Adaptive distance: how to interpret and fix 'smaller than lower bound' warnings?

[lm1909]

I am performing an inference with an InfoWeightedPNormDistance as in:

abc = pyabc.ABCSMC(model_function,
                   prior_distribution,
                   pyabc.InfoWeightedPNormDistance(p=1,
                                                   scale_function=pyabc.distance.mad, # adaptive scale normalization
                                                   predictor=pyabc.GPPredictor(), # regression model used to define sensitivity weights
                                                   fit_info_ixs=pyabc.EventIxs(sims=30), # when to fit the regression model
                                                   ),
                   population_size=20)

However, when I am running the inference, I am getting warnings like

RuntimeWarning: divide by zero encountered in log
  return np.log(np.hstack(theta))

and

.../python3.9/site-packages/sklearn/gaussian_process/kernels.py:420: ConvergenceWarning: The optimal value found for dimension 0 of parameter k1__k1__constant_value is close to the specified lower bound 1e-05. Decreasing the bound and calling fit again may find a better value.

Some value in GPPredictor seems to go out of bound. However, to fix this, I am now wondering what these types of warning mean on a more abstract level - is it that the optimisation landscape is very rough, and thus GPPredictor is hard to fit? Or is it about the information content of the parameters, and means that some are are non-informative (and thus the corresponding parameter becomes zero)?

Are there any arguments that could be tuned to fix this? Or can this issue be ignored safely?

Thank you very much in advance for your help!

[yannikschaelte]

Hi @lm1909 , as a first thing, I would recommend to not use GPPPredictor, but e.g. linear or NN models, as sensitivity calculation for Gaussian Processes (which will be needed downstream here, unlike when using it to calculate summary statistics) is not stable. Do the warnings also appear when using other approaches?

[lm1909]

Hi @yannikschaelte, thank you for your answer (and for all your work on pyabc in general)!

Yes, this indeed works; with neither LinearPredictor nor MLPPredictor the issue occurs.

[yannikschaelte]

You're welcome! (And I guess we should document this more properly)