P. Kairouz, S. Oh, and P. Viswanath. The composition theorem for differential privacy. IEEE Transactions on Information Theory, 63(6):4037-4049, 2017. doi: 10.1109/TIT.2017.2685505.
J. M. Lee. Riemannian manifolds: an introduction to curvature. Springer Science & Business Media, 2006.
Y. Liu, K. Sun, B. Jiang, and L. Kong. Identification, amplification and measurement: A bridge to gaussian differential privacy. In A. H. Oh, A. Agarwal, D. Belgrave, and K. Cho, editors, Advances in Neural Information Processing Systems, 2022. URL https://openreview.net/forum?id=UpNCpGvD96A.
K. V. Mardia, P. E. Jupp, and K. Mardia. Directional statistics. Wiley, 2000.
F. McSherry and K. Talwar. Mechanism design via differential privacy. Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS, pages 94-103, 11 2007. doi: 10.1109/FOCS.2007.66.
J. Milnor and D. W. Weaver. Topology from the differentiable viewpoint. Princeton university press, 1997.
I. Mironov. Rényi differential privacy. In 2017 IEEE 30th computer security foundations symposium (CSF), pages 263-275. IEEE, 2017.
P. Niyogi. Manifold regularization and semi-supervised learning: Some theoretical analyses. Journal of Machine Learning Research, 14(37):1229-1250, 2013. URL http://jmlr.org/papers/v14/niyogi13a.html.
X. Pennec. Intrinsic statistics on riemannian manifolds: Basic tools for geometric measurements. Journal of Mathematical Imaging and Vision, 25:127-154, 07 2006. doi: 10.1007/s10851-006-6228-4.
X. Pennec, S. Sommer, and T. Fletcher. Riemannian geometric statistics in medical image analysis. Academic Press, 2019.
P. Petersen. Riemannian geometry. Springer, 3rd edition, 2006.
M. Reimherr and J. Awan. Kng: The k-norm gradient mechanism. In H. Wallach, H. Larochelle, A. Beygelzimer, F. d'Alché-Buc, E. Fox, and R. Garnett, editors, Advances in Neural Information Processing Systems, volume 32. Curran Associates, Inc., 2019. URL https://proceedings.neurips.cc/paper_files/paper/2019/file/ faefec47428cf9a2f0875ba9c2042a81-Paper.pdf.
M. Reimherr, K. Bharath, and C. Soto. Differential privacy over riemannian manifolds. In M. Ranzato, A. Beygelzimer, Y. Dauphin, P. Liang, and J. W. Vaughan, editors, Advances in Neural Information Processing Systems, volume 34, pages 12292-12303. Curran Associates, Inc., 2021. URL https://proceedings.neurips.cc/paper_files/paper/2021/file/6600e06fe9350b62c1e343504d4a7b86-Paper.pdf.
S. Said. Statistical models and probabilistic methods on riemannian manifolds, 2021.
S. Said, L. Bombrun, Y. Berthoumieu, and J. H. Manton. Riemannian gaussian distributions on the space of symmetric positive definite matrices. IEEE Transactions on Information Theory, 63(4): 2153-2170, 2017. doi: 10.1109/TIT.2017.2653803.
S. Said, H. Hajri, L. Bombrun, and B. C. Vemuri. Gaussian distributions on riemannian symmetric spaces: Statistical learning with structured covariance matrices. IEEE Transactions on Information Theory, 64(2):752-772, 2018. doi: 10.1109/TIT.2017.2713829.
C. Soto, K. Bharath, M. Reimherr, and A. Slavković. Shape and structure preserving differential privacy. In S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, and A. Oh, editors, Advances in Neural Information Processing Systems, volume 35, pages 24693-24705. Curran Associates, Inc., 2022. URL https://proceedings.neurips.cc/paper_files/paper/2022/file/9c84feb75eae1ef6389f31b3ef050b6a-Paper-Conference.pdf.