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Title: Weighted empirical risk minimization: Transfer learning based on importance sampling Authors:  Charles Tillier - Telecom ParisTech (France) [presenting]
Stephan Clemencon - Telecom ParisTech (France)
Robin Vogel - Telecom ParisTech (France)
Mastane Achab - Telecom ParisTech (France)
Abstract: Statistical learning problems are considered when the distribution $P'$ of the training observations $Z'_1,\; \ldots,\; Z'_n$ differs from the distribution $P$ involved in the risk one seeks to minimize (referred to as the test distribution) but is still defined on the same measurable space as $P$ and dominates it. In the unrealistic case where the likelihood ratio $\Phi(z)=dP/dP'(z)$ is known, one may extend the Empirical Risk Minimization (ERM) approach to this specific transfer learning setup using the same idea as that behind Importance Sampling, by minimizing a weighted version of the empirical risk functional computed from the 'biased' training data $Z'_i$ with weights $\Phi(Z'_i)$. Although the importance function $\Phi(z)$ is generally unknown in practice, in various situations frequently encountered in practice, it takes a simple form and can be directly estimated from the $Z'_i$'s and some auxiliary information on the statistical population $P$. Besides, we will see that the generalization capacity of the approach aforementioned is preserved when plugging the resulting estimates of the $\Phi(Z'_i)$'s into the weighted empirical risk.