PAC-Bayesian Learning and Domain Adaptation

TL;DR

This paper introduces a novel PAC-Bayesian framework for domain adaptation in machine learning, providing theoretical bounds and an algorithm that optimally weights hypotheses to improve transfer learning across different data distributions.

Contribution

It develops the first PAC-Bayesian domain adaptation bound and proposes an algorithm based on minimizing this bound for better transfer learning.

Findings

Proposed a new PAC-Bayesian domain adaptation bound.

Designed a DA-PAC-Bayesian algorithm based on bound minimization.

Demonstrated improved adaptation by balancing complexity, empirical risk, and structural differences.

Abstract

In machine learning, Domain Adaptation (DA) arises when the distribution gen- erating the test (target) data differs from the one generating the learning (source) data. It is well known that DA is an 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 an 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 an 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.