Joint Distribution Weighted Alignment for Multi-Source Domain Adaptation via Kernel Relative Entropy Estimation

The objective of Multi-Source Domain Adaptation (MSDA) is to train a neural network on labeled data from multiple joint source distributions (source domains) and unlabeled data from a joint target distribution (target domain), and use the trained network to estimate the target data labels. The challenge in this MSDA problem is that the multiple joint source distributions are relevant but distinct from the joint target distribution. To address this challenge, we propose a Joint Distribution Weighted Alignment (JDWA) approach to align a weighted joint source distribution to the joint target distribution under the relative entropy. Specifically, the weighted joint source distribution is defined as the weighted sum of the multiple joint source distributions, and is parameterized by the relevance weights. Since the relative entropy is unknown in practice, we propose a Kernel Relative Entropy Estimation (KREE) method to estimate it from data. Our KREE method first reformulates relative entropy as the negative of the minimal value of a functional, then exploits a function from the Reproducing Kernel Hilbert Space (RKHS) as the functional’s input, and finally solves the resultant convex problem with a global optimal solution. We also incorporate entropy regularization to enhance the network’s performance. Together, we minimize cross entropy, relative entropy, and entropy to learn both the relevance weights and the neural network. Experimental results on benchmark image classification datasets demonstrate that our JDWA approach performs better than the comparison methods. Intro video and Pytorch code are available at https://github.com/sentaochen/Joint-Distribution-Weighted-Alignment. Interested readers are also welcome to visit https://github.com/sentaochen for more source codes of the domain adaptation, partial domain adaptation, multi-source domain adaptation, and domain generalization approaches.