In practical problems, where we want to for instance predict if a subject has a certain disease or not, we usually take classification accuracy as a measure which has the straightforward interpretation of the ratio of subjects diagnosed correctly. My question: Would the loss function give us any additional, useful information with this regards? E.g. has hinge-loss a useful interpretation when we base our predictions on Support Vector Machines (SVM)?
Edit: What I also do not yet fully understand: Is accuracy based on loss? For instance back to binary SVM, is predicting a new sample to belong to either group based on which loss would be minimal? And is this the so called "score" when for instance using fitcsvm in Matlab?
Best Answer
Accuracy is essentially the mean of the Losses under a zero-one loss function, so to answer your question, yes accuracy is just a loss function.
More specifically: For the Zero-one loss function is defined as:
$L(y,y^*) =\begin{cases} 0,& \text{if } y = y*\\ 1, & \text{otherwise} \end{cases}$
So the mean across all y is obviously the accuracy.