I understand that one of the main points of using the sigmoid function on responses in binary classification is that we can interpret value outputted as the probability that an instance belongs to 1 of the classes say A, and as it's binary classification, 1-(this probability) gives the probability of it belonging to class B.

My question is: what if there are more than 2 classes, say n, what is the generalization of the sigmoid function?

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    $\begingroup$ In the case of 3+ labels, are the labels mutually exclusive? In other words, if there are 3 classes, can the same observation have class labels A & B, or A &C, or B &C? Or can a single observation only have exactly 1 label? If the labels are mutually exclusive, then you're looking for this stats.stackexchange.com/questions/145272/… or stats.stackexchange.com/questions/484809/… $\endgroup$
    – Sycorax
    Feb 16 at 15:51
  • $\begingroup$ I'll give those a read, thanks! Yes labels mutually exclusive. Are there classification models where an instance could be both A and B? $\endgroup$ Feb 16 at 16:28
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    $\begingroup$ Yes. The term of art for observation taking 1or more labels is "multi-label" classification. You're asking about mutually exclusive labels, which is multinomial classification. $\endgroup$
    – Sycorax
    Feb 16 at 16:41