Using the scale of the time series

We used GroupNormlizer in TimeSeriesDataset to scale each household using its own mean and standard deviation. We did this because we wanted to make the target zero mean and unit variance so that the model does not waste effort trying to change its parameters to capture the scale of individual household consumption. Although this is a good strategy, we do have some information loss here. There may be patterns that are specific to households whose consumption is on the larger side and some other patterns that are specific to households that consume much less. But now, they are both lumped in together and the model tries to learn common patterns. In such a scenario, these unique patterns seem like noise to the model because there is no variable to explain those.

The bottom line is that there is information in the scale that we removed, and adding that information back would be beneficial. So, how do we add it back? Definitely not by including the...