# Stability and Hypothesis Transfer Learning

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Ilja Kuzborskij,
Francesco Orabona
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Proceedings of the 30th International Conference on Machine Learning, PMLR 28(3):942-950, 2013.

#### Abstract

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.

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