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Found 5 papers, 1 papers with code
Fast and Accurate Estimation of Low-Rank Matrices from Noisy Measurements via Preconditioned Non-Convex Gradient Descent
Recently, the technique of preconditioning was shown to be highly effective at accelerating the local convergence of non-convex gradient descent when the measurements are noiseless.
Simple Alternating Minimization Provably Solves Complete Dictionary Learning
This paper focuses on complete dictionary learning problem, where the goal is to reparametrize a set of given signals as linear combinations of atoms from a learned dictionary.
Accelerating SGD for Highly Ill-Conditioned Huge-Scale Online Matrix Completion
The matrix completion problem seeks to recover a $d\times d$ ground truth matrix of low rank $r\ll d$ from observations of its individual elements.
Preconditioned Gradient Descent for Overparameterized Nonconvex Burer--Monteiro Factorization with Global Optimality Certification
We consider using gradient descent to minimize the nonconvex function $f(X)=\phi(XX^{T})$ over an $n\times r$ factor matrix $X$, in which $\phi$ is an underlying smooth convex cost function defined over $n\times n$ matrices.
How Many Samples is a Good Initial Point Worth in Low-rank Matrix Recovery?
Optimizing the threshold over regions of the landscape, we see that for initial points around the ground truth, a linear improvement in the quality of the initial guess amounts to a constant factor improvement in the sample complexity.
