Research map / Learning theory and algorithms / Matrix and tensor methods
Sparse Convex Optimization via Adaptively Regularized Hard Thresholding
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Apply hard thresholding to an adaptively regularized objective, with sampling-based unregularization | ARHT · Sparse convex optimization | sparsity required for f(x) ≤ f(x*) + ε: O(s^*κ) vs. O(s^*min{κ(f(x^0)-f(x^*) )/ε, κ^2}) | Helped |
| Use OMPR with sparsity s satisfying the stated RIP tradeoff | OMPR · General functions satisfying the RIP condition | RIP condition: δ_{2s^*} < 0.33; δ_{3s^*} < 0.47; δ_{4s^*} < 0.55; δ_{31s^*} < 0.83 | Mixed |
| Use OMPR with s = s* | OMPR · Compressed sensing | RIP condition: δ_{2s^*} < 1/3≈0.33 | Helped |
| Use ARHT with the stated signal-to-noise condition | ARHT · Sparse support recovery | support recovery: s = O(s^*κ) | Helped |
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