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We study nonconvex methods for matrix completion, the problem of recovering a low-rank matrix from a subset of its entries.
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We study nonconvex methods for matrix completion, the problem of recovering a low-rank matrix from a subset of its entries. Convex methods achieve sample complexity linear in the matrix dimension and the rank, up to logarithmic factors, whereas global guarantees for commonly used nonconvex methods require a higher polynomial dependence on the rank. We close this gap by analyzing Riemannian gradient descent (RGD) and Riemannian Gauss--Newton (RGN) methods. For an $n\times n$ matrix of rank $r$ with incoherence parameter $μ$ and condition number $κ$, the two methods achieve exact recovery with h...
Discovered via ArXiv
Research papers and preprints from arXiv.
Publisher: arxiv.org
ID: http://arxiv.org/abs/2609.17048v1 · Indexed about 1 hour ago