Research map / Learning theory and algorithms / Matrix and tensor methods
Toward Efficient and Accurate Covariance Matrix Estimation on Compressed Data
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace data-oblivious projection (Gauss-Inverse/Sparse/UniSample-HD) with data-aware weighted sampling (alpha=0.9 mixing l1 and l2 sampling probabilities) for compressed covariance estimation | covariance matrix estimation from compressed data · synthetic datasets X1-X6 | relative spectral-norm estimation error ||Ce-C||2/||C||2 vs m/d | Helped |
| Replace data-oblivious projection with weighted sampling | covariance matrix estimation from compressed data · real-world datasets (nine datasets, e.g. Mnist, Cifar10, Gist1M) | relative estimation error vs m/d | Helped |
| Use weighted sampling instead of UniSample-HD on X1 (uniform magnitudes, phi=0.81 sqrt(d)) | proposed method · synthetic X1 (d=1024, n=20000) | relative estimation error | Mixed |
| Sparse projection (biased/unbiased variant) instead of the proposed weighted sampling | covariance matrix estimation · synthetic datasets | relative estimation error | Hurt |
| Gauss-Inverse projection instead of weighted sampling (much higher computational time) | covariance matrix estimation · synthetic datasets | running time relative to standard | Hurt |
| Sampling probability mixing parameter alpha varied from 1 to 0 (l1 to l2 sampling) (ablation) | proposed method · theory and appendix experiments | estimation error | Mixed |
| Increase number of samples n (data size) with fixed d for proposed method | proposed method · synthetic Cp7/Cp8, d=1000, varied n | scaled error (error times sqrt(n)) | Helped |
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