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I am modeling a physical process using a regression(XGBoost).
I'm looking for ways improving my model, have tried different things without success. Decided to get a better intuition on where my model is wrong.

After training the model the predicting on a hold-out test set, I compare the predicted values distribution to the real values.
The comparison reveals the 'learnt' variance is different from real.

What are the possible explanations for this 'wrong' variance learning?

This is how the variances look

enter image description here

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