Research map / Learning theory and algorithms / Matrix and tensor methods
Semidefinite Programming versus Burer-Monteiro Factorization for Matrix Sensing
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use SDP instead of B-M factorization | structured low-complexity matrix completion · Structured matrix completion, low-complexity class | ground-truth recovery | Helped |
| Apply B-M factorization | structured low-complexity matrix completion · Structured matrix completion, low-complexity class | spurious local minima: at least 2^{r|\mathcal{S}(\mathcal{G}_1)|}-2^r | Hurt |
| Use SDP instead of B-M factorization | matrix sensing · Matrix sensing, rank-r | sufficient RIP threshold δ₂ᵣ: δ_{2r} < \max \left\{1/2, \frac{2r}{n+(n-2r)(2l-5)}\right\} versus δ_{2r} < 1/2 | Helped |
| Use B-M factorization instead of SDP | rank-1 matrix completion · Chain graph with one self-loop | spurious solutions | Helped |
| Use B-M factorization instead of SDP | rank-1 matrix completion · Chain graph with one self-loop and specified ground truth | ground-truth recovery | Helped |
| Use B-M factorization instead of SDP | rank-1 matrix completion · Odd simple cycle with the stated condition | ground-truth recovery | Helped |
Closest papers by meaning
- Robust Matrix Sensing in the Semi-Random Model (NeurIPS 2023 · similarity 0.89)
- Symmetric Matrix Completion with ReLU Sampling (ICML 2024 · similarity 0.87)
- A Non-convex One-Pass Framework for Generalized Factorization Machine and Rank-One Matrix Sensing (NeurIPS 2016 · similarity 0.87)
- The non-convex Burer-Monteiro approach works on smooth semidefinite programs (NeurIPS 2016 · similarity 0.87)
- Polynomial Optimization Methods for Matrix Factorization (AAAI 2017 · similarity 0.87)
- RGNMR: A Gauss-Newton method for robust matrix completion with theoretical guarantees (NeurIPS 2025 · similarity 0.86)
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