multiclassification using mlogloss objective function

[sxpyggy]

I would like to know the exact expression of multi:softprob in terms of probabilities and labels. What is the difference between multi:softprob and mlogloss? Can I use the mlogloss objective function when boosting a multi-classification task?

[gdubs89]

To be clear, multi:softprob is a loss function. My understanding is that it's functionallty equivalent to multi:softmax but it somehow differs in the shape of the output of the predict_proba method once the model is fit. So let's not worry about that detail.

So basically, multi:softprob / multi:softmax are the multi-class equivalents of using binary:logistic loss when training a binary classifier, and mlogloss is the multi-class equivalent of using logloss as your eval metric.

I believe that multi:softmax and mlogloss are numerically equivalent, that is to say that if after X training iterations, your training Loss=x, then if you track your eval_metric on the training set, you'll get the same number (it's not even the case that one is the negative of the other)

The reason they have this separation, is that you can use eval metrics that are not suitable as loss functions because they're not twice differentiable, like accuracy. So it makes senes to have a list of permissible loss functions, and a list of eval metrics, although for eval metrics that have a corresponding loss function, they could have overloaded the naming