Robust Streaming PCA
This work addresses robust PCA for streaming data, providing theoretical guarantees for applications with non-stationary data, though it is incremental as it builds on existing algorithms.
The paper tackles streaming PCA under perturbations by modeling covariance within a temporal uncertainty set, establishing fundamental convergence limits and showing the noisy power method is rate-optimal.
We consider streaming principal component analysis when the stochastic data-generating model is subject to perturbations. While existing models assume a fixed covariance, we adopt a robust perspective where the covariance matrix belongs to a temporal uncertainty set. Under this setting, we provide fundamental limits on convergence of any algorithm recovering principal components. We analyze the convergence of the noisy power method and Oja's algorithm, both studied for the stationary data generating model, and argue that the noisy power method is rate-optimal in our setting. Finally, we demonstrate the validity of our analysis through numerical experiments on synthetic and real-world dataset.