Research map / Learning theory and algorithms / Matrix and tensor methods
A novel variational form of the Schatten-$p$ quasi-norm
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add rank-one updates (ablation) | Variational Schatten-0.5 · Simulated matrix completion (true rank 20, missing rate=0.4, SNR=10dB; initial rank 0.5r) | RE: 0.5260 -> 0.2241 | Helped |
| add rank-one updates (ablation) | Variational Schatten-0.3 · Simulated matrix completion (true rank 20, missing rate=0.4, SNR=10dB; initial rank 0.5r) | RE: 0.5263 -> 0.2425 | Helped |
| add rank-one updates (ablation) | Variational Schatten-0.5 · Simulated matrix completion (true rank 20, missing rate=0.4, SNR=10dB; initial rank 0.5r) | estimated rank: 10 -> 20 | Helped |
| use the proposed Schatten-p factorization instead of FGSR | Matrix completion · Simulated matrix completion (true rank 20, missing rate=0.4, SNR=10dB; initial rank 0.5r) | RE: 0.5259 -> 0.2241 | Helped |
| use the proposed Schatten-p factorization instead of FGSR | Matrix completion · Simulated matrix completion (true rank 20, missing rate=0.4, SNR=10dB; initial rank r) | RE: 0.1320 -> 0.1225 | Helped |
| use p=0.3 rather than p=0.5 (ablation) | Variational Schatten-p · Simulated matrix completion (true rank 20, missing rate=0.4, SNR=10dB; initial rank r) | RE: 0.1228 -> 0.1225 | Helped |
| use p=0.3 rather than p=0.5 (ablation) | Variational Schatten-p · Simulated matrix completion (true rank 20, missing rate=0.4, SNR=10dB; initial rank 0.5r) | RE: 0.2241 -> 0.2425 | Hurt |
| use the proposed method rather than softImpute-ALS | Matrix completion · Simulated matrix completion | RE | Helped |
| use the proposed method rather than IRNN or softImpute-ALS | MovieLens-100K · MovieLens-100K (50% and 25% observed entries) | NMAE | Helped |
| use the proposed method rather than FGSR | MovieLens-100K · MovieLens-100K (50% and 25% observed entries) | NMAE | No clear effect |
Closest papers by meaning
- Scalable Algorithms for Tractable Schatten Quasi-Norm Minimization (AAAI 2016 · similarity 0.94)
- A Unified Convex Surrogate for the Schatten-p Norm (AAAI 2017 · similarity 0.93)
- Guarantees of a Preconditioned Subgradient Algorithm for Overparameterized Asymmetric Low-rank Matrix Recovery (ICML 2025 · similarity 0.86)
- Flat Minima in Linear Estimation and an Extended Gauss Markov Theorem (ICLR 2024 · similarity 0.86)
- Fast exact recovery of noisy matrix from few entries: the infinity norm approach (NeurIPS 2025 · similarity 0.85)
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