arXiv Machine Learning September 29, 2026 By Alina Ene, Huy L. Nguyen

Gap-free Differentially Private PCA for Gaussian Data

Read the original on arXiv Machine Learning →

The paper presents a gap‑free differentially private algorithm for performing principal component analysis on Gaussian data. It addresses the PCA problem while ensuring privacy guarantees without relying on a spectral gap assumption. The work is announced on arXiv with the identifier 2609.31614v1.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

arXiv Machine Learning

Sep 23

Gap-Free Streaming PCA Beyond Rank-One Updates: Near-Optimal Rates and Applications to Differential Privacy

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

safety

arXiv Machine Learning

Jun 2

PE-means: Improved Differentially Private $k$-means Clustering through Private Evolution

arXiv:2606. 00342v1 Announce Type: new Abstract: We study the problem of differentially private (DP) $k$-means clustering in Euclidean space.

By Thomas Humphries, Zinan Lin, Sergey Yekhanin

benchmarks

arXiv Machine Learning

Jun 24

A Private Approximation of the 2nd-Moment Matrix of Any Subsamplable Input

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.

By Bar Mahpud, Or Sheffet

safety

arXiv Machine Learning

Jun 17

Differential Privacy of Gaussian Process Posterior Sampling

arXiv:2606. 17995v1 Announce Type: cross Abstract: We study the privacy of releasing posterior sample paths from a Gaussian process (GP) when the entire training set including covariates and responses is private.

By Tomasz Maciazek

safety

arXiv Machine Learning

Jun 9

On Choosing the $\mu$ Parameter in Gaussian Differential Privacy

arXiv:2606. 09582v1 Announce Type: new Abstract: Recent work argues for using Gaussian differential privacy (GDP) to report the privacy guarantees in privacy-preserving machine learning.

By Bogdan Kulynych, Antti Honkela

safety

arXiv Machine Learning

Jun 9

Improved Analysis of the Accelerated Noisy Power Method with Applications to Decentralized PCA

arXiv:2602. 03682v2 Announce Type: replace-cross Abstract: We analyze the Accelerated Noisy Power Method, an algorithm for Principal Component Analysis in the setting where only inexact matrix-vector products are available, which can arise for instance in decentralized PCA.

By Pierre Agui\'e, Mathieu Even, Laurent Massouli\'e

One email a morning, machine-written

Related stories

Gap-Free Streaming PCA Beyond Rank-One Updates: Near-Optimal Rates and Applications to Differential Privacy

PE-means: Improved Differentially Private $k$-means Clustering through Private Evolution

A Private Approximation of the 2nd-Moment Matrix of Any Subsamplable Input

Differential Privacy of Gaussian Process Posterior Sampling

On Choosing the $\mu$ Parameter in Gaussian Differential Privacy

Improved Analysis of the Accelerated Noisy Power Method with Applications to Decentralized PCA