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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 poly...
Stochastic gradient methods have gained increasing attention for solving large-scale inverse problems due to their computational efficiency. However, their theoretical justification in the context of ill-posed problems remains underdeveloped, particularly regarding convergence rate analysis, where existing results...
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