Barycentric-alignment and reconstruction loss minimization for domain generalization

Domain generalization theory and methods are important for the success of Open World Pattern Recognition. The paper advances the current state-of-art works in this context by proposing a novel theoretical analysis and piratical algorithm. In particular, we revisit Domain Generalization (DG) problem, where the hypotheses are composed of a common representation mapping followed by a labeling function. Popular DG methods optimize a well-known upper bound of the risk in the unseen domain to learn both the optimal representation and labeling functions. However, the widely used bound contains a term that is not optimized due to its dual dependence on the representation mapping and the unknown optimal labeling function in the unseen domain. To fill this gap, we derive a new upper bound free of terms having such dual dependence. Our derivation leverages old and recent transport inequalities that link optimal transport metrics with information-theoretic measures. Compared to previous bounds, our bound introduces two new terms: (i) the Wasserstein-2 barycenter term for the distribution alignment between domains and (ii) the reconstruction loss term for measuring how well the data can be reconstructed from its representation. Based on the new upper bound, we propose a novel DG algorithm that simultaneously minimizes the classification loss, the barycenter loss, and the reconstruction loss. Experiments on several datasets demonstrate superior performance of the proposed method compared to the state-of-the-art DG algorithms.