Mathematical error in gamma-nloglik eval_metric calculation?

[rwjmiller]

I notice that this seems to have changed a few months ago following this discussion:

https://github.com/dmlc/xgboost/pull/6778/files/625c374b493612f90c1c242cfe7c215571a48a52#diff-67879cd710406fb4e525362b7317b91633f3881b2813cd0e36e2e1ed8b5293b5

Before this change, the expression for the row-wise log-likelihood, in terms of p = prediction and y = response value, simplified down to:

gamma-nloglik = log(p) + y/p

After this change, the expression simplifies down to:

gamma-nloglik = 1 + y/p

I believe the original expression is the correct one, and this change should be reverted - i.e. this line should be un-commented:

xgboost/src/metric/elementwise_metric.cu

Line 312 in b2d8431

// b = -std::log(-theta);

and this line should be removed:

xgboost/src/metric/elementwise_metric.cu

Line 313 in b2d8431

float b = 1.0f;

The two definitions are definitely not equivalent as suggested in the discussion - I get very different values when calculating this metric for the same data with different XGBoost versions from before and after this change.

[trivialfis]

Thanks for opening the issue! Let me double check, can't remember how did I put it in there but seems you are right.