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Sharp Restricted Isometry Property Bounds for Low-Rank Matrix Recovery Problems with Corrupted Measurements
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Allow arbitrary noise distributions and use the event $\|\mathbf A^Tw\|\leq\epsilon$ | Global local-minimizer guarantee · Noisy low-rank matrix recovery | RIP constant threshold: $\delta<1/10$ -> $\delta<1/2$ | Helped |
| Reduce the RIP constant | Low-rank matrix recovery · Noisy low-rank matrix recovery | distance from the ground truth | Helped |
| Use the local guarantee rather than the global guarantee when the solution is in its specified neighborhood | Low-rank matrix recovery · Noisy low-rank matrix recovery, local neighborhood | RIP constant threshold | Mixed |
| Use the exact Gaussian noise distribution to calculate the success probability | Global local-minimizer guarantee · Isotropic Gaussian noise | tightness of the bound | Helped |
| Use perturbed gradient descent to find an approximate second-order critical point | Strict-saddle guarantee · Noisy low-rank matrix recovery | convergence: $O(\mathrm{poly}(1/\kappa))$ | Helped |
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