Best Practices for Using PCE in UQlab for High-Dimensional Models with Discrete Variables

UQ with UQLab Community Q&A and How To
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Hello everyone,

I am currently working on modeling and sensitivity analysis using Polynomial Chaos Expansion (PCE) in UQlab. My model has about 180 input variables, many of which are discrete (either 0 or 1). I have several questions and would appreciate any guidance:

  1. Is it feasible to use PCE in UQlab for this problem? If so, how should I handle the discrete variables? What should the IOpts.Marginals.Type be set to? Is it suitable to use arbitrary PCE in UQlab?

  2. Is setting the PCE degree to 2 appropriate given the high number of input variables? Higher degrees might lead to computational difficulties.

  3. How many input samples should I use? Currently, I have set it to 1000 samples due to the high computational cost for each run. Is this sufficient?

  4. I have also been using the method from “Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion” (S. Oladyshkin, W. Nowak, 2012) to construct the orthogonal polynomial basis. Then I employed the uq_lar program for sparsity and coefficient calculation. However, the final error(LOO) is quite large. i understand the method is not used in UQlab, but do you have any suggestions on how to improve this?

Thank you for your help!

Best regards,
Harvey

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Dear Harvey

thanks for your question. Polynomial chaos expansions are not meant in general for problems with discrete 0/1 variables, although in theory this would be possible. However, UQLab does not support (yet) discrete variables in the various modules.

What could be possible is to use Gaussian processes with a “custom” auto-correlation function (kernel) meant for discrete variables. However, in 180 dimensions, this may also be quite complex to fit.
For such a setting (high dim and discrete inputs) other machine learning techniques may be more suitable (e.g., random forest), although I haven’t tried myself.
Best regards
Bruno

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thank you very much for your answer. I find Gaussian processes quite useful in some area.

i will update my progress here.

Best regards