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Improved Analysis of the Accelerated Noisy Power Method with Applications to Decentralized PCA

Announce Type: replace-cross Abstract: We analyze the Accelerated Noisy Power Method, an algorithm for Principal Component Analysis in the setting where only inexact matrix-vector products are available, which can arise for instance in decentralized PCA. While previous works have established that acceleration can improve convergence rates compared to the standard Noisy Power Method, these guarantees require overly restrictive upper bounds on the magnitude of the perturbations, limiting their...

arXiv CS 1d ago

Consecutive Support Matching Induced Parameter Tuning Accelerates Momentum Iterative Hard Thresholding

Announce Type: new Abstract: Momentum-based acceleration of iterative hard thresholding (IHT) can dramatically speed up sparse signal recovery from linear measurements, but its effectiveness hinges on careful parameter tuning -- a task complicated by the frequent support changes inherent to hard thresholding. We propose CosMIHT(Consecutive Support Matching Induced Momentum IHT), which resolves this difficulty through a simple adaptive rule: start with the conservative parameters and whenever...

arXiv CS 1d ago

Microsoft’s AI chief says superintelligence is near, but won’t take your job

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