Research map / Probabilistic and scientific modeling / Uncertainty and Gaussian processes
Bayesian Quadrature for Multiple Related Integrals
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Jointly model related low- and high-fidelity integrands with multi-output BQ instead of integrating them independently | Step function and Forrester function with jump · Multi-fidelity integration | absolute integration error | Helped |
| Use multi-output BQ instead of uni-output BQ | Global illumination integrands · Global illumination | integration error | Helped |
| Increase the number of jointly modeled integrands from one to two or five | LMC multi-output BQ · Global illumination | posterior variance | Helped |
| Use a variational approximation to the multi-output GP | Multi-output BQ with process convolution kernel · Cosine-function integration | computation cost | Helped |
| Use a separable multi-output kernel rather than a uni-output kernel | Multi-output BQ · Global illumination | asymptotic convergence rate | No clear effect |
| Use a separable kernel that is smoother than the true integrands | Multi-output BQ · Quasi-uniform sampling, misspecified smoothness | integration error rate: O(N^{-\frac{\beta}{p}+\epsilon}) | Mixed |
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