Consider a multi$-$class classification problem of C classes.

Based on the parametric forms of the conditional probabilities of each class introduced

on the Uploaded image $($Extension to Multiple Classes$)$ of the lecture notes of L$4($Linear Models: Classification$),$ derive

the learning procedure of regularized logistic regression for multi$-$class classification

problems.

Hint: define a loss function by borrowing an idea from binary classification, and

derive the gradient descent rules to update $\{$w$($c$)\}$s$.$