Research map / Probabilistic and scientific modeling / Uncertainty and Gaussian processes
Fast Matrix Square Roots with Applications to Gaussian Processes and Bayesian Optimization
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace Cholesky with msMINRES-CIQ | SVGP training · 3DRoad, Precipitation, and CoverType | training time: 3.2x faster; 5.6x faster; 2.0x faster | Helped |
| Increase inducing points from M=5,000 to M=10,000 | CIQ SVGP · 3DRoad | test NLL: reduces test-set NLL by 0.1 nats | Helped |
| Increase inducing points from M=5,000 to M=10,000 | CIQ SVGP · Precipitation | test NLL: reduces test-set NLL by 0.1 nats | Helped |
| Use msMINRES-CIQ rather than Cholesky | SVGP · 3DRoad, Precipitation, and CoverType | test NLL | No clear effect |
| Increase candidate set size from T=1,000 to T=50,000 | CIQ Thompson sampling · Hartmann and Lunar Lander | regret | Helped |
| Use CIQ-50k rather than RFF-50k | Thompson sampling · Hartmann and Lunar Lander | regret | Helped |
| Add a rank-200 pivoted Cholesky preconditioner (ablation) | msMINRES-CIQ · Hartmann posterior covariance, N=50,000 | final relative residual: final residual is cut by orders of magnitude; converges 2× faster | Helped |
| Add a rank-400 pivoted Cholesky preconditioner (ablation) | msMINRES-CIQ · Hartmann posterior covariance, N=50,000 | final relative residual: final residual is cut by orders of magnitude; converges 4× faster | Helped |
| Use Q=8 quadrature points (ablation) | msMINRES-CIQ · Random covariance matrices and Matérn 5/2 kernels | relative error: < 10−4 | Helped |
| Increase the number of right-hand sides (ablation) | msMINRES-CIQ compared with Cholesky · RBF and Matérn kernels | speedup over Cholesky | Hurt |
| Use rank-50, rank-100, rank-200, or rank-400 preconditioning instead of no preconditioner (ablation) | msMINRES-CIQ · Hartmann posterior covariance, N=50,000 | relative residual | Helped |
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