MVG Mechanism: Differential Privacy under Matrix-Valued Query

Differential privacy mechanism design has traditionally been tailored for a scalar-valued query function. Although many mechanisms such as the Laplace and Gaussian mechanisms can be extended to a matrix-valued query function by adding i.i.d. noise to each element of the matrix, this method is often suboptimal as it forfeits an opportunity to exploit the structural characteristics typically associated with matrix analysis. To address this challenge, we propose a novel differential privacy mechanism called the Matrix-Variate Gaussian (MVG) mechanism, which adds a matrix-valued noise drawn from a matrix-variate Gaussian distribution, and we rigorously prove that the MVG mechanism preserves $(\epsilon,\delta)$-differential privacy. Furthermore, we introduce the concept of directional noise made possible by the design of the MVG mechanism. Directional noise allows the impact of the noise on the utility of the matrix-valued query function to be moderated. Finally, we experimentally demonstrate the performance of our mechanism using three matrix-valued queries on three privacy-sensitive datasets. We find that the MVG mechanism notably outperforms four previous state-of-the-art approaches, and provides comparable utility to the non-private baseline.Comment: Appeared in CCS'1

Underdetermined source separation using a sparse STFT framework and weighted laplacian directional modelling

The instantaneous underdetermined audio source separation problem of K-sensors, L-sources mixing scenario (where K < L) has been addressed by many different approaches, provided the sources remain quite distinct in the virtual positioning space spanned by the sensors. This problem can be tackled as a directional clustering problem along the source position angles in the mixture. The use of Generalised Directional Laplacian Densities (DLD) in the MDCT domain for underdetermined source separation has been proposed before. Here, we derive weighted mixtures of DLDs in a sparser representation of the data in the STFT domain to perform separation. The proposed approach yields improved results compared to our previous offering and compares favourably with the state-of-the-art.Comment: EUSIPCO 2016, Budapest, Hungar

The random component of mixer-based nonlinear vector network analyzer measurement uncertainty

The uncertainty, due to random noise, of the measurements made with a mixer-based nonlinear vector network analyzer are analyzed. An approximate covariance matrix corresponding to the measurements is derived that can be used for fitting models and maximizing the dynamic range in the measurement setup. The validity of the approximation is verified with measurements

On high-dimensional sign tests

Sign tests are among the most successful procedures in multivariate nonparametric statistics. In this paper, we consider several testing problems in multivariate analysis, directional statistics and multivariate time series analysis, and we show that, under appropriate symmetry assumptions, the fixed-$p$ multivariate sign tests remain valid in the high-dimensional case. Remarkably, our asymptotic results are universal, in the sense that, unlike in most previous works in high-dimensional statistics, $p$ may go to infinity in an arbitrary way as $n$ does. We conduct simulations that (i) confirm our asymptotic results, (ii) reveal that, even for relatively large $p$, chi-square critical values are to be favoured over the (asymptotically equivalent) Gaussian ones and (iii) show that, for testing i.i.d.-ness against serial dependence in the high-dimensional case, Portmanteau sign tests outperform their competitors in terms of validity-robustness.Comment: Published at http://dx.doi.org/10.3150/15-BEJ710 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm