arXiv Machine Learning

High-Dimensional Asymptotics of Differentially Private PCA

arXiv:2511. 07270v4 Announce Type: replace-cross Abstract: In differential privacy, random noise is introduced to privatize summary statistics of a sensitive dataset before releasing them.

arXiv Machine Learning
4d ago

High-Dimensional Asymptotics and Dataset Selection for Private Transfer Learning

The paper addresses the challenge of selecting external datasets for private transfer learning by modeling high‑dimensional regression with heterogeneous sources and a weighted ridge estimator. It relies solely on aggregated statistics and offers privacy guarantees under $ ho$‑zero‑concentrated differential privacy for labels or both features and labels. A deterministic equivalent of test error is derived, enabling optimization of hyperparameters and decision‑making about the utility of private external data without accessing individual records.

By Filip Kova\v{c}evi\'c, Edwige Cyffers, Stefano Sarao Mannelli, Marco Mondelli
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