What is the use of Hessian for custom objective?

[liujxing]

I read the paper of LightGBM and it seems the splitting is chosen by the criterion of variance gain calculated using gradient, so where does the Hessian defined in custom objective come into play here?

[guolinke]

gradient is the first order optimization.
gradient with hessian is the second order optimization, like the newton optimization.
Refer to https://xgboost.readthedocs.io/en/latest/model.html

[liujxing]

Of course, but I thought LightGBM used a different algorithm for choosing the best split point, and in no where your paper mentions second order Hessian optimization in your algorithm. Could you be more specific about this?

[guolinke]

just replace the count with hessian, and the variance gain becomes to the hessian optimization.

[liujxing]

Thanks.