What parameterization of the gamma distribution is used when using ‘reg:gamma’. Github has the following code:
XGBOOST_DEVICE bst_float EvalRow(bst_float y, bst_float py) const {
bst_float psi = 1.0;
bst_float theta = -1. / py;
bst_float a = psi;
bst_float b = -std::log(-theta);
bst_float c = 1. / psi * std::log(y/psi) - std::log(y) - common::LogGamma(1. / psi);
return -((y * theta - b) / a + c);
}
After expanding this and exponentiating back to a likelihood function, I can’t seem to match it to any of the parameterizations I can find. For example, it doesn’t match the two on Wikipedia or this stack exchange answer.
So what parameterization of gamma is used?