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In a survey disclosure model, we consider an additive noise privacy mechanismand 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 principalcomponent analysis, statistical utility is measured via the spectral gap of acertain covariance matrix. This formulation and its motivation rely onclassical results from random matrix theory. We prove some properties of thisstatistical utility function and discuss a simple numerical method to evaluateit.

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