Domain Generalization by Marginal Transfer Learning

TL;DR

This paper develops a theoretical framework for domain generalization, viewing it as supervised learning with augmented features, and introduces a kernel-based algorithm with experimental validation on synthetic and real data.

Contribution

It formalizes the domain generalization problem, proposes new models and risk analysis, and provides a universally consistent kernel method with efficient implementation.

Findings

The framework connects DG to supervised learning via marginal distribution augmentation.

A new kernel-based algorithm for DG is proposed and shown to be universally consistent.

Experimental results demonstrate the effectiveness of the proposed method on multiple datasets.

Abstract

In the problem of domain generalization (DG), there are labeled training data sets from several related prediction problems, and the goal is to make accurate predictions on future unlabeled data sets that are not known to the learner. This problem arises in several applications where data distributions fluctuate because of environmental, technical, or other sources of variation. We introduce a formal framework for DG, and argue that it can be viewed as a kind of supervised learning problem by augmenting the original feature space with the marginal distribution of feature vectors. While our framework has several connections to conventional analysis of supervised learning algorithms, several unique aspects of DG require new methods of analysis. This work lays the learning theoretic foundations of domain generalization, building on our earlier conference paper where the problem of DG was introduced (Blanchard et al., 2011). We present two formal models of data generation, corresponding notions of risk, and distribution-free generalization error analysis. By focusing our attention on kernel methods, we also provide more quantitative results and a universally consistent algorithm. An efficient implementation is provided for this algorithm, which is experimentally compared to a pooling strategy on one synthetic and three real-world data sets.