Differentially private low-dimensional representation of high-dimensional data

Differentially private synthetic data provide a powerful mechanism to enable data analysis while protecting sensitive information about individuals. However, when the data lie in a high-dimensional space, the accuracy of the synthetic data suffers from the curse of dimensionality. In this paper, we propose a differentially private algorithm to generate low-dimensional synthetic data efficiently from a high-dimensional dataset with a utility guarantee with respect to the Wasserstein distance. A key step of our algorithm is a private principal component analysis (PCA) procedure with a near-optimal accuracy bound that circumvents the curse of dimensionality. Different from the standard perturbation analysis using the Davis-Kahan theorem, our analysis of private PCA works without assuming the spectral gap for the sample covariance matrix.Comment: 21 page

Nearly Optimal Private Convolution

We study computing the convolution of a private input $x$ with a public input $h$, while satisfying the guarantees of $(\epsilon, \delta)$-differential privacy. Convolution is a fundamental operation, intimately related to Fourier Transforms. In our setting, the private input may represent a time series of sensitive events or a histogram of a database of confidential personal information. Convolution then captures important primitives including linear filtering, which is an essential tool in time series analysis, and aggregation queries on projections of the data. We give a nearly optimal algorithm for computing convolutions while satisfying $(\epsilon, \delta)$-differential privacy. Surprisingly, we follow the simple strategy of adding independent Laplacian noise to each Fourier coefficient and bounding the privacy loss using the composition theorem of Dwork, Rothblum, and Vadhan. We derive a closed form expression for the optimal noise to add to each Fourier coefficient using convex programming duality. Our algorithm is very efficient -- it is essentially no more computationally expensive than a Fast Fourier Transform. To prove near optimality, we use the recent discrepancy lowerbounds of Muthukrishnan and Nikolov and derive a spectral lower bound using a characterization of discrepancy in terms of determinants

Are Credit Cycles Different in the MENA Countries Compared to Advanced Countries?

This paper estimates private sector credit cycles for most of the oil-importing and oil-exporting countries in the Middle East and North Africa. Credit cycles are the medium-term component in spectral analysis of real private sector credit growth. Besides, the paper estimates the credit cycles for several developed countries. The analysis finds substantial differences and rare similarities between credit cycles in the Middle East and North Africa and advanced countries. Between 19642017, credit cycles in the Middle East and North Africa do not appear to be associated with GDP growth. They only explain a fraction of the growth in private sector credit, and they do not seem to be synchronized across oil exporters and oil importers

Методы аппаратурного спектрального анализа случайных сигналов

У статті наведений порівняльний аналіз відомих методів вимірювання оцінок спектральної щільності потужності випадкових сигналів (класичних и корреляційно-фільтрового), аналіз основ (структур, принципів) побудови відомих цифрових фільтрових аналізаторів спектру, обгрунтування напрямів, приватних завдань і методів досліджень.This article covers known methods (classic and filter-correlation) of random signals spectral density measuring estimations comparative analysis, analysis of known digital filter spectrum analyzer construction basics (both structure and working principles), justification of research course, private tasks and research methods

Characterizing user requirements for future land observing satellites

The objective procedure was developed for identifying probable sensor and mission characteristics for an operational satellite land observing system. Requirements were systematically compiled, quantified and scored by type of use, from surveys of federal, state, local and private communities. Incremental percent increases in expected value of data were estimated for critical system improvements. Comparisons with costs permitted selection of a probable sensor system, from a set of 11 options, with the following characteristics: 30 meter spatial resolution in 5 bands and 15 meters in 1 band, spectral bands nominally at Thematic Mapper (TM) bands 1 through 6 positions, and 2 day data turn around for receipt of imagery. Improvements are suggested for both the form of questions and the procedures for analysis of future surveys in order to provide a more quantitatively precise definition of sensor and mission requirements