Discrete mathematics

Physics

Pattern recognition (psychology)

Mathematics

Domain (mathematical analysis)

Kernel (algebra)

Reproducing kernel Hilbert space

Discriminative model

Algorithm

Statistics

Gaussian

Mathematical analysis

Artificial intelligence

Matching (statistics)

Moment (physics)

Computer science

Quantum mechanics

Hilbert space

Classical mechanics

Minimizing the discrepancy of feature distributions between different domains is one of the most promising directions in unsupervised domain adaptation. From the perspective of moment matching, most existing discrepancy-based methods are designed to match the second-order or lower moments, which however, have limited expression of statistical characteristic for non-Gaussian distributions. In this work, 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 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, HoMM (order≥ 3) is expected to perform fine-grained 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 https://github.com/chenchao666/HoMM-Master

HoMM: Higher-Order Moment Matching for Unsupervised Domain Adaptation