## Correcting log-bias in the output of an XGB

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I have previously worked with GAMs, where I was trying to do regression on a log-transformed variable. The log-transformation introduced a negative bias in the average of the predicted variable, and I corrected for this by multiplying each of the predictions $\exp(\hat y)$ by the factor

$$\langle \exp( \delta \hat y) \rangle$$

where $\delta \hat y$ was the residuals from the GAM.

Now I am using XGB, and trying to do regression on a log-transformed variable $y$ once again. The predictions $\hat y$ satisfy

$$\frac{\sum_i \hat y_i}{\sum_i y_i} = 0.999$$

so overall it looks good. However, when I exp-transform the variables I get

$$\frac{\sum_i \exp(\hat y_i)}{\sum_i \exp(y_i)} = 0.861$$

which is considerably worse. I suspect that this is due to the negative bias. Is there a way to correct for the bias in the XGB as in a GAM/GLM?