Sharp statistically optimal recovery guarantees for second-order critical points of nonconvex matrix LASSO under RIP, with counterexamples showing overparametrization does not always improve the landscape.
Estimation of (near) low-rank matrices with noise and high- dimensional scaling,
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Mild logarithmic overparametrization in Burer-Monteiro nonconvex optimization yields optimal sample complexity and error for phase retrieval and rank-1 matrix sensing via a new semidefinite-structure analysis of second-order critical points.
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Sharp recovery and landscape guarantees for the nonconvex matrix LASSO
Sharp statistically optimal recovery guarantees for second-order critical points of nonconvex matrix LASSO under RIP, with counterexamples showing overparametrization does not always improve the landscape.
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Phase retrieval and matrix sensing via benign and overparametrized nonconvex optimization
Mild logarithmic overparametrization in Burer-Monteiro nonconvex optimization yields optimal sample complexity and error for phase retrieval and rank-1 matrix sensing via a new semidefinite-structure analysis of second-order critical points.