H20 says in the documentation that splitting on a feature for regression gbms is based on the reduction in squared error.
Is this squared error based on the node residuals, i.e., (resid - mean resid)^2 or is it the true response, i.e., (response - mean response)? I'm using gamma/ Poisson distributions.
In the case of gamma/Poisson, the loss is the deviance so why is the squared error used instead?
In H2O the mean squared error is calculated from the node residuals. The goal there is to have an unbiased estimator, so the SE to be minimized is calculated as:
SE = MSE * N = Var * N = wyy - (w * y)^2/N
where y means node residuals not response, w means weights and N means the number of observations. You can read more about H2O GBM tree learning in this booklet: https://docs.h2o.ai/h2o/latest-stable/h2o-docs/booklets/GBMBooklet.pdf in chapter Theory and Framework.
