A Floating-Point Safe Sampler for Differentially Private PCA

Authors:

Rita Ionides, Walter McKelvie, Elena Ghazi, Salil Vadhan

Date Created:

2025-01-01

Course Title:

Professor:

Not specified

About Paper:

Principal Components Analysis (PCA) is a widely used technique show that standard rejection sampling over the sphere introduces for dimensionality reduction, with critical applications in rounding-based leakage in finite precision, enabling adversarial genomics, healthcare, and finance. Differentially private variants inference on a dataset through subtle deviations in acceptance of PCA are therefore essential in order to protect sensitive patient probabilities. and client data. To address this, we propose a floating-point safe alternative A popular implementation of differentially private PCA, used in based on a regularized approximate Hamiltonian sampler. By both diffprivlib and OpenDP libraries, relies on the Bingham discretizing score functions in log-space and bounding sensitivity distributionandtheexponentialmechanismtoprivatelyreleasetop in the presence of rounding, our method provably restores principal components. While the original algorithm is provably differential privacy guarantees under IEEE-754 arithmetic. We (▯, 0)-differentially private in real arithmetic, we demonstrate thatalso provide a practical implementation in the OpenDP library. its floating-point implementation violates differential privacy. We

Abstract:

Principal Components Analysis (PCA) is a widely used technique show that standard rejection sampling over the sphere introduces for dimensionality reduction, with critical applications in rounding-based leakage in finite precision, enabling adversarial genomics, healthcare, and finance. Differentially private variants inference on a dataset through subtle deviations in acceptance of PCA are therefore essential in order to protect sensitive patient probabilities. and client data. To address this, we propose a floating-point safe alternative A popular implementation of differentially private PCA, used in based on a regularized approximate Hamiltonian sampler. By both diffprivlib and OpenDP libraries, relies on the Bingham discretizing score functions in log-space and bounding sensitivity distributionandtheexponentialmechanismtoprivatelyreleasetop in the presence of rounding, our method provably restores principal components. While the original algorithm is provably differential privacy guarantees under IEEE-754 arithmetic. We (▯, 0)-differentially private in real arithmetic, we demonstrate thatalso provide a practical implementation in the OpenDP library. its floating-point implementation violates differential privacy. We

Source:

Harvard / Haoyang "Harlan" Huang, Ibrahim Abdelwahab, William Wilson / 2025

Topics:

differentially, private, pca, floating, implementation, safe, sampler, principal, component, used, rounding, opendp

Co-authors:

@ritaionides428 , @waltermckelvie429 , @elenaghazi430 , @salilvadhan431