The Gaussian Mixing Mechanism: Renyi Differential Privacy via Gaussian Sketches

Omri Lev, Vishwak Srinivasan, Moshe Shenfeld, Katrina Ligett, Ayush Sekhari, Ashia C. Wilson

Keywords: Differential Privacy; Renyi Divergence; Sketching; Private Linear Regression;

Abstract: Gaussian sketching, which consists of pre-multiplying the data with a random Gaussian matrix, is a widely used technique in data science and machine learning. Beyond computational benefits, this operation also provides differential privacy guarantees due to its inherent randomness. In this work, we revisit this operation through the lens of \Renyi Differential Privacy (RDP), providing a refined privacy analysis that yields significantly tighter bounds than prior results. We then demonstrate how this improved analysis leads to performance improvement in different linear regression settings, establishing theoretical utility guarantees. Empirically, our methods improve performance across multiple datasets and, in several cases, reduce runtime.

Primary Area: Other (please use sparingly, only use the keyword field for more details)

Submission Number: 25236