Objective function for 'reg:gamma'

bcoltman · January 24, 2020, 12:18pm

Who can tell me the function that is minimised when objective=‘reg:gamma’ is used in an XGBoost regression?

hcho3 · January 29, 2020, 9:45pm

Here is the implementation of negative log-likelihood for the gamma objective:

dmlc/xgboost/blob/7663de956c37eb4dd528132214e68ba2851d9696/src/metric/elementwise_metric.cu#L270-L286


struct EvalGammaNLogLik {
static const char *Name() {
  return "gamma-nloglik";
}


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);
}
static bst_float GetFinal(bst_float esum, bst_float wsum) {
  return wsum == 0 ? esum : esum / wsum;
}
};

jmpanfil · July 17, 2020, 7:13pm

I am looking to implement gamma regression with some changes possibly. Starting off simply, how would I implement the same gamma function as custom objective function? How would the gradient and hessian be defined in the custom function?