Research map / Learning theory and algorithms / Matrix and tensor methods
Universality in Learning from Linear Measurements
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace iid measurement vectors with vectors from another admissible distribution having the same mean and covariance | Convex estimator for structured-signal recovery · Linear measurements | perfect-recovery phase transition | No clear effect |
| Use quadratic measurements with nuclear-norm recovery for a rank-r PSD matrix | Low-rank matrix recovery · Quadratic measurements, rank-r PSD matrix | required measurements: 3nr | Helped |
| Use PhaseLift for rank-one phase retrieval | Phase retrieval · PhaseLift | required measurements: 3n | Helped |
| Use quadratic measurements with ℓ1 penalty for sparse matrix recovery | Sparse matrix recovery · Quadratic measurements, sparse matrix | required measurements: n^2 \delta^\star | Helped |
| Use a weighted sum of ℓ1 and trace penalties for simultaneous sparsity and low rank | Simultaneously sparse and low-rank matrix recovery · Quadratic measurements, simultaneously sparse and rank-r PSD matrix | required measurements: \mathcal O(\min (k^2,rn)) | Helped |
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