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Is there a reason why the most popular criterion for node splitting is MSE?

Why can't we use RMSLE (Root Mean Square Logarithmic Error), for example?

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To check the performance of a split, as you mentioned MSE and RMSE are the popular approaches.

RMSLE penalizes an under-predicted estimate greater than an over-predicted estimate

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ϵ is the RMSLE value (score) n is the total number of observations in the (public/private) data set, pi is your prediction, and ai is the actual response for i. log(x) is the natural logarithm of x.

Ref:

https://www.kaggle.com/wiki/RootMeanSquaredLogarithmicError https://stats.stackexchange.com/a/110610/86202

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