Research map / Learning theory and algorithms / Matrix and tensor methods
On Learning Sparsely Used Dictionaries from Incomplete Samples
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use democratic, incoherent dictionaries and partial samples in the descent-style learning procedure | Dictionary learning from incomplete samples · Incomplete samples | column-wise dictionary error: O(\sqrt{k/n}) | Helped |
| Add a small fully observed hold-out set for spectral initialization | Proposed dictionary learning method · Incomplete samples | initialization error: \delta = O^*(1/\log n) | Helped |
| Scale the thresholding encoder by 1/ρ | Gradient descent-style algorithm · Incomplete samples | sparse-code support recovery | Helped |
| Use a small fully observed hold-out set rather than relying only on partial samples for initialization | Spectral initialization algorithm · Incomplete samples | initialization success: \widetilde{\Omega}(m) full samples | Helped |
| Use the proposed method at ρ = 0.6, 0.8, or 1.0 | Proposed dictionary learning method · Synthetic 256×256 Gaussian dictionary; 6-sparse codes | successful recovery | Helped |
| Reduce the observation probability to ρ = 0.4 | Proposed dictionary learning method · Synthetic 256×256 Gaussian dictionary; 6-sparse codes | successful recovery sample requirement: p = 10,000 | Mixed |
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