Difference between multinomial and one vs rest schemes in logistic regression [duplicate]

Question

I am dealing with multiclass classification problem where I have 10 classes to predict. I came across Logistic regression model in scikit-learn which can be applied to multiclass settings as well. The parameter 'multi_class' in logistic regression function can take two values 'ovr' and 'multinomial'.

What's the difference between ovr (one vs rest ) and multinomial in terms of logistic regression. I am using logloss as my evaluation metric. I applied both 'ovr' and 'multinomial' to my problem, so far 'ovr' gives less logloss value. But I really want to know how both works.

Answer 1

It's like this OVR has separate classifiers to each classes. If you have 3 classes it has 3 classifiers and the class that gives the maximum number of score is from each oh three score functions will be selected as the class. In multinational case it has the same classifier and it's quit like a perception where you will get range of score values to each classes. It use the cross entropy error. and hard to coverage the loss function.