# Gap-free Differentially Private PCA for Gaussian Data

arXiv: https://arxiv.org/abs/2609.31614 · HTML: https://mlsanity.com/paper/2609.31614/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 16 references that are in the map.
- First posted on arXiv 25 Sep 2026.

## Builds on (most cited first, 11 of 11)

- [Finite Sample Differentially Private Confidence Intervals](https://mlsanity.com/paper/1711.03908/) (2017)
- [Differential privacy and robust statistics in high dimensions](https://mlsanity.com/paper/2111.06578/) (2021)
- [The Noisy Power Method: A Meta Algorithm with Applications](https://mlsanity.com/paper/1311.2495/) (2013)
- [High Probability Convergence of Stochastic Gradient Methods](https://mlsanity.com/paper/2302.14843/) (2023)
- [First Efficient Convergence for Streaming k-PCA: a Global, Gap-Free, and Near-Optimal Rate](https://mlsanity.com/paper/1607.07837/) (2016)
- [An Improved Gap-Dependency Analysis of the Noisy Power Method](https://mlsanity.com/paper/1602.07046/) (2016)
- [DP-PCA: Statistically Optimal and Differentially Private PCA](https://mlsanity.com/paper/2205.13709/) (2022)
- [Convergence of Stochastic Gradient Descent for PCA](https://mlsanity.com/paper/1509.09002/) (2015)
- [Tight Differentially Private PCA via Matrix Coherence](https://mlsanity.com/paper/2510.26679/) (2025)
- [Adaptive Power Iteration Method for Differentially Private PCA](https://mlsanity.com/paper/2602.11454/) (2026)
- [Gap-Free Streaming PCA Beyond Rank-One Updates: Near-Optimal Rates and Applications to Differential Privacy](https://mlsanity.com/paper/2609.26508/) (2026)

## Abstract (arXiv)

We give a gap-free (ε,δ)-differentially private algorithm for the principal component analysis (PCA) problem with Gaussian data. The algorithm is based on a private variant of the power iteration method, and it is computationally efficient.