I am trying to train a neural network model to solve a regression problem. The specificity of my dataset is that it has something like an exponential distribution of target values (imbalanced). Therefor, the model seems to output just values less than 2 (if the range is [0,6]), for instance, and it absolutely ignores bigger target's values, which have a smaller performance in the dataset. How is it possible to improve the model's results in such a case?
For example, when it comes to a multiclass classification, we can weigh penalties for errors on a smaller class to enhance performance with imbalanced data. Are there any tricks in terms of regression? Which loss-functions could be useful? It seems, that MSE loss function is more preferable than RMSE. Is it more powerful loss functions for this problem?
There is a paper about such a problem of imbalanced regression (http://proceedings.mlr.press/v74/branco17a/branco17a.pdf) which might be helpful to someone. However, I'm more interested in special tricks for a neural network, not pre-processing approaches (I can't generate more data for example).