Peilin He

Peilin He, Liou Tang, M. Amin Rahimian et al.

Differential Privacy (DP) is being increasingly adopted for non-Euclidean data that lie on complex, high-dimensional manifolds. Existing DP mechanisms for manifold data consider geometric properties when calibrating privacy perturbations, but they largely fail to capture variations in data density within datasets, leading to biased perturbations and suboptimal privacy-utility trade-offs due to heterogeneous data distributions. In this paper, we propose a novel density-aware differential privacy mechanism on Riemannian manifolds, referred to as Conformal-DP, that leverages conformal transformations to calibrate perturbations based on local densities and to induce a density-balanced geometry. We prove that our mechanism satisfies $ε$-differential privacy on any complete Riemannian manifold under mild regularity assumptions. In addition, we derive a closed-form expected geodesic error bound that depends only on the underlying data density ratio and is independent of global curvature. Our empirical results on synthetic and real-world datasets demonstrate that the proposed Conformal-DP mechanism substantially improves the privacy-utility trade-off in heterogeneous data distribution settings, with worst-case performance comparable to state-of-the-art manifold DP mechanisms that assume uniformly distributed data.

Zakk Heile, Peilin He, Jayson Tran et al.

Comparing probability measures modulo unknown rigid transformations is a central challenge in geometric data analysis. Classical optimal transport (OT) distances, including Wasserstein and sliced Wasserstein, are sensitive to rotations and reflections, whereas Gromov-Wasserstein (GW) and Procrustes-Wasserstein (PW) distances are invariant to isometries but computationally prohibitive for large datasets. We introduce Rigid-Invariant Sliced Wasserstein via Independent Embeddings (RISWIE), a scalable distance that combines the invariance of NP-hard approaches with the efficiency of projection-based OT. RISWIE utilizes data-adaptive bases and matches optimal signed permutations along axes according to distributional similarity to achieve rigid invariance with nearly linear complexity in the sample size. We prove bounds relating RISWIE to GW in special cases and demonstrate dimension-independent statistical stability. Our experiments on cellular imaging and 3D human meshes demonstrate that RISWIE outperforms GW and PW in clustering tasks and discriminative capability while significantly reducing runtime.

Peilin He, James Joshi

Reconstructing high-quality images from low-resolution inputs using Residual Dense Spatial Networks (RDSNs) is crucial yet challenging. It is even more challenging in centralized training where multiple collaborating parties are involved, as it poses significant privacy risks, including data leakage and inference attacks, as well as high computational and communication costs. We propose a novel Privacy-Preserving Federated Learning-based RDSN (PPFL-RDSN) framework specifically tailored for encrypted lossy image reconstruction. PPFL-RDSN integrates Federated Learning (FL), local differential privacy, and robust model watermarking techniques to ensure that data remains secure on local clients/devices, safeguards privacy-sensitive information, and maintains model authenticity without revealing underlying data. Empirical evaluations show that PPFL-RDSN achieves comparable performance to the state-of-the-art centralized methods while reducing computational burdens, and effectively mitigates security and privacy vulnerabilities, making it a practical solution for secure and privacy-preserving collaborative computer vision applications.