Differentially Private Fr\'echet Mean on the Manifold of Symmetric Positive Definite (SPD) Matrices with log-Euclidean Metric

S Utpala, P Vepakomma, N Miolane - arXiv preprint arXiv:2208.04245, 2022 - arxiv.org
Differential privacy has become crucial in the real-world deployment of statistical and
machine learning algorithms with rigorous privacy guarantees. The earliest statistical …

Improved differentially private Riemannian optimization: Fast sampling and variance reduction

S Utpala, A Han, P Jawanpuria… - Transactions on Machine …, 2023 - openreview.net
A common step in differentially private ({DP}) Riemannian optimization is sampling from the
(tangent) Gaussian distribution as noise needs to be generated in the tangent space to …

Changes from classical statistics to modern statistics and data science

K Zhang, S Liu, M Xiong - arXiv preprint arXiv:2211.03756, 2022 - arxiv.org
A coordinate system is a foundation for every quantitative science, engineering, and
medicine. Classical physics and statistics are based on the Cartesian coordinate system …

Connecting silos with distributed and private computation

P Vepakomma - 2024 - dspace.mit.edu
Data in today's world is increasingly siloed across a wide variety of entities with varying
resource constraints. The quality of wisdom generated from a collaborative processing of …