arXiv:2505. 14251v2 Announce Type: replace Abstract: We study the problem of differentially private second moment estimation and present a new algorithm that achieve strong privacy-utility trade-offs even for worst-case inputs under subsamplability assumptions on the data.
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.
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.
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.
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.
arXiv:2603. 19703v2 Announce Type: replace-cross Abstract: Estimating covariance matrices is fundamental to a wide range of statistical applications.
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.
arXiv:2508. 18037v2 Announce Type: replace Abstract: Leveraging information from public data has become increasingly crucial in enhancing the utility of differentially private (DP) methods.
arXiv:2609. 22783v1 Announce Type: new Abstract: We study differentially private covariance estimation in operator norm for mean-zero sub-Gaussian distributions with unknown covariance support and at most $k$ nonzero entries per row.
arXiv:2508.04800v2 Announce Type: replace-cross Abstract: We introduce a novel privatization framework for high-dimensional controlled variable selection. Our framework enables rigorous False Discove...
arXiv:2608. 11003v1 Announce Type: cross Abstract: In this work, we study the information bottleneck under perfect privacy, with particular emphasis on the active-rate regime, where the representation-rate constraint is binding and directly limits the achievable utility.
arXiv:2504.00919v3 Announce Type: replace-cross Abstract: We study the problem of estimating the spectral density of a centered stationary Gaussian time series under local differential privacy constr...
arXiv:2601. 10237v3 Announce Type: replace Abstract: Differentially Private Stochastic Gradient Descent (DP-SGD) is the dominant paradigm for private training, but its fundamental limitations under worst-case adversarial privacy definitions remain poorly understood.