## Section: New Results

### Axis 2: PAC-Bayes and Domain Adaptation

**Participant:** Pascal Germain

In machine learning, Domain Adaptation (DA) arises when the distribution generating the test (target) data differs from the one generating the learning (source) data. It is well known that DA is a hard task even under strong assumptions, among which the covariate-shift where the source and target distributions diverge only in their marginals, i.e. they have the same labeling function. Another popular approach is to consider a hypothesis class that moves closer the two distributions while implying a low-error for both tasks. This is a VC-dim approach that restricts the complexity of a hypothesis class in order to get good generalization. Instead, we propose a PAC-Bayesian approach that seeks for suitable weights to be given to each hypothesis in order to build a majority vote. We prove a new DA bound in the PAC-Bayesian context. This leads us to design the first DA-PAC-Bayesian algorithm based on the minimization of the proposed bound. Doing so, we seek for a $\rho $-weighted majority vote that takes into account a trade-off between three quantities. The first two quantities being, as usual in the PAC-Bayesian approach, (a) the complexity of the majority vote (measured by a Kullback-Leibler divergence) and (b) its empirical risk (measured by the $\rho $-average errors on the source sample). The third quantity is (c) the capacity of the majority vote to distinguish some structural difference between the source and target samples.

This work has been published in the journal Neurocomputing [25].

It is a joint work with Emilie Morvant and Amaury Habrard from Université Jean Monnet de Saint-Etienne (France), and with François Laviolette from Université Laval (Québec, Canada).