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Information-theoretic lower bounds for distributed statistical estimation with communication constraints
2013
Neural Information Processing Systems
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We establish lower bounds on minimax risks for distributed statistical estimation under a communication budget. ...
Such lower bounds reveal the minimum amount of communication required by any procedure to achieve the centralized minimax-optimal rates for statistical estimation. ...
Acknowledgments We thank the anonymous reviewers for their helpful feedback and comments. JCD was supported by a Facebook Graduate Fellowship. Our work was supported in part by the U.S. ...
dblp:conf/nips/ZhangDJW13
fatcat:5wsm6igub5e4vhauzsqjuky6pi
Distributed Gaussian Mean Estimation under Communication Constraints: Optimal Rates and Communication-Efficient Algorithms
[article]
2020
arXiv
pre-print
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We study distributed estimation of a Gaussian mean under communication constraints in a decision theoretical framework. ...
This critical decomposition provides a framework for both the lower bound analysis and optimal procedure design. ...
Han et al. (2018) developed a geometric lower bound for distributed Gaussian mean estimation. ...
arXiv:2001.08877v1
fatcat:ur6i7pgg5resnjw2rh3geodhty
Distributed Nonparametric Function Estimation: Optimal Rate of Convergence and Cost of Adaptation
[article]
2021
arXiv
pre-print
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Distributed minimax estimation and distributed adaptive estimation under communication constraints for Gaussian sequence model and white noise model are studied. ...
We then quantify the exact communication cost for adaptation and construct an optimally adaptive procedure for distributed estimation over a range of Besov classes. ...
2020a) ; Szabo and van Zanten (2020) considered information-theoretical limits under communication constraints for various distributed estimation problems, such as Gaussian mean estimation, linear regression ...
arXiv:2107.00179v1
fatcat:lwwt56xhynfozpufjhjljg6gem
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. ...
We prove bounds on information-theoretic quantities, including mutual information and Kullback-Leibler divergence, that influence estimation rates as a function of the amount of privacy preserved. ...
Acknowledgments We thank Guy Rothblum for very helpful discussions. JCD was supported by a Facebook Graduate Fellowship and an NDSEG fellowship. Our work was supported in part by the U.S. ...
doi:10.1109/allerton.2013.6736718
dblp:conf/allerton/DuchiJW13
fatcat:eto4hsyebfcmtng4emvtynhrs4
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. ...
We prove bounds on information-theoretic quantities, including mutual information and Kullback-Leibler divergence, that influence estimation rates as a function of the amount of privacy preserved. ...
Acknowledgments We thank Guy Rothblum for very helpful discussions. JCD was supported by a Facebook Graduate Fellowship and an NDSEG fellowship. Our work was supported in part by the U.S. ...
doi:10.1109/focs.2013.53
dblp:conf/focs/DuchiJW13
fatcat:7giskrwqdjc5tpytgf4tdg7oby
Interactive Inference under Information Constraints
[article]
2021
arXiv
pre-print
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We study the role of interactivity in distributed statistical inference under information constraints, e.g., communication constraints and local differential privacy. ...
As an application, we obtain optimal bounds for both estimation and testing under local differential privacy and communication constraints. ...
The bounds are simple and highlighted separately here for easy reference -in essence, they say that small loss implies large information, the first step in any information-theoretic lower bound for statistical ...
arXiv:2007.10976v5
fatcat:cgzoyloslneizouiafonroo4qq
Breaking the Communication-Privacy-Accuracy Trilemma
[article]
2021
arXiv
pre-print
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For mean estimation, we propose a scheme based on Kashin's representation and random sampling, with order-optimal estimation error under both constraints. ...
As a by-product, we also construct a distribution estimation mechanism that is rate-optimal for all privacy regimes and communication constraints, extending recent work that is limited to b=1 and ε=O(1 ...
This was helpful in achieving order-optimality for mean estimation. ...
arXiv:2007.11707v3
fatcat:xtorfz27cjdurjdwogrt44aqbq
Geometric Lower Bounds for Distributed Parameter Estimation under Communication Constraints
[article]
2021
arXiv
pre-print
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Our approach significantly deviates from existing approaches for developing information-theoretic lower bounds for communication-efficient estimation. ...
We develop lower bounds for the minimax risk of estimating the underlying parameter for a large class of losses and distributions. ...
For a large class of statistical models, we develop a novel geometric approach that builds on a new representation of the communication constraint to establish information-theoretic lower bounds for distributed ...
arXiv:1802.08417v4
fatcat:b62ox2ojkbb5dedhqplx6rwqly
Molecular Communication in Fluid Media: The Additive Inverse Gaussian Noise Channel
2012
IEEE Transactions on Information Theory
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We consider molecular communication, with information conveyed in the time of release of molecules. ...
The main contribution of this paper is the development of a theoretical foundation for such a communication system. ...
This forms the basis of the theoretical developments that follow. 2) Using the AIGN framework, we obtain upper and lower bounds on the information theoretic capacity of a molecular communication system ...
doi:10.1109/tit.2012.2193554
fatcat:ftwbzz5edzhtvlp5eaid6ynifq
Distributed Nonparametric Regression under Communication Constraints
[article]
2018
arXiv
pre-print
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Our results give both asymptotic lower bounds and matching upper bounds on the statistical risk under various settings. ...
This paper studies the problem of nonparametric estimation of a smooth function with data distributed across multiple machines. ...
Unlike for the lower bound, we shall work under the individual constraint on the communication budget, instead of the sum constraint. ...
arXiv:1803.01302v2
fatcat:ticgmvavgfaq3fktfpapeo6l7y
Signal Processing for Location Estimation and Tracking in Wireless Environments
2008
EURASIP Journal on Advances in Signal Processing
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Theoretical limits for location estimation provide lower bounds on the mean squared error of location estimators [7-10], which can be used as guidelines for designing positioning systems. ...
Recent efforts for incorporating location estimation into wireless systems include the Federal Communications Commission requirement for wireless providers to locate mobile users within tens of meters ...
Theoretical limits for location estimation provide lower bounds on the mean squared error of location estimators [7] [8] [9] [10] , which can be used as guidelines for designing positioning systems. ...
doi:10.1155/2008/356546
fatcat:ln6jufq6pjfxpnh7lsbqufco2y
The communication cost of security and privacy in federated frequency estimation
[article]
2022
arXiv
pre-print
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In this paper, we develop an information-theoretic model for secure aggregation that allows us to characterize the fundamental cost of security and privacy in terms of communication. ...
Can we reduce the communication needed for secure aggregation, and does security come with a fundamental cost in communication? ...
trade-offs. • We specialize these information-theoretic lower bounds to frequency estimation with and without differential privacy constraints. ...
arXiv:2211.10041v1
fatcat:l6lcfbl3zvhf3fzdpiwobqtk2a
Fundamental Limits of Online and Distributed Algorithms for Statistical Learning and Estimation
[article]
2014
arXiv
pre-print
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Many machine learning approaches are characterized by information constraints on how they interact with the training data. ...
For example, are there learning problems where any algorithm which has small memory footprint (or can use any bounded number of bits from each example, or has certain communication constraints) will perform ...
We thank John Duchi, Yevgeny Seldin and Yuchen Zhang for helpful comments. ...
arXiv:1311.3494v6
fatcat:fkr2asnqhfaldhyea3stmynyla
Distributed inference in wireless sensor networks
2011
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
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communication network connecting the sensors and the resource constraints at the sensors. ...
In particular, results on distributed detection, parameter estimation and tracking in WSNs will be discussed, with a special emphasis on solutions to these inference problems that take into account the ...
The authors would like to thank Dr Engin Masazade for his help with the preparation of this paper. ...
doi:10.1098/rsta.2011.0194
pmid:22124084
fatcat:jtwubvrlnnfgpkcu46jvqim3ra
Capacity estimates of additive inverse Gaussian molecular channels with relay characteristics
2016
Proceedings of the 9th EAI International Conference on Bio-inspired Information and Communications Technologies (formerly BIONETICS)
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To address this issue, in this paper we derive a theorem that estimates the upper and lower bounds of the channel capacity for a relay channel, which structurally corresponds to a feed-forward loop, by ...
be used as information processing and forwarding units. ...
We can observe that both the upper and lower bounds increase monotonically with increasing delay constraint. ...
doi:10.4108/eai.3-12-2015.2262539
dblp:journals/eetws/RanaGPPWM16
fatcat:2fylqbw44nevbjmjqzhcgcny6e
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