The Poisson loss is usually more suited for regression with count data than the squared loss.
Mathematically, it is defined as
It's gradient w.r.t. to \(p_i\) is
Returns the loss.
Return the gradient with respect to y_pred.
This is the inverse of the link function. Typically, a loss function takes as input the raw output of a model. In the case of classification, the raw output would be logits. The mean function can be used to convert the raw output into a value that makes sense to the user, such as a probability.
The adjusted prediction(s).