Inference and Uncertainty Quantification for Streaming $r$-PCA

Key points

It removed a persistent remainder term from Oja's algorithm's error bound, obtaining a sharp operator-norm rate for general rank and sub-Gaussian data.
It proved lower bounds matching up to logarithmic factors in both dense-tail and sparse-tail covariance regimes, supporting the optimality of the convergence rate.
By linearizing the iterates, it derived a high-dimensional Gaussian approximation for the general-rank error and an explicit limiting covariance.
It proved the consistency of an online multiplier bootstrap, enabling estimates and uncertainty intervals to be computed together in a single pass through the data.
The current theory is limited to a constant learning rate, leaving extensions to varying learning rates and data with sparsity, Markov dependence, or quantization open.

External research summaries. These are not HDATF publications or measured product results.