Learning Domain Invariant Representations by Joint Wasserstein Distance Minimization

TL;DR

This paper introduces a theoretical framework linking classical supervised learning losses with the Wasserstein distance to improve domain-invariant representations, leading to more stable and accurate models across different data sources.

Contribution

It establishes mathematical relations between traditional losses and Wasserstein distance, providing a new foundation for learning domain-invariant representations with theoretical guarantees.

Findings

Theoretical bounds relate supervised losses to Wasserstein distance.

Empirical results show improved domain invariance and accuracy.

Proposed method outperforms baselines in stability across domains.

Abstract

Domain shifts in the training data are common in practical applications of machine learning; they occur for instance when the data is coming from different sources. Ideally, a ML model should work well independently of these shifts, for example, by learning a domain-invariant representation. However, common ML losses do not give strong guarantees on how consistently the ML model performs for different domains, in particular, whether the model performs well on a domain at the expense of its performance on another domain. In this paper, we build new theoretical foundations for this problem, by contributing a set of mathematical relations between classical losses for supervised ML and the Wasserstein distance in joint space (i.e. representation and output space). We show that classification or regression losses, when combined with a GAN-type discriminator between domains, form an upper-bound to the true Wasserstein distance between domains. This implies a more invariant representation and also more stable prediction performance across domains. Theoretical results are corroborated empirically on several image datasets. Our proposed approach systematically produces the highest minimum classification accuracy across domains, and the most invariant representation.