Gap-Free Streaming PCA Beyond Rank-One Updates: Near-Optimal Rates and Applications to Differential Privacy
Streaming principal component analysis (PCA) seeks to recover a leading spectral subspace in a single pass over a data stream. We give a new analysis of the ubiquitous Oja's algorithm [Oja82] for the most general, gap-free variant of this problem, where no eigengap assumptions are made on the underlying mean matrix, complemented by a nearly-matching lower bound. Prior works achieving near-optimal rates for streaming PCA either required gap assumptions [JJK+16, HNWW21], or were limited to rank-one updates [AZL17, Lia23]. Our proof only uses a second moment bound on the individual stochastic updates, bypassing the almost sure bounds needed by prior near-optimal analyses, and the analogous o...
| Authors | Anming Gu, Syamantak Kumar, Kevin Tian et al. |
|---|---|
| Primary category | cs.LG |
| Published | 22 September 2026 |
| Last updated at source | 22 September 2026 |
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