I have a task to make a decision, say to classify an object as $X$ or $ overline X$. However, $overline X$ usually means everything else and you only have positive examples of $X$ and not so many negative examples of $overline X$. So estimation of probability distribution of $overline X$ is hard. But the good thing is that the space has the metric defined on it.
Common sense suggests that something non-probabilistic might make much more sense there, in particular since metric is defined, for example SVM is much more suitable for this task because you can estimate the margin to reject $overline X$. However, there is no complete discussion on that.
I’m looking for a book or survey paper to discuss this problem and non-probabilistic approaches to it compared to probabilistic ones.
