In this work, we connect two distinct concepts for unsupervised domain adaptation: feature distribution alignment between domains by utilizing the task-specific decision boundary and the Wasserstein metric. Our proposed sliced Wasserstein discrepancy (SWD) is designed to capture the natural notion of dissimilarity between the outputs of task-specific classifiers. It provides a geometrically meaningful guidance to detect target samples that are far from the support of the source and enables efficient distribution alignment in an end-to-end trainable fashion. In the experiments, we validate the effectiveness and genericness of our method on digit and sign recognition, image classification, semantic segmentation, and object detection.
@cite_15: In this work, we present a method for unsupervised domain adaptation (UDA), where we aim to transfer knowledge from a label-rich domain (i.e., a source domain) to an unlabeled domain (i.e., a target domain). Many adversarial learning methods have been proposed for this task. These methods train domain classifier networks (i.e., a discriminator) to discriminate distinguish the features as either a source or target and train a feature generator network to mimic the discriminator.However, the domain classifier only tries to distinguish the features as a source or target and thus does not consider task-specific decision boundaries between classes. Therefore, a trained generator can generate ambiguous features near class boundaries. To solve the problem, we propose a new approach that attempts to align distributions of source and target by utilizing the task-specific decision boundaries. We propose to utilize task-specific classifiers as discriminators that try to detect target samples that are far from the support of the source. A feature generator learns to generate target features inside the support to fool the classifiers. Since the generator uses feedback from task-specific classifiers, it avoids generating target features near class boundaries. Our method outperforms other methods on several datasets of image classification and semantic segmentation.
@cite_45: Couplings and changes of variables.- Three examples of coupling techniques.- The founding fathers of optimal transport.- Qualitative description of optimal transport.- Basic properties.- Cyclical monotonicity and Kantorovich duality.- The Wasserstein distances.- Displacement interpolation.- The Monge-Mather shortening principle.- Solution of the Monge problem I: global approach.- Solution of the Monge problem II: Local approach.- The Jacobian equation.- Smoothness.- Qualitative picture.- Optimal transport and Riemannian geometry.- Ricci curvature.- Otto calculus.- Displacement convexity I.- Displacement convexity II.- Volume control.- Density control and local regularity.- Infinitesimal displacement convexity.- Isoperimetric-type inequalities.- Concentration inequalities.- Gradient flows I.- Gradient flows II: Qualitative properties.- Gradient flows III: Functional inequalities.- Synthetic treatment of Ricci curvature.- Analytic and synthetic points of view.- Convergence of metric-measure spaces.- Stability of optimal transport.- Weak Ricci curvature bounds I: Definition and Stability.- Weak Ricci curvature bounds II: Geometric and analytic properties.
In this work, we propose a principled framework to marry the two powerful concepts: distribution alignment by task-specific decision boundary @cite_15 and the Wasserstein distance @cite_45 . The Wasserstein metric serves as a reliable discrepancy measure between the task-specific classifiers, which directly measures the support of target samples from source samples instead of producing explicit one-to-one mapping in label space. A variational version of the Wasserstein discrepancy further provides straightforward and geomatrically meaningful gradients to jointly train the feature generator and classifiers in the framework efficiently.