I'm trying to design a continuous loss function for a logistic classifier.
Suppose I have the following confusion matrix:
[tn fp fn tp]
I want the loss function to be
A*tn + B*fn + C*fp + D*tp
where A, B, C, and D can be different. It's easy enough to implement this discrete version of course, but how can I make this cost function continuous so that my cost function is well-behaved when I try to minimize it?