Minimizing the discrepancy of feature distributions between different domains is one of the most promising directions in unsupervised domain adaptation. From the perspective of distribution matching, most existing discrepancy-based methods are designed to match the second-order or lower statistics, which however, have limited expression of statistical characteristic for non-Gaussian distributions. In this work, we explore the benefits of using higher-order statistics (mainly refer to third-order and fourth-order statistics) for domain matching. We propose a Higher-order Moment Matching (HoMM) method, and further extend the HoMM into reproducing kernel Hilbert spaces (RKHS). In particular, our proposed HoMM can perform arbitrary-order moment tensor matching, we show that the first-order HoMM is equivalent to Maximum Mean Discrepancy (MMD) and the second-order HoMM is equivalent to Correlation Alignment (CORAL). Moreover, the third-order and the fourth-order moment tensor matching are expected to perform comprehensive domain alignment as higher-order statistics can approximate more complex, non-Gaussian distributions. Besides, we also exploit the pseudo-labeled target samples to learn discriminative representations in the target domain, which further improves the transfer performance. Extensive experiments are conducted, showing that our proposed HoMM consistently outperforms the existing moment matching methods by a large margin. Codes are available at \url{https://github.com/chenchao666/HoMM-Master}

本研究提出了 Higher-order Moment Matching (HoMM) 方法，将其扩展到再生核希尔伯特空间 (RKHS) 中，利用高阶统计量进行领域匹配并利用伪标记目标样本提高转移学习性能，验证结果证明 HoMM 方法明显优于现有的基于矩匹配的方法。

HoMM: 无监督域自适应的高阶矩匹配