Research map / Learning theory and algorithms / Matrix and tensor methods
Polynomial Tensor Sketch for Element-wise Function of Low-Rank Matrix
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Coreset-TS instead of RFF | RBF kernel approximation · segment, satimage, anuran, usps, grid, mapping, letter | kernel approximation error: 1.7\times10^{-3} -> 3.21\times 10^{-4} (segment); 3.06 \times 10^{3} -> 1.29 (letter) | Helped |
| Use Coreset-TS instead of RFF | RBF kernel SVM · segment, satimage, anuran, usps, grid, mapping, letter | classification error (%): 3.28 -> 3.22 (segment); 6.50 -> 5.36 (usps); 40.33 -> 37.36 (anuran); 24.11 -> 23.74 (satimage) | Mixed |
| Use Coreset-TS instead of exact RBF SVM | RBF kernel SVM · segment, satimage, anuran, usps, grid, mapping, letter | classification error (%): 3.20 -> 3.22 (segment); 23.54 -> 23.74 (satimage); 37.26 -> 37.36 (anuran); 2.11 -> 5.36 (usps) | Mixed |
| Increase sketch dimension m (ablation) | Coreset-TS · usps, grid, mapping, letter | classification error (%): 5.36 -> 3.33 (usps); 15.99 -> 11.17 (grid); 17.35 -> 17.11 (mapping); 10.30 -> 5.13 (letter) | Helped |
| Increase coreset size k (ablation) | Coreset-TS · segment | kernel approximation error: 5.52\times 10^{-4} -> 5.23\times 10^{-4} (k=5 -> k=30) | Helped |
| Replace optimal coefficients with coreset-estimated coefficients (ablation) | Poly-TensorSketch · segment | kernel approximation error: 5.17 \times 10^{-4} -> 5.39\times 10^{-4} | Hurt |
| Use coefficients optimized for total approximation error rather than Taylor or Chebyshev series coefficients (ablation) | Poly-TensorSketch · RBF kernel approximation | relative approximation error | Helped |
| Increase sketch dimension m in the neural-network linearization (ablation) | Coreset-TS sigmoid linearization · MNIST | test error (%): 11.45 -> 7.62 | Helped |
Closest papers by meaning
- Near Optimal Sketching of Low-Rank Tensor Regression (NeurIPS 2017 · similarity 0.90)
- Learning-Based Low-Rank Approximations (NeurIPS 2019 · similarity 0.89)
- Tensor-Based Sketching Method for the Low-Rank Approximation of Data Streams. (ICLR 2023 · similarity 0.88)
- Few-Shot Data-Driven Algorithms for Low Rank Approximation (NeurIPS 2021 · similarity 0.88)
- Fast Sampling-Based Sketches for Tensors (ICML 2024 · similarity 0.86)
- Matrix Product Sketching via Coordinated Sampling (ICLR 2025 · similarity 0.85)
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