Research map / Optimization / Implicit bias and generalization
Matrix Completion has No Spurious Local Minimum
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add the regularizer R(X) penalizing rows with large norm to the matrix completion objective | Burer-Monteiro factorized PSD matrix completion objective · theoretical analysis (symmetric PSD matrix completion) | presence of spurious local minima | Helped |
| Use the rank-1 regularizer h(t)=(|t|-alpha)^4 I(|t|>alpha) so that the regularizer is zero on incoherent vectors and has Lipschitz second derivative | rank-1 matrix completion objective · theoretical analysis (rank-1 case) | presence of spurious local minima | Helped |
| Use the simple (linear-in-indicator) proof strategy and concentration to pass from the full-observation objective to the partially observed one | proof technique for matrix completion geometry · theoretical analysis (rank-1 case) | qualitative proof generalizability | No clear effect |
| Stochastic gradient descent with arbitrary/random initialization on the regularized objective | regularized PSD matrix completion objective · theoretical guarantee (informal) | convergence to global minimum XX^T=ZZ^T=M | Helped |
Closest papers by meaning
- Provable Efficient Online Matrix Completion via Non-convex Stochastic Gradient Descent (NeurIPS 2016 · similarity 0.90)
- Rank-1 Matrix Completion with Gradient Descent and Small Random Initialization (NeurIPS 2023 · similarity 0.90)
- Symmetric Matrix Completion with ReLU Sampling (ICML 2024 · similarity 0.90)
- No Spurious Local Minima in Nonconvex Low Rank Problems: A Unified Geometric Analysis (ICML 2017 · similarity 0.90)
- Generalization Analysis of Deep Non-linear Matrix Completion (ICML 2024 · similarity 0.88)
- Online Matrix Completion: A Collaborative Approach with Hott Items (ICML 2024 · similarity 0.87)
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