In this paper, we tackle Multi-Source Domain Adaptation (MSDA), a task in transfer learning where one adapts multiple heterogeneous, labeled source probability measures towards a different, unlabeled target measure. We propose a novel framework for MSDA, based on Optimal Transport (OT) and Gaussian Mixture Models (GMMs). Our framework has two key advantages. First, OT between GMMs can be solved efficiently via linear programming. Second, it provides a convenient model for supervised learning, especially classification, as components in the GMM can be associated with existing classes. Based on the GMM-OT problem, we propose a novel technique for calculating barycenters of GMMs. Based on this novel algorithm, we propose two new strategies for MSDA: GMM-WBT and GMM-DaDiL. We empirically evaluate our proposed methods on four benchmarks in image classification and fault diagnosis, showing that we improve over the prior art while being faster and involving fewer parameters.

翻译：本文针对迁移学习中的多源域自适应（Multi-Source Domain Adaptation, MSDA）任务展开研究，该任务旨在将多个异质的有标签源概率测度适配至一个不同的无标签目标测度。我们提出了一种基于最优传输（Optimal Transport, OT）和高斯混合模型（Gaussian Mixture Models, GMMs）的新型MSDA框架。该框架具有两大核心优势：首先，GMM之间的最优传输可通过线性规划高效求解；其次，GMM各分量可与已有类别关联，为监督学习（尤其是分类任务）提供了便捷模型。基于GMM-OT问题，我们提出了一种计算GMM重心（barycenter）的新技术。依托该算法，进一步提出了两种MSDA新策略：GMM-WBT和GMM-DaDiL。我们在图像分类与故障诊断领域的四个基准数据集上对提出方法进行了实证评估，结果表明：在保持更快速度和更少参数量的前提下，本方法性能超越了现有技术。