Research map / Learning theory and algorithms / Matrix and tensor methods
Gaussian quadrature for matrix inverse forms with applications
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Retrospective Gauss-Radau bounds for DPP MH sampling (vs. original exact sampler) | DPP sampler · Abalone/Wine/GR/HEP/Epinions/Slashdot | speedup: 14.4x to 823.9x | Helped |
| Retrospective Gauss-Radau bounds for double greedy | Double greedy (log-det) · Abalone/Wine/GR/HEP | speedup: 4.6x (Wine) to 247.8x (HEP) | Mixed |
| Retrospective Gauss-Radau bounds for DPP and k-DPP on large sparse Laplacians | k-DPP sampler · Slashdot | speedup: 1183x | Helped |
| Gauss quadrature bounds on u^T A^-1 u with lower/upper bounds iteratively tightened (monotonicity) | Gauss, Gauss-Radau, Gauss-Lobatto quadrature · synthetic 100x100 matrix | bound tightness per iteration | Helped |
| Right Gauss-Radau instead of Gauss quadrature for lower bounds | BIF lower bounds · synthetic 100x100 matrix | bound tightness at same iteration | Helped |
| Poor spectral bound estimate (lambda_min=0.1 lambda_1) for left Gauss-Radau (ablation) | left Gauss-Radau · synthetic 100x100 matrix | convergence iterations | Hurt |
| Poor spectral bound estimate (lambda_max=10 lambda_N) for right Gauss-Radau (ablation) | right Gauss-Radau · synthetic 100x100 matrix | bound quality | Hurt |
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