Logistic Regression

Question 1

Can we use the MSE as a loss function for Logistic Regression, just as we do for a regular Linear Regression?

Answer 1

No, we have to use a different loss/cost function because for the classification problem the MSE does not give a convex surface.

The function used for Logistic regression is:
(at  each sample ):
-(ylog(y')+(1-y)log(1-y')
y' = prediction
y  = real value (0/1)

Question 2

How can we transform the linear regression equation to make it work for logistic regression? Why?

Answer 2

The transformation we do is to pass it through the sigmoid function, so the resultant values are between 0 and 1.