Research map / Learning theory and algorithms / Matrix and tensor methods
Is Input Sparsity Time Possible for Kernel Low-Rank Approximation?
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Compute a relative-error rank-k approximation of the kernel matrix | Gaussian, polynomial, or linear kernel approximation · Kernel matrix low-rank approximation | runtime lower bound: o(nnz(A)k) + O(nk^{2}) | Hurt |
| Use random Fourier features and fast multiplication by random Gaussian matrices | Kernel PCA for shift- and rotation-invariant kernels · Kernel PCA | runtime: O(nnz(A)) + \tilde O\left(n^{\omega+ 1.5} \cdot \left(\frac{k}{\sigma_{k+1}\epsilon^2}\right)^{\omega-1.5}\right) | Helped |
| Use sketching to approximate AA^T | Rank-k approximation of AA^T · AA^T | runtime: O(nnz(A)k) + n\cdot \mathop\mathrm{poly}(k/\epsilon) | Helped |
Closest papers by meaning
- Hardness of Low Rank Approximation of Entrywise Transformed Matrix Products (NeurIPS 2023 · similarity 0.90)
- Input-Sparsity Low Rank Approximation in Schatten Norm (ICML 2020 · similarity 0.89)
- Improved Algorithms for Kernel Matrix-Vector Multiplication Under Sparsity Assumptions (ICLR 2025 · similarity 0.89)
- Near Input Sparsity Time Kernel Embeddings via Adaptive Sampling (ICML 2020 · similarity 0.88)
- Entrywise error bounds for low-rank approximations of kernel matrices (NeurIPS 2024 · similarity 0.88)
- Learning-Based Low-Rank Approximations (NeurIPS 2019 · similarity 0.88)
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