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

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,

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

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

i will update my progress here.

Best regards