The cost of privacy: Optimal rates of convergence for parameter estimation with differential privacy

Abstract In this work we demonstrate that allowing differentially private leakage can significantly improve the concrete performance of secure 2-party computation (2PC) protocols. Specifically, we focus on the private set intersection (PSI) protocol of Rindal and Rosulek (CCS 2017), which is the fastest PSI protocol with security against malicious participants. We show that if differentially private leakage is allowed, the cost of the protocol can be reduced by up to 63%, depending on the desired level of differential privacy. On the technical side, we introduce a security model for differentially-private leakage in malicious-secure 2PC. We also introduce two new and improved mechanisms for “differentially private histogram overestimates,” the main technical challenge for differentially-private PSI.

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UNIFORM ASYMPTOTIC NORMALITY IN STATIONARY AND UNIT ROOT AUTOREGRESSION

Econometric Theory ◽

10.1017/s0266466611000016 ◽

2011 ◽

Vol 27 (6) ◽

pp. 1117-1151 ◽

Cited By ~ 16

Author(s):

Chirok Han ◽

Peter C. B. Phillips ◽

Donggyu Sul

Keyword(s):

Normal Distribution ◽

Rate Of Convergence ◽

Unit Root ◽

Asymptotic Theory ◽

Signal Strength ◽

Rates Of Convergence ◽

Moment Conditions ◽

First Order ◽

The Cost ◽

Artificial Shrinkage

While differencing transformations can eliminate nonstationarity, they typically reduce signal strength and correspondingly reduce rates of convergence in unit root autoregressions. The present paper shows that aggregating moment conditions that are formulated in differences provides an orderly mechanism for preserving information and signal strength in autoregressions with some very desirable properties. In first order autoregression, a partially aggregated estimator based on moment conditions in differences is shown to have a limiting normal distribution that holds uniformly in the autoregressive coefficient ρ, including stationary and unit root cases. The rate of convergence is $\root \of n $ when $\left| \rho \right| < 1$ and the limit distribution is the same as the Gaussian maximum likelihood estimator (MLE), but when ρ = 1 the rate of convergence to the normal distribution is within a slowly varying factor of n. A fully aggregated estimator (FAE) is shown to have the same limit behavior in the stationary case and to have nonstandard limit distributions in unit root and near integrated cases, which reduce both the bias and the variance of the MLE. This result shows that it is possible to improve on the asymptotic behavior of the MLE without using an artificial shrinkage technique or otherwise accelerating convergence at unity at the cost of performance in the neighborhood of unity. Confidence intervals constructed from the FAE using local asymptotic theory around unity also lead to improvements over the MLE.

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Simplified Sensorless Current Predictive Control of Synchronous Reluctance Motor Using Online Parameter Estimation

Energies ◽

10.3390/en13020492 ◽

2020 ◽

Vol 13 (2) ◽

pp. 492 ◽

Cited By ~ 5

Author(s):

Ahmed Farhan ◽

Mohamed Abdelrahem ◽

Amr Saleh ◽

Adel Shaltout ◽

Ralph Kennel

Keyword(s):

Parameter Estimation ◽

Predictive Control ◽

Operating Conditions ◽

Parameter Mismatch ◽

Speed Controller ◽

Synchronous Reluctance Motor ◽

Reluctance Motor ◽

Finite Set ◽

Insufficient Response ◽

The Cost

In this paper, a simplified efficient method for sensorless finite set current predictive control (FSCPC) for synchronous reluctance motor (SynRM) based on extended Kalman filter (EKF) is proposed. The proposed FSCPC is based on reducing the computation burden of the conventional FSCPC by using the commanded reference currents to directly calculate the reference voltage vector (RVV). Therefore, the cost function is calculated for only three times and the necessity to test all possible voltage vectors will be avoided. For sensorless control, EKF is composed to estimate the position and speed of the rotor. Whereas the performance of the proposed FSCPC essentially necessitates the full knowledge of SynRM parameters and provides an insufficient response under the parameter mismatch between the controller and the motor, online parameter estimation based on EKF is combined in the proposed control strategy to estimate all parameters of the machine. Furthermore, for simplicity, the parameters of PI speed controller and initial values of EKF covariance matrices are tuned offline using Particle Swarm Optimization (PSO). To demonstrate the feasibility of the proposed control, it is implemented in MATLAB/Simulink and tested under different operating conditions. Simulation results show high robustness and reliability of the proposed drive.

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