Differentially Private Fréchet Mean on the Manifold of Symmetric Positive Definite (SPD) Matrices

Utpala, S., Vepakomma, P., Miolane, N.

Transactions of Machine Learning Research (TMLR).

We introduce the Tangent Gaussian mechanism for computing a differentially private Fréchet mean on the SPD manifold, achieving quadratic utility improvement in data dimension, eliminating the need for Markov Chain Monte Carlo MCMC sampling, and significantly boosting computational efficiency.