Research map / Learning theory and algorithms / Matrix and tensor methods
Low-Rank Extragradient Method for Nonsmooth and Low-Rank Matrix Optimization Problems
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| increase dimension n from 100 to 600 (with lambda scaled down) | Extragradient with rank-r SVDs · Sparse PCA | recovery error: 0.0425 -> 0.0100 | Helped |
| increase dimension n from 100 to 600 | Extragradient with rank-r SVDs · Robust PCA | recovery error: 0.0079 -> 0.0065 | No clear effect |
| increase dimension n from 100 to 600 | Extragradient with rank-r SVDs · Linearly-constrained low-rank estimation | recovery error: 0.0437 -> 0.0735 | Hurt |
| increase dimension n from 100 to 600 | Extragradient with rank-r SVDs · Low-rank and sparse recovery (rank 5) | recovery error: 0.0641 -> 0.0274 | Helped |
| increase dimension n from 100 to 600 | Extragradient with rank-r SVDs · Low-rank and sparse recovery (rank 10) | recovery error: 0.0702 -> 0.0356 | Mixed |
| run extragradient from simple warm start versus initialization point | Extragradient with rank-r SVDs · Sparse PCA | relative error: 1.7456 -> 0.0425 | Helped |
| replace full-rank SVD projections with rank-r truncated projections, r = rank(M0) (ablation) | Extragradient method · all five tasks | iterate sequence | No clear effect |
| low-rank projected subgradient step instead of saddle-point extragradient (ablation) | Projected subgradient method · Sparse PCA (Lemma 5) | rank of iterate | Hurt |
| increase SVD rank r above optimal rank | Extragradient with rank-r SVDs · Theory (Theorem 1) | initialization radius | Helped |
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