 1-dimensional Gaussian distribution.  ... 
arXiv:1901.06413v2 fatcat:g3vyqzkyrvh5bbaqwssuthxffu

Public-Sector Wage Comparability: The Role of Earnings Dispersion

Dale Belman, John S. Heywood
2004 Public Finance Review  
Economists use average wage differentials to examine whether public-and private-sector workers have comparable earnings.  ...  In short, if average earnings in the public and private sectors are identical, earnings need not be comparable.  ...  Thus, individual earnings differentials favor the public sector at the bottom of the earnings distribution and the private sector at the top of the distribution.  ... 
doi:10.1177/1091142104269657 fatcat:tqciw2mn2rawblctg3ofhksb4q

Exponential random graph estimation under differential privacy

Wentian Lu, Gerome Miklau
2014 Proceedings of the 20th ACM SIGKDD international conference on Knowledge discovery and data mining - KDD '14  
Differential privacy mechanism for addressing high global sensitivity ▪ Local sensitivity[NRS07] input x GS LS LS f (x) = max 8x 0 , s.t. neighbors x,x 0 |f (x) f (x 0 )| However, local sensitivity cannot  ...  ▪ However, most ERGMs don't have analytical estimate Infinite global sensitivity Contributions ERGM specification + Private estimated parameters Sufficient statistics Private sufficient  ...  Summary of contributions ▪ Solve the problem of estimating parameters for ERGM under differential privacy !  ... 
doi:10.1145/2623330.2623683 dblp:conf/kdd/LuM14 fatcat:b3mvubo4a5ggzlw5riogzug7kq

The Right Complexity Measure in Locally Private Estimation: It is not the Fisher Information [article]

John C. Duchi, Feng Ruan
2020 arXiv   pre-print
of convergence under locally private estimation for many notions of privacy, including differential privacy and its relaxations.  ...  private estimation and learning problems by developing the local minimax risk.  ...  with locally private estimation.  ... 
arXiv:1806.05756v3 fatcat:5myltsf4xvdwzktqwsejrj4kku
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