Research map / Learning theory and algorithms / Matrix and tensor methods
Estimating Rank-One Spikes from Heavy-Tailed Noise via Self-Avoiding Walks
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace the top-eigenvector estimator with a self-avoiding-walk estimator | Spiked Wigner recovery under heavy-tailed noise · Spiked Wigner recovery | squared correlation | Helped |
| Restrict the polynomial to self-avoiding walks, making it multilinear in the noise entries | Spiked Wigner recovery under heavy-tailed noise · Spiked Wigner recovery | recoverability under unit-variance noise | Helped |
| Use non-backtracking walks instead of fully self-avoiding walks | Synthetic spiked matrices · Synthetic spiked matrices | performance | No clear effect |
| Clip large matrix entries before PCA | Spiked Wigner recovery with adversarially chosen, non-identically distributed noise · Spiked Wigner recovery | correlation with the planted vector | Hurt |
| Use self-avoiding-walk polynomials for tensor estimation | Order-3 spiked tensor recovery with heavy-tailed noise · Order-3 spiked tensor recovery | normalized expected correlation | Helped |
| Increase computation using the sub-exponential-time tensor estimator | Order-3 spiked tensor recovery · Order-3 spiked tensor recovery | normalized expected correlation at lower signal levels | Helped |
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