How to evaluate bootstrap PCE for completed SSE?

UQ with UQLab Community Q&A and How To
,
1

I am trying to calculate the bootstrap PCE (bPCE) bounds on the predictions from a trained SSE metamodel. It seems this should be possible from the SSER documentation, but I don’t see a syntax or usage option in the SSE documentation.

I would like to do something similar to what’s in the last PCE example to generate the predictions, variance, and bootstrap values, but for all the partitions in an SSE model:
PCE case: [YPCval,YPC_var,YPCval_Bootstrap] = uq_evalModel(myPCE,Xval);

Looking through some of the code where this seems to be implemented for SSER Pf confidence bounds, I have tried a couple of ways to modify the first SSE tutorial to output the bPCE info, but have not been successful. The ways I have tried are listed below.

Attempts in SSE case:

Adding the option specifying the number of replications to the SSE metaOpts metaOpts.ExpOptions.Bootstrap.Replications = 100;

  • Then training the model, and using the tutorial output y_model_test = uq_evalModel(x_test); which gives a vector of doubles only.

  • Or then trying to set the output args to match the bPCE case as `[y_model_test, temp1, temp2] = uq_evalModel(x_test);’ gives an error that the number of output args is too high (with the SSE metamodel selected).

  • Or trying to use the function on the SSE class that seems be used for SSER Pf: [y_ex, yvar_ex, yrep_ex] = mySSE_sequential.SSE.evalSSE(x_test) results in an error in uq_PCE_eval of “unrecognized field name “PCE””

Is there a specific way the functionality is supposed to work for getting bPCE for an SSE metamodel?

I am using:
MATLAB: 2022a
UQLab: 2.0.0

Thanks!
Alex

2

Dear @alex.b

Bootstrapping for SEE is currently not supported in UQLab.
However, it would be relatively easy to implement it yourself if you really think it is necessary. But it might be slow since SEE in general is already computationally intensive. There is no fast path like with standard PCE, as e.g. partitioning and thus also the structure of the PCEs depends on your samples.

Basically, you just write an outer loop that performs the following steps:

  • draw (with replacement!) bootstrap samples from your dataset;
  • fit an SSE model to these bootstrap samples;
  • evaluate your SEE and save the results.

Best regards
Styfen

3

Thanks @styfen.schaer ! I did implement a version of bSSE, but it needs some work on how to access the PCE partitioned layers correctly. A top-level approximation didn’t have great results.

As for sampling with replacement, the static SSE fitting ran into some issues with repeated points in the ExpDesign.