Research map / Learning theory and algorithms / Matrix and tensor methods
The price of ignorance: how much does it cost to forget noise structure in low-rank matrix estimation?
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Gaussian AMP rather than the mismatched Bayes estimator | Low-rank rank-one estimation with structured rotationally invariant noise · All simulated mismatch settings | MSE | Hurt |
| Assume Gaussian noise instead of using the true noise statistics | Mismatched Bayes and Gaussian AMP · Structured-noise estimation | MSE | Hurt |
| Use the correct noise statistics and corresponding Onsager corrections | Gaussian AMP · Structured-noise estimation | MSE | Helped |
| Use the noise-aware optimal spectral scaling | Leading-eigenvector spectral estimator · Structured-noise estimation | MSE | Helped |
| Use the correct noise statistics rather than Gaussian assumptions | Mismatched Bayes and Gaussian AMP · High-SNR regime | overlap | No clear effect |
| Use the mismatched Bayes estimator rather than Gaussian AMP | Structured-noise estimation · High-SNR regime | overlap | No clear effect |
| Use mismatched Bayes instead of GauSpec | Spherical-prior estimation with no SNR mismatch and h̄ ≥ 1 · Structured-noise estimation | MSE | No clear effect |
| Increase the true SNR while retaining a mismatched Gaussian model | Mismatched Bayes and Gaussian spectral estimators · Some structured-noise settings | MSE | Mixed |
| Use the correct noise model and SNR instead of assuming Gaussian noise | Gaussian spectral estimator · Structured rotationally invariant noise | MSE: MSE(M_GS) = MSE(M_OS) + 1/2( C(ρ,λ*) - (1 - 1/λ))^2 | Helped |
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