Learning Domain Invariant Representations by Joint Wasserstein Distance Minimization
This work addresses domain shifts for practical ML applications, providing a theoretical foundation to enhance model robustness across different data sources, though it is incremental in building on existing GAN and Wasserstein concepts.
The paper tackles the problem of domain shifts in machine learning by establishing theoretical links between supervised losses and the Wasserstein distance, showing that combining classification/regression losses with a GAN-type discriminator bounds this distance to improve domain invariance and prediction stability. Empirical results on image datasets demonstrate that the approach achieves the highest minimum classification accuracy across domains and the most invariant representation.
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.