Domain adaptation of weighted majority votes via perturbed variation-based self-labeling

• A framework for learning a PAC-Bayes majority vote for domain adaptation is proposed.
• We generalize the C-bound (for the target vote’s error) to domain adaptation.
• We propose an original self-labeling procedure based on the perturbed variation.
• We design a hyperparameter validation process suitable for our approach.
• Experiments are promising and show the usefulness of our self-labeling procedure.

In machine learning, the domain adaptation problem arrives when the test (target) and the train (source) data are generated from different distributions. A key applied issue is thus the design of algorithms able to generalize on a new distribution, for which we have no label information. We focus on learning classification models defined as a weighted majority vote over a set of real-valued functions. In this context, Germain et al. [1] have shown that a measure of disagreement between these functions is crucial to control. The core of this measure is a theoretical bound—the C-bound [2]—which involves the disagreement and leads to a well performing majority vote learning algorithm in usual non-adaptative supervised setting: MinCq. In this work, we propose a framework to extend MinCq to a domain adaptation scenario. This procedure takes advantage of the recent perturbed variation divergence between distributions proposed by Harel and Mannor [3]. Justified by a theoretical bound on the target risk of the vote, we provide to MinCq a target sample labeled thanks to a perturbed variation-based self-labeling focused on the regions where the source and target marginals appear similar. We also study the influence of our self-labeling, from which we deduce an original process for tuning the hyperparameters. Finally, our framework called PV-MinCq shows very promising results on a rotation and translation synthetic problem.