Introduction to Statistical Learning Exercise 4.12(c) and (e) How can we figure out coefficients of the softmax logistic regression using the coefficients from the standard logistic regression?
This is from Chapter 4 of ISLR 2nd edition.
Also, can you please help me with question (e)? I am just a poor soul going through ISLR alone.



Divide both numerator and denom. to the numerator term:
$$p=\frac{1}{1+\exp((\hat\alpha_{apple,0}-\hat\alpha_{orange,0})+(\hat\alpha_{apple_1}-\hat\alpha_{orange,1})x)}$$
Basically, they're equivalent models and when fitted to the same data, they'll predict the same outcomes when trained enough. This is because the minimum is unique for logistic regression (using cross-entropy loss).
