Stability and Hypothesis Transfer Learning

We consider the transfer learning scenario, where the learner does not have access to the source domain directly, but rather operates on the basis of hypotheses induced from it - the Hypothesis Transfer Learning (HTL) problem. Particularly, we conduct a theoretical analysis of HTL by considering the algorithmic stability of a class of HTL algorithms based on Regularized Least Squares with biased regularization. We show that the relatedness of source and target domains accelerates the convergence of the Leave-One-Out error to the generalization error, thus enabling the use of the Leave-One-Out error to find the optimal transfer parameters, even in the presence of a small training set. In case of unrelated domains we also suggest a theoretically principled way to prevent negative transfer, so that in the limit we recover the performance of the algorithm not using any knowledge from the source domain.