On the Privacy-preserving Generalized Eigenvalue Problem

Generalized eigenvalues serve as a foundational tool for extracting insights from data and constructing robust statistical learning models, while differential privacy ensures the protection of individual information within these models by minimizing the impact of any single data point. In this work, we propose an $(\\epsilon,\\delta)$-differential privacy algorithm to solve the generalized eigenvalue problem (GEP). Our algorithm gives better classification accuracy over existing methods and has the nearly optimal $\\ell_2$-norm error bounds in both low and high dimensions. Furthermore, our algorithm guarantees convergence to the solution regardless of the initial vector and this improves a previous method that requires a specific procedure to find a proper starting vector. Our experiments confirm the effectiveness of our algorithm in safeguarding privacy while simultaneously boosting classification accuracy.