Research map / Learning theory and algorithms / Matrix and tensor methods
Mutual information for symmetric rank-one matrix estimation: A proof of the replica formula
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add a seed and spatially couple neighboring blocks | AMP for symmetric rank-one matrix estimation · Symmetric rank-one estimation | AMP threshold | Helped |
| Use spatial coupling to relate the coupled and original systems | Mutual-information analysis · Symmetric rank-one estimation | Mutual information per variable | No clear effect |
| Run AMP without additional initialization knowledge | Symmetric rank-one matrix estimation · Noise variance Δ < Δ_AMP or Δ > Δ_RS | Matrix-MMSE | Helped |
| Use AMP instead of the information-theoretic optimum | Symmetric rank-one matrix estimation · Δ_AMP < Δ < Δ_RS | Matrix-MMSE | Hurt |
| Use AMP or spectral methods instead of information-theoretic inference | Sparse spiked Wigner model · Low-density regime, Δ_AMP < Δ < Δ_RS | Matrix-MMSE | Hurt |
| Use AMP or spectral methods instead of information-theoretic inference | Asymmetric community detection · ρ < 1/2 − √(1/12), Δ > 1 below the information-theoretic transition | Overlap with hidden communities | Hurt |
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