Some problems about MLE optimization

[NWPU-XuChenzhou]

Hi,
I have two questions about hyperparamter tunning of KRG:

1. What is the difference between reduced_likelihood_function in krg_based.py and the basic formulas of MLE:
   $$\ln L\left( \boldsymbol{\theta} \right)=-\frac{n}{2}\ln \left( \sigma^{2}\right)-\frac{1}{2}\ln \left( \left| \boldsymbol{R} \right|\right)$$
2. When I use COBYLA to minimize reduced_likelihood_function, why the convergency history looks so strange?
   image
   I'm looking forward to receiving your answer. Thank you!

[relf]

Hi. Regarding 1., basically reduced_likelihood_function implements MLE formula as stated in the reference paper (eq. 8) which could give you some insights about the code.

[Paul-Saves]

Hi. Regarding 2., we are using a multistart option referred as n_start in the documentation https://smt.readthedocs.io/en/latest/_src_docs/surrogate_models/krg.html.

Default is n_start =10 so you have 10 peaks.

[NWPU-XuChenzhou]

Okay, I've got it. Thank you very much!