arXiv:2602. 17284v2 Announce Type: replace Abstract: We consider the privacy amplification properties of a sampling scheme in which a user's data isused in $k$ steps chosen randomly and uniformly from a sequence (or set) of $t$ steps.
By Vitaly Feldman, Moshe Shenfeld
The paper presents a new analysis of Oja's algorithm for streaming principal component analysis (PCA) that works without any eigengap assumptions, achieving near‑optimal rates and matching lower bounds. It extends the results to a Rayleigh quotient notion of approximate PCA, resolving an open question, and applies the findings to provide gap‑free differentially private PCA guarantees for sub‑Gaussian data. The analysis relies solely on a second‑moment bound of stochastic updates, avoiding the almost‑sure bounds used in previous work.
By Anming Gu, Syamantak Kumar, Kevin Tian, Chutong Yang
arXiv:2607. 29675v1 Announce Type: cross Abstract: Density modes provide a localized and interpretable summary of multimodal distributions, but their estimation under rigorous differential privacy constraints remains largely unexplored.
By Arkajyoti Bhattacharjee, Arnab Auddy
arXiv:2609. 05034v1 Announce Type: cross Abstract: We consider density estimation under the relaxed local differential privacy condition that the privatized distributions are $\alpha$-close in total variation distance.
By Cristina Butucea, Huiyun Tang, Marie-Luce Taupin
arXiv:2603. 19703v2 Announce Type: replace-cross Abstract: Estimating covariance matrices is fundamental to a wide range of statistical applications.
By T. Tony Cai, Yicheng Li
arXiv:2602. 01607v3 Announce Type: replace-cross Abstract: Differentially private synthetic data enables the sharing and analysis of sensitive datasets while providing rigorous privacy guarantees for individual contributors.
By Rundong Ding, Yiyun He, Yizhe Zhu