Choice of Error measure for Logistic Regression

[Yew Lee]

From the textbook (page 91), it seems intuitive that the likelyhood function is the hypothesis.

However, for the case of logistic regression in another book, the choice of the likelyhood function is the bernoulli distribution where y_n is {0, 1}.

In the case of heart attacks as specified in the book, I could have changed the label of y_n from {-1, 1} to {0, 1} and used the bernoulli distribution as the likelyhood function instead.
eg. (h(x)^y_n)*(1-h(x)^(1-y_n)

Therefore, what are the factors involved in the consideration of choosing the error measure and what are the pros and cons in this case?

[Yew Lee]

eg. (h(x)^y_n)*(1-h(x)^(1-y_n)

where h(x) is the sigmoid function being the probability of getting heart attack

[htlin]

There are different ways of deriving the cross-entropy error function. The book presents a specific way based on the notation of our choice. Indeed other ways (from other notations/assumptions) are possible.

Hope this helps.