Research map / Probabilistic and scientific modeling / Uncertainty and Gaussian processes
Practical and Rigorous Uncertainty Bounds for Gaussian Process Regression
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the dataset-specific a-posteriori frequentist bound instead of a bound based on an upper bound of maximum information gain | Gaussian Process Regression · Nominal SE and Matern kernel experiments | uncertainty-set coverage: no violations in all repetitions | Helped |
| Use the nominal bound with an underestimated SE length-scale (0.2 in GPR; 0.5 for the target) | Gaussian Process Regression · Benign SE kernel misspecification | uncertainty-set coverage: no violations in all repetitions | Helped |
| Use the nominal bound with an overestimated SE length-scale (0.5 in GPR; 0.2 for the target) | Gaussian Process Regression · Problematic SE kernel misspecification | coverage violation frequency: 2, 6, 12, 13 out of 50 functions for δ=0.1,0.01,0.001,0.0001 | Hurt |
| Use the robust kernel-mismatch bound rather than the nominal bound | Gaussian Process Regression under problematic kernel misspecification · Problematic SE kernel misspecification | uncertainty-set coverage: all functions being contained in the uncertainty set in all repetitions | Helped |
| Account for kernel mismatch using the robust bound | Gaussian Process Regression · Problematic SE kernel misspecification | uncertainty-set width: Mean: $71.68 \pm 5.36$ to $77.33 \pm 5.37$ across δ=0.1 to 0.0001 | Hurt |
| Use the a-posteriori bounds to construct learned disturbance sets in robust MPC | Learning-based robust model predictive control · Mass-spring-damper control example | probabilistic control guarantees: δ:=0.001 | Helped |
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