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What is the difference Cross-entropy and KL divergence?

Some answers are already provided, while I would like to point out regarding the question itself measure the distance between two probability distributions that neither of cross-entropy and KL ...
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Normalized Cross Entropy

the closer p is to 0 or 1, the easier it is to achieve a better log loss (i.e. cross entropy, i.e. numerator). If almost all of the cases are of one category, then we can always predict a high ...
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cross entropy logistic test set

The issue you're encountering is that, in a regression problem, most people optimize the loss function of interest, often MSE (or something equivalent like SSE, RMSE, or $−R^2$, all of which are ...
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XGBoost Objective Derivation Problem

Since you mention probabilities, I assume you are thinking about a binary classification, in which case the trees all operate in the log-odds space, the $x$s in your notation. So the $\hat{y}$ and $...
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