(2405.20779) Asymptotic utility of spectral anonymization

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Abstract:In the contemporary data landscape characterized by multi-source data collection and third-party data sharing, ensuring individual privacy is a key concern. Although various anonymization methods exist, their utility preservation and privacy guarantees remain difficult to quantify. In this work, we address this gap by studying the utility and privacy of the spectral anonymization (SA) algorithm, particularly in an asymptotic setting. Unlike conventional anonymization methods that directly modify the original data, SA works by perturbing the data in a spectral basis and then returning it to its original basis. Alongside the original $\mathcal{P}$-SA, using a random permutation transformation, we introduce two new SA variants: $\mathcal{J}$-spectral anonymization and $\mathcal{O}$-spectral anonymization, which use sign-change and orthogonal matrix transformations, respectively. We show to what extent, under certain practical assumptions, these SA algorithms preserve the first and second moments of the original data. In particular, our results reveal that the asymptotic efficiency of the three SA algorithms in estimating the covariance is exactly 50% with respect to the original data. To assess the applicability of these asymptotic results in practice, we conduct a simulation study with finite data and also evaluate the privacy protection offered by these algorithms using distance-based record linkage. Our research reveals that while no method exhibits clear superiority in utility over finite samples, $\mathcal{O}$-SA stands out for its exceptional privacy preservation, never producing identical records, albeit with increased computational complexity. Conversely, $\mathcal{P}$-SA emerges as a computationally efficient alternative, demonstrating unmatched efficiency in mean estimation.