A Theoretical Analysis of Metric Hypothesis Transfer Learning
نویسندگان
چکیده
We consider the problem of transferring some a priori knowledge in the context of supervised metric learning approaches. While this setting has been successfully applied in some empirical contexts, no theoretical evidence exists to justify this approach. In this paper, we provide a theoretical justification based on the notion of algorithmic stability adapted to the regularized metric learning setting. We propose an on-averagereplace-two-stability model allowing us to prove fast generalization rates when an auxiliary source metric is used to bias the regularizer. Moreover, we prove a consistency result from which we show the interest of considering biased weighted regularized formulations and we provide a solution to estimate the associated weight. We also present some experiments illustrating the interest of the approach in standard metric learning tasks and in a transfer learning problem where few labelled data are available.
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A Theoretical Analysis of Metric Hypothesis Transfer Learning Supplementary Material
This supplementary material is organised into three parts. In the first two parts we respectively state the proofs of the onaverage and uniform stability analysis. In the last part, we show that the specific loss presented in the paper is k-lipschitz. For the sake of readability we start by recalling our setting. Let T be a training set drawn from a distribution DT over X × Y . We consider the ...
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