Research map / Learning theory and algorithms / Matrix and tensor methods
Fast and accurate randomized algorithms for low-rank tensor decompositions
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use new HOOI-style sketched rank-constrained Tucker-ALS instead of one-factor-at-a-time sketched ALS | sketched Tucker-ALS (TensorSketch/leverage sampling) · synthetic dense tensors | final fitness: 4.5% to 22.0% relative improvement | Helped |
| use new HOOI-style sketched Tucker-ALS instead of the reference | sketched Tucker-ALS · synthetic sparse tensors p=0.1,0.5 | final fitness: 3.6% to 12.7% relative improvement | Helped |
| use new scheme instead of reference at p=0.02 sparsity | sketched Tucker-ALS · sparse tensors p=0.02 | final fitness | No clear effect |
| add RRF-based initialization instead of random initialization for leverage score sampling (ablation) | leverage score sampling Tucker-ALS · high-coherence tensors | final fitness | Helped |
| RRF-based vs random initialization for TensorSketch (ablation) | TensorSketch Tucker-ALS · high-coherence tensors | final fitness | No clear effect |
| RRF initialization for deterministic leverage sampling (ablation) | deterministic leverage sampling Tucker-ALS · dense tensors | variability of fitness | Helped |
| RRF vs random initialization on tensors without high coherence (ablation) | sketched Tucker-ALS · dense tensors | final fitness | No clear effect |
| increase sketch size factor K (ablation) | sketched Tucker-ALS · synthetic tensors | final fitness | Helped |
| deterministic vs random leverage sampling at small sketch size K=4 (ablation) | leverage score sampling · tensors with strong low-rank signal | final fitness | Helped |
| Tucker compression then CP on core instead of direct CP-ALS | CP-ALS · synthetic sparse CP tensors | final fitness | Helped |
| sketched Tucker-ALS instead of HOOI before CP | Tucker+CP · synthetic CP tensors | final fitness | No clear effect |
Closest papers by meaning
- Low-Rank Tucker Decomposition of Large Tensors Using TensorSketch (NeurIPS 2018 · similarity 0.91)
- More Efficient Sampling for Tensor Decomposition With Worst-Case Guarantees (ICML 2022 · similarity 0.90)
- Fitting Low-Rank Tensors in Constant Time (NeurIPS 2017 · similarity 0.90)
- SPALS: Fast Alternating Least Squares via Implicit Leverage Scores Sampling (NeurIPS 2016 · similarity 0.90)
- Efficient Leverage Score Sampling for Tensor Train Decomposition (NeurIPS 2024 · similarity 0.88)
- Debiasing Random Oblique Projections for Subsampled OLS and Fast CUR in High Dimensions (NeurIPS 2026 · similarity 0.86)
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