Research map / Probabilistic and scientific modeling / Uncertainty and Gaussian processes
Convergence Guarantees for Adaptive Bayesian Quadrature Methods
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Require the data-dependent acquisition factor to stay uniformly bounded above and away from zero (weak adaptivity) | Adaptive Bayesian quadrature · Compact cube with an infinitely smooth kernel | quadrature error rate: O(exp (- D_1 n^{1/d}) ) | Helped |
| Require the data-dependent acquisition factor to stay uniformly bounded above and away from zero (weak adaptivity) | Adaptive Bayesian quadrature · Finite-smoothness kernels with r > d/2 | quadrature error rate: O(n^{-r/d + 1/2}) | Helped |
| Use WSABI-L with zero prior mean, so its acquisition factor is the squared posterior mean | WSABI-L · General quadrature setting | consistency | Hurt |
| Add a positive offset to the WSABI-L acquisition factor: b_n(x) := 1/2 (m_{g,X_n}(x))^2 + alpha | WSABI-L · General quadrature setting | consistency | Helped |
| Use the MMLT acquisition factor exp(k_{X_n}(x,x) + 2 m_{g,X_n}(x)) | MMLT · General quadrature setting | consistency | Helped |
| Allow approximate rather than exact maximization of the acquisition function, provided each selected point reaches a fixed positive fraction of the maximum | Adaptive Bayesian quadrature · Theoretical convergence under the paper's assumptions | consistency | Helped |
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