t-distributed/robust likelihood In this paper, the authors claim to be using a robust likelihood function:

The code for this paper is on github and is referred to as t_likelihood. Isn't this just a log Gaussian likelihood? What's robust about this function?
If you want to trace through the code:

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*The model described in this paper is here

*The paper describes modelling the mean and variance of a distribution using two neural networks and is trained at approximately here
 A: I'm not claiming to understand the paper in its entirety, but if I understand it correctly, the authors use the term "robust" when describing how they use a Bayesian hierarchical model with an inverse gamma prior on the sigma parameter of the Gaussian distribution. The resulting predictive distribution is a Student-t which is the common substitute for the normal when the variance is unknown.
The authors use the HT algorithm to "unbias" the mini-batch estimator which they claim has better convergence properties than a full estimate being sparser due to having less data to crunch in each of the individual samples.
A: My intuition is that for many non-normal probability models the likelihood has the appearance of a normal likelihood with increasing sample size.
The justification in this setting may be similar to using a chi-square approximation for the sampling distribution of the likelihood ratio test statistic, or using a normal approximation for the sampling distribution of the Wald test statistic when the data generative process is non-normal.  Here is a related thread on Wilk's theorem.
