Research map / Learning theory and algorithms / Matrix and tensor methods
A Scalable Second Order Method for Ill-Conditioned Matrix Completion from Few Samples
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use MatrixIRLS instead of the compared fixed-rank methods | Matrix completion · 1000 × 1000 rank-5 matrices, κ=10 | oversampling ratio for recovery: ρ=1.5 | Helped |
| Use rank-adaptive LRGeomCG Pursuit rather than fixed-rank LRGeomCG (ablation) | LRGeomCG · 1000 × 1000 rank-5 matrices, κ=10^5 | oversampling ratio at phase transition: ρ= 1.8 | Helped |
| Use rank-adaptive R3MC w/ Rank Update rather than fixed-rank R3MC (ablation) | R3MC · 1000 × 1000 rank-5 matrices, κ=10^5 | oversampling ratio at phase transition: ρ= 1.7 | Helped |
| Use rank-adaptive LRGeomCG Pursuit instead of MatrixIRLS | Matrix completion · 1000 × 1000 rank-5 matrices, κ=10^5 | oversampling ratio at phase transition: ρ= 1.9; ρ= 1.8 | Helped |
| Use rank-adaptive R3MC w/ Rank Update instead of MatrixIRLS | Matrix completion · 1000 × 1000 rank-5 matrices, κ=10^5 | oversampling ratio at phase transition: ρ= 1.9; ρ= 1.7 | Helped |
| Use MatrixIRLS rather than fixed-rank LRGeomCG or R3MC | Matrix completion · 1000 × 1000 matrices, κ=10^5 | exact recovery | Helped |
| Use MatrixIRLS rather than R2RILS | Matrix completion · 1000 × 1000 rank-10 matrix, κ=10^10, ρ=4 | recovery of singular values: 10^{10}; 15 digits | Helped |
| Use rank-adaptive LRGeomCG Pursuit rather than MatrixIRLS | Matrix completion · 1000 × 1000 rank-30 matrices with a singular-value plateau, κ=10^10, ρ=1.5 | runtime to reach relative Frobenius error around 10^{-12}: 5 seconds; 13 seconds; around 10^{-12} | Helped |
| Use MatrixIRLS rather than LRGeomCG Pursuit | Matrix completion · 1000 × 1000 rank-30 matrices with a singular-value plateau, κ=10^10, ρ=1.5 | monotonicity of error decrease: 13 seconds | Helped |
| Use MatrixIRLS rather than fixed-rank LRGeomCG or R3MC | Matrix completion · 1000 × 1000 rank-30 matrices with a singular-value plateau, κ=10^10, ρ=1.5 | completion | Helped |
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