The Function in the paper

[ahustr]

Thank you for your wonderful paper, but I have a question about a formula:

In my understanding. If we ask for maximum likelihood, the parameters of the model have a certain value but are unknown, and we estimate it using a sample from the population, but you have a formula here where the parameters are constantly changing. If we look at the following equation in the paper:

You seem to have used only a single point for estimating the parameters.

[udion]

I am not sure I follow the question here, how is the above any different than learning \mu, \sigma of typical Gaussian with maximum likelihood?

Maybe refer here (aleatoric uncertainty), here: https://arxiv.org/pdf/1703.04977 which describes the similar process, but standard Gaussian.