[2305.17224] Quick and Correct Estimation of Low-Rank Matrices from Noisy Measurements through Preconditioned Non-Convex Gradient Descent

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Obtain a PDF of the paper titled Quick and Correct Estimation of Low-Rank Matrices from Noisy Measurements through Preconditioned Non-Convex Gradient Descent, by Gavin Zhang and a couple of different authors

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Summary:Non-convex gradient descent is a typical method for estimating a low-rank $ntimes n$ floor reality matrix from noisy measurements, as a result of it has per-iteration prices as little as $O(n)$ time, and is in concept able to converging to a minimax optimum estimate. Nonetheless, the practitioner is commonly constrained to only tens to lots of of iterations, and the sluggish and/or inconsistent convergence of non-convex gradient descent can stop a high-quality estimate from being obtained. Not too long ago, the strategy of preconditioning was proven to be extremely efficient at accelerating the native convergence of non-convex gradient descent when the measurements are noiseless. On this paper, we describe how preconditioning needs to be accomplished for noisy measurements to speed up native convergence to minimax optimality. For the symmetric matrix sensing downside, our proposed preconditioned methodology is assured to domestically converge to minimax error at a linear price that’s proof against ill-conditioning and/or over-parameterization. Utilizing our proposed preconditioned methodology, we carry out a 60 megapixel medical picture denoising job, and observe considerably diminished noise ranges in comparison with earlier approaches.

Submission historical past

From: Jialun Zhang [view email]
[v1]
Fri, 26 Might 2023 19:32:07 UTC (2,498 KB)
[v2]
Wed, 28 Feb 2024 04:14:13 UTC (8,874 KB)



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