  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}
