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

TL;DR

This paper investigates how additive noise mechanisms affect privacy and utility in principal component analysis, using information theory and spectral gap analysis based on random matrix theory.

Contribution

It introduces a novel framework combining information and estimation theory to analyze privacy-utility trade-offs in PCA with additive noise.

Findings

Spectral gap serves as a measure of utility in noisy PCA.

Properties of the utility function are characterized theoretically.

A numerical method for evaluating the utility function is proposed.

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.