arXiv subjects

James Mingo

Publications and source records attributed to James Mingo.

2 recordsLinked to original sources

arXiv2018

On the Noise-Information Separation of a Private Principal Component Analysis Scheme

In a survey disclosure model, we consider an additive noise privacy mechanism and study the trade-off between privacy guarantees and statistical utility. Privacy is approached from two different but complementary viewpoints: information and estimation theoretic. Motivated by the performance of principal component analysis, statistical utility is measured via the spectral gap of a certain covariance matrix. This formulation and its motivation rely on classical results from random matrix theory. We prove some properties of this statistical utility function and discuss a simple numerical method to evaluate it.

cs.IT↗

arXiv2017

On the Global Fluctuations of Block Gaussian Matrices

In this paper we study the global fluctuations of block Gaussian matrices within the framework of second-order free probability theory. In order to compute the second-order Cauchy transform of these matrices, we introduce a matricial second-order conditional expectation and compute the matricial second-order Cauchy transform of a certain type of non-commutative random variables. As a by-product, using the linearization technique, we obtain the second-order Cauchy transform of non-commutative rational functions evaluated on selfadjoint Gaussian matrices.

math.PR↗