Comments (4)
Is it O(N^3)
where N is the number of points the RBF interpolant uses to build the surface?
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pySOT is currently solving the entire RBF system from scratch each time, so each iteration is O(n^3). This adds up to O(n^4). It's possible to do each iteration in O(n^2) by updating the LU-factorization of the RBF system incrementally and that's something that I can easily add to the code. This gives you the desired O(n^3) complexity.
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Then why is Kriging slower?
From the documentation
By default we recommend the CubicRBFSurface (with capping if necessary). We recommend not using Kriging since it is very slow.
Gaussian processes are generally considered slow since the inference time grows cubically in the number of observations, as it necessitates the inversion of a dense covariance matrix. But if RBF is also cubic, I don't see where is the difference. Can you please explain to me?
Thanks
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Good question. I'm not that familiar with Kriging and I'm not sure if I can be very helpful without looking at the Kriging implementation that we rely on: https://github.com/capaulson/pyKriging. From numerical tests it looks like Kriging is at least an order of magnitude slower than RBFs.
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Related Issues (20)
- Implement SO-MI
- MPI example gets stuck HOT 3
- PendingDeprecationWarning from use of NumPy matrices HOT 2
- how to surrogate model with multiple variable? HOT 5
- Multiple threads does not work HOT 10
- Evaluates the uncertainty of the surrogate model at points x HOT 3
- pySOT may propose the same point twice on pure integer problems HOT 1
- Add back option to restart algorithms when they converge early HOT 1
- mpiexample_simple.py fails after the increase of number of workers HOT 3
- Documentation has an error HOT 1
- `examples` and `tests` are being installed as top-level packages (directly in site-packages) HOT 5
- SurrogateUnitBox not longer required for RBF? HOT 1
- comparisons HOT 1
- MIssing parentheses
- Use of "extra" and "extra_vals"
- add_points() does not handle objective functions that output integers
- Comments in ei_merit() do not match the actual sizes of parameters passed to the function
- In gp.py, predict() returns incorrectly-sized array, causing IndexError exception in ei_merit().
- pySOT is slow to generate new points with large dataset HOT 1
- Stopping criteria based on objective and/or decision variable tolerance
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