|M.Sc Student||Derbeko Philip|
|Subject||Explicit Learning Curves for Transduction and Application|
to Clustering and Compression Algorithms
|Department||Department of Computer Science||Supervisor||Professor Ran El-Yaniv|
Inductive learning is based on inferring a general rule from a finite data set and using it to label new data. In transduction one attempts to solve the problem of using a labeled training set to label a set of unlabeled points, which are given to the learner prior to learning. Although transduction seems at the outset to be an easier task than induction, there have not been many provably useful algorithms for transduction. Moreover, the precise relation between induction and transduction has not yet been determined.
The main theoretical developments related to transduction were presented by Vapnik more than twenty years ago. One of Vapnik's basic results is a rather tight error bound for transduction based on exact computation of the hyper-geometric tail. While being tight, this bound is given implicitly via a computational routine. Our first contribution is a somewhat looser but explicit characterization of a slightly extended PAC-Bayesian version of Vapnik's transductive bound. This characterization is obtained using large deviation bounds on the tail of the hyper-geometric distribution. We then derive error bounds for compression schemes such as (transductive) support vector machines and for transduction algorithms based on clustering. The main observation used for deriving these new error bounds and algorithms is that the unlabeled test points, which in the transductive setting are known in advance, can be used in order to construct useful data dependent prior distributions over the hypothesis space.