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I'm newly introduced to the LightGBM for a regression problem. Having read the documentation of LightGBM (here), I got puzzled about the score. You can track a few metrics as well as the objective value as the training goes by. But this score is not any of them. It probably, somehow, represents the goodness of fit, but I didn't find any mathematical formula for that.

Can someone explain what does this quantity represent and what are the links, if any, between that and the objective value during the training, validation, and testing? I'm particularly interested in huber loss.

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Having a look at sklearn documentation, I guess I found the answer to my question. I'm dealing with a regression decision tree and for a regression problem, a measure for goodness of fit is defined similar to $R^2$ in OLS; If $\hat{y}_i$ is the prediction of data point $i$ with features $\textbf{x}_i$ and label $y_i$, then score is defiend as:

$$ S = 1- \frac{ \sum_i {(y_i - \hat{y}_i)^ 2}}{\sum_i{(y_i - \langle y \rangle )^ 2}} $$

although it's not mentioned anywhere in LightGBM's doc.

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