BuresNet: Conditional Bures Metric for Transferable Representation Learning

As a fundamental manner for learning and cognition, transfer learning has attracted widespread attention in recent years. Typical transfer learning tasks include unsupervised domain adaptation (UDA) and few-shot learning (FSL), which both attempt to sufficiently transfer discriminative knowledge from the training environment to the test environment to improve the model's generalization performance. Previous transfer learning methods usually ignore the potential conditional distribution shift between environments. This leads to the discriminability degradation in the test environments. Therefore, how to construct a learnable and interpretable metric to measure and then reduce the gap between conditional distributions is very important in the literature. In this article, we design the Conditional Kernel Bures (CKB) metric for characterizing conditional distribution discrepancy, and derive an empirical estimation with convergence guarantee. CKB provides a statistical and interpretable approach, under the optimal transportation framework, to understand the knowledge transfer mechanism. It is essentially an extension of optimal transportation from the marginal distributions to the conditional distributions. CKB can be used as a plug-and-play module and placed onto the loss layer in deep networks, thus, it plays the bottleneck role in representation learning. From this perspective, the new method with network architecture is abbreviated as BuresNet, and it can be used extract conditional invariant features for both UDA and FSL tasks. BuresNet can be trained in an end-to-end manner. Extensive experiment results on several benchmark datasets validate the effectiveness of BuresNet.