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Quoting from this answer that explains how to do boosting when a 'link' function is involved:

"Instead, we can re-express this as a function of $L_i$, (in this case also known as the log odds)

$$ \sum_i y_i L_i - \log(1 + \exp(L_i)) $$

Then we can take the gradient of this with respect to $L$, and boost to directly minimize this quantity."

Is there a name for $L$ instead of the "quantity being boosted"?

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    $\begingroup$ I think that "quantity being boosted" is pretty good. We might have particular explanation for specific implementations (e.g. residuals in the case of Adaboost for regression, or deviance residuals in the case of a "standard GBM") but that in reality it is just a "quantity being boosted". Referring to it as a "cost function"/"utility function" is pretty generic and less accurate. $\endgroup$ – usεr11852 Apr 16 '19 at 8:26

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