Maximum Likelihood Estimation

[AhmedThahir]

Hi there!
I really love LightGBM's speed & performance all into one.

I want the model to output mean and variance, to be optimized using Maximum Likelihood Estimation. I'm guessing I would need to create a custom loss function, but I've not been able to wrap my head around it - ie, I know how to create a custom loss function, but I don't know how to create one that would allow me to perform MLE wrt mean and variance.

I want to create this question in the discussions forum, but couldn't find it, so I'm asking here.

Would really appreciate any help!