Inference and Uncertainty Quantification for Streaming $r$-PCA
We address two open questions in streaming PCA via Oja's algorithm: sharp operator-norm convergence for general rank under sub-Gaussian data, and distributional inference for the resulting subspace estimator. Existing convergence analyses, even in the rank-one case, either assume bounded data or leave non-vanishing remainder terms that prevent adaptation to a polynomially vanishing tail spectrum, while existing distributional results are confined to the rank-one case. Our convergence theory removes these remainder terms and yields a sharp rate. In the dense-tail spiked covariance regime, this rate matches the minimax rate up to logarithmic factors. More generally, we prove a matching lowe...
| Authors | Haoshu Xu, Hongzhe Li |
|---|---|
| Primary category | stat.ML |
| Published | 18 August 2026 |
| Last updated at source | 18 August 2026 |
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