Research map / Learning theory and algorithms / Matrix and tensor methods
On the Statistical Limits of Convex Relaxations
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use exhaustive subset scanning instead of a convex relaxation | Sparse principal submatrix estimation · Sparse principal submatrix estimation | absolute estimation error: C vs. C√(1/s* · log(d/s*)) | Helped |
| Use exhaustive subset scanning instead of a convex relaxation | Stochastic block model edge probability estimation · Stochastic block model edge probability estimation | absolute estimation error: 1/4 vs. C√(1/s* · log(d/s*)) | Helped |
| Use the convex relaxation hierarchy H(ℓ) rather than an unrestricted estimator | Sparse principal submatrix estimation · Sparse principal submatrix estimation | minimax absolute estimation error: C√(1/s* · log(d/s*)) vs. C | Hurt |
| Use the convex relaxation hierarchy H(ℓ) rather than an unrestricted estimator | Stochastic block model edge probability estimation · Stochastic block model edge probability estimation | minimax absolute estimation error: C√(1/s* · log(d/s*)) vs. 1/4 | Hurt |
| Use β̂max as a computationally tractable estimator | Sparse principal submatrix estimation · Sparse principal submatrix estimation | absolute estimation error: C√log d | Mixed |
| Use the basic β̂avg estimator | Sparse principal submatrix estimation · Sparse principal submatrix estimation | absolute estimation error rate: d/(s*)2 vs. √(1/s* · log(d/s*)) | Hurt |
| Increase the SoS level ℓ | Convex relaxation hierarchy for sparse principal submatrix estimation · Sparse principal submatrix estimation | relaxation tightness | No clear effect |
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