Research map / Learning theory and algorithms / Matrix and tensor methods
Generalization Bounds for Inductive Matrix Completion in Low-Noise Settings
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use a noise-aware bound that combines perturbed exact-recovery analysis with generalization-complexity analysis | Nuclear-norm inductive matrix completion · Noisy uniform-sampling IMC | expected generalization loss: scales as \sdv ... \sqrt{\frac{1}{N}} | Helped |
| Reduce the subgaussian noise level | Nuclear-norm inductive matrix completion · Noisy uniform-sampling IMC | expected generalization loss: proportional to the subgaussianity constant \sdv | Helped |
| Increase the number of samples beyond the exact recovery threshold | Nuclear-norm inductive matrix completion · Noisy uniform-sampling IMC | expected generalization loss: \sqrt{\frac{1}{N}} | Helped |
| Use Talagrand-type inequalities for the absolute loss | Nuclear-norm inductive matrix completion · Noisy uniform-sampling IMC | expected absolute loss: \sqrt{\frac{1}{N}} | Helped |
| Allow non-orthonormal side information instead of requiring orthonormal columns | Exact recovery for inductive matrix completion · Noiseless uniform-sampling IMC | exact recovery guarantee | Helped |
| Cross the exact recovery threshold as the sample count grows | Classic inductive matrix completion with square loss · Synthetic 100×100 rank-10 matrices with rank-40 side information | RMSE | Helped |
| Increase the sample count after crossing the threshold | Classic inductive matrix completion with square loss · Synthetic low-noise matrices | RMSE: at least as \widetilde{O}(\frac{\sigma}{\sqrt{N}}) | Helped |
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