PAC-Bayes and Domain Adaptation

TL;DR

This paper advances PAC-Bayesian theory for domain adaptation by introducing tighter bounds based on disagreement measures and divergence ratios, and develops new algorithms evaluated on real data.

Contribution

It proposes novel PAC-Bayesian bounds for domain adaptation and derives two new learning algorithms for linear classifiers.

Findings

New tighter domain adaptation bounds based on disagreement averaging.

A divergence ratio-based bound controlling source error and target disagreement.

Empirical evaluation of the proposed algorithms on real datasets.

Abstract

We provide two main contributions in PAC-Bayesian theory for domain adaptation where the objective is to learn, from a source distribution, a well-performing majority vote on a different, but related, target distribution. Firstly, we propose an improvement of the previous approach we proposed in Germain et al. (2013), which relies on a novel distribution pseudodistance based on a disagreement averaging, allowing us to derive a new tighter domain adaptation bound for the target risk. While this bound stands in the spirit of common domain adaptation works, we derive a second bound (introduced in Germain et al., 2016) that brings a new perspective on domain adaptation by deriving an upper bound on the target risk where the distributions' divergence-expressed as a ratio-controls the trade-off between a source error measure and the target voters' disagreement. We discuss and compare both results, from which we obtain PAC-Bayesian generalization bounds. Furthermore, from the PAC-Bayesian specialization to linear classifiers, we infer two learning algorithms, and we evaluate them on real data.