Research map / Learning theory and algorithms / Matrix and tensor methods
Sublinear Time Numerical Linear Algebra for Structured Matrices
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use matrix-vector-product-based sampling for low rank approximation | Low rank approximation · General structured matrices | running time: O\left(T(A)\log n + n \cdot \mbox{poly}(k/\epsilon)\right) | Helped |
| Use matrix-vector-product-based sampling for regression | ℓ_p-regression · General structured matrices | running time: O\left(T(A)\log n + \mbox{poly}(d/\epsilon)\right) | Helped |
| Reuse inner products across Toeplitz autoregression blocks | Kernel autoregression · General kernels | running time: O(n^2 t) -> O(ndt + d^{\omega}) | Helped |
| Sample rows of the lifted polynomial-kernel system instead of materializing the full lifted target | Polynomial-kernel autoregression · Degree 2 polynomial kernel | running time: O\big(\mbox{nnz}(A) \log^2 n + n \log^3 n + (pd^2 \log n + d^3)(\frac 1 \epsilon + \log d)\big) | Helped |
| Use sampling-based methods instead of input-sparsity sketching | Autoregression · Toeplitz design matrix | running time: O(nd) + \mbox{poly}(d/\epsilon) -> O\left((n \log^2 n + (d^2 \log^2 n)/\epsilon^2 + d^3 (\log n)/\epsilon^2)\log(1/\delt | Helped |
Closest papers by meaning
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