How does the softmax function come about?

Question

I'm unsure how the softmax function comes about. I understand that the sigmoid function is a result of phrasing the log-odds as a linear equation and then rearranging the formula to model for the probability of an event occurring, but I'm not sure how to do this for softmax. Can someone point me in the right direction?

Answer 1

Answer on how logistic regression is extended to the multinomial case is presented here:

https://en.wikipedia.org/w/index.php?title=Logistic_regression&oldid=755697139#As_a_.22log-linear.22_model