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Global Optimality of Local Search for Low Rank Matrix Recovery
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add RIP-based incoherence condition (delta_2r<1/5) to factorized matrix sensing objective | factorized non-convex matrix sensing f(U) · noiseless matrix sensing | existence of spurious local minima | Helped |
| Random initialization instead of SVD initialization for gradient descent | factorized gradient descent for matrix sensing · n=100 random PSD matrix sensing | phase transition at m ~ 2nr | No clear effect |
| Counterexample: unconstrained rank-r and rank-1 objectives in Examples 1-2 without RIP | factorized objective without RIP · constructed low-rank examples | existence of non-global local minima | Hurt |
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