On the Noise-Information Separation of a Private Principal Component Analysis Scheme
Information Theory
2018-01-12 v1 math.IT
Abstract
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.
Keywords
Cite
@article{arxiv.1801.03553,
title = {On the Noise-Information Separation of a Private Principal Component Analysis Scheme},
author = {Mario Diaz and Shahab Asoodeh and Fady Alajaji and Tamás Linder and Serban Belinschi and James Mingo},
journal= {arXiv preprint arXiv:1801.03553},
year = {2018}
}
Comments
Submitted to the International Symposium on Information Theory (ISIT) 2018