Transductive Learning

Q: I've come across transductive learning while I was reading about the classification task in ML. At first I thought it was just another name for semi-supervised learning, but then some people claim that the key difference is that in transductive learning the point is not to construct a classification function f, but rather to "transfer" the information from labeled examples to unlabeled. Can you elaborate more on transductive learning please? Is it really different from semi-supervised learning? In which settings is it proper?

A: What I understand about transductive learning is that you are given beforehand the data-cases on which you are going to be tested. If we denote by Xtrn the training features and Ytrn the training labels, then supervised learning learns a function Y=F(X) assuming perhaps that the test cases will be sampled from the same distribution as the training examples: [Xtst,Ytrn]~P, [Xtrn,Ytst]~P. However, in transductive learning you know more: you are given Xtst explicitly. This extra information can be used to improve performance on just those Xtst. Semi-supervised learning uses both labeled and unlabeled training data to build a classifier on any test data. So the difference lies in what you will be tested on. For a more in-depth discussion please read: http://www.kyb.tuebingen.mpg.de/ssl-book/discussion.pdf