Research map / Learning theory and algorithms / Matrix and tensor methods
Towards Faster Rates and Oracle Property for Low-Rank Matrix Estimation
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| replace nuclear norm penalty with nonconvex SCAD penalty on singular values | low-rank matrix estimation (image inpainting) · Image inpainting (6 images, 512x512, 50% observed) | RMSE (x10^-2): e.g., Lenna 2.79 vs 5.05 (nuclear) ; Girl 2.06 vs 4.77 | Helped |
| replace nuclear norm penalty with nonconvex MCP penalty on singular values | low-rank matrix estimation (image inpainting) · Image inpainting (6 images, 512x512, 50% observed) | RMSE (x10^-2): e.g., Lenna 2.81 vs 5.05 (nuclear) | Helped |
| replace nuclear norm penalty with nonconvex SCAD penalty | low-rank matrix estimation (collaborative filtering) · Jester1/Jester2/Jester3 recommendation | averaged RMSE: Jester1 4.1721 vs 4.6910 (nuclear) | Helped |
| replace nuclear norm penalty with nonconvex MCP penalty | low-rank matrix estimation (collaborative filtering) · Jester1/Jester2/Jester3 recommendation | averaged RMSE: Jester1 4.1719 vs 4.6910 (nuclear) | Helped |
| nonconvex SCAD penalty on singular values in matrix sensing simulations | low-rank matrix estimation (matrix sensing, simulation) · Simulated matrix sensing, rank 10 | Frobenius norm error (log scale) | Helped |
| nonconvex SCAD penalty in matrix completion simulations | low-rank matrix estimation (matrix completion, simulation) · Simulated matrix completion, rank floor(log2 m) | MSE vs rescaled sample size | Helped |
| nonconvex penalty (SCAD) with rank recovery when n >= 3rm | low-rank matrix estimation (matrix sensing, simulation) · Simulated matrix sensing, rank 10 | probability of exact rank recovery | Helped |
Closest papers by meaning
- A Unified Variance Reduction-Based Framework for Nonconvex Low-Rank Matrix Recovery (ICML 2017 · similarity 0.90)
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- Recovery guarantee of weighted low-rank approximation via alternating minimization (ICML 2016 · similarity 0.87)
- Symmetric Matrix Completion with ReLU Sampling (ICML 2024 · similarity 0.86)
- Flat Minima in Linear Estimation and an Extended Gauss Markov Theorem (ICLR 2024 · similarity 0.86)
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