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This research establishes fundamental convergence limits for streaming principal component analysis under temporal perturbations, identifying the noisy power method as rate-optimal in this robust setting. By addressing covariance uncertainty rather than assuming a fixed model, the work advances theoretical understanding of dimensionality reduction algorithms facing real-world data instability. The findings are validated through numerical experiments on both synthetic and real-world datasets, offering practical insights for scalable ML systems.
Robust Streaming PCA
arXiv:1902.03223v4 Announce Type: replace-cross Abstract: 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 datasets.
Abstract: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 datasets.
The authors are ordered alphabetically. 36th Conference on Neural Information Processing Systems (NeurIPS 2022). This version corrects several steps in the proofs, expands the appendices, and revises the exposition throughout
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:1902.03223 [stat.ML]
(or arXiv:1902.03223v4 [stat.ML] for this version)
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