Research map / Learning theory and algorithms / Matrix and tensor methods
On the Power of Truncated SVD for General High-rank Matrix Estimation Problems
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Apply top-k truncated SVD to a matrix estimate that is close in spectral norm | General high-rank PSD matrix estimation · General high-rank PSD matrix | Frobenius estimation error: (1+32\epsilon)\|\mathbf A-\mathbf A_k\|_F + 102\sqrt{2k}\epsilon^2\|\mathbf A-\mathbf A_k\|_2 | Helped |
| Use truncated SVD of re-scaled zero-filled observations | High-rank matrix completion · High-rank matrix completion | Frobenius estimation error: \left(1+O(\epsilon)\right)\|\mathbf A-\mathbf A_k\|_F | Helped |
| Use truncated SVD of the noisy observation | High-rank matrix denoising · High-rank matrix denoising | Frobenius estimation error: \left(1+O\left(\sqrt{\frac{\nu}{\sigma_{k+1}(\mathbf A)}}\right)\right)\|\mathbf A-\mathbf A_k\|_F + O(\sqrt{k}\nu) | Helped |
| Use truncated SVD of sample covariance | High-dimensional Gaussian covariance estimation · High-dimensional Gaussian covariance estimation | Frobenius estimation error: \left(1+O(\epsilon)\right)\|\mathbf A-\mathbf A_k\|_F | Helped |
| Use truncated SVD under a spectral-gap error condition | General high-rank PSD matrix estimation · General high-rank PSD matrix with a spectral gap | Frobenius estimation error: \|\mathbf A-\mathbf A_k\|_F + 102\sqrt{2k}\epsilon\left(\sigma_{k}(\mathbf A)-\sigma_{k+1}(\mathbf A)\right) | Helped |
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