# HoMM: Higher-order Moment Matching for Unsupervised Domain Adaptation

arXiv: https://arxiv.org/abs/1912.11976 · HTML: https://mlsanity.com/paper/1912.11976/

## Key facts

- Cited by 89 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Dec 2019.

## Built on by (most cited first, 30 of 89)

- [Robust Mean Teacher for Continual and Gradual Test-Time Adaptation](https://mlsanity.com/paper/2211.13081/) (2022)
- [Deep Unsupervised Domain Adaptation: A Review of Recent Advances and Perspectives](https://mlsanity.com/paper/2208.07422/) (2022)
- [Invariant Information Bottleneck for Domain Generalization](https://mlsanity.com/paper/2106.06333/) (2021)
- [Deep Clustering: A Comprehensive Survey](https://mlsanity.com/paper/2210.04142/) (2022)
- [Universal Test-time Adaptation through Weight Ensembling, Diversity Weighting, and Prior Correction](https://mlsanity.com/paper/2306.00650/) (2023)
- [A Survey on Time-Series Pre-Trained Models](https://mlsanity.com/paper/2305.10716/) (2023)
- [C-SFDA: A Curriculum Learning Aided Self-Training Framework for Efficient Source Free Domain Adaptation](https://mlsanity.com/paper/2303.17132/) (2023)
- [A Theory of Label Propagation for Subpopulation Shift](https://mlsanity.com/paper/2102.11203/) (2021)
- [ADATIME: A Benchmarking Suite for Domain Adaptation on Time Series Data](https://mlsanity.com/paper/2203.08321/) (2022)
- [Contrastive Learning for Unsupervised Domain Adaptation of Time Series](https://mlsanity.com/paper/2206.06243/) (2022)
- [ProxyMix: Proxy-based Mixup Training with Label Refinery for Source-Free Domain Adaptation](https://mlsanity.com/paper/2205.14566/) (2022)
- [Prototype-Guided Continual Adaptation for Class-Incremental Unsupervised Domain Adaptation](https://mlsanity.com/paper/2207.10856/) (2022)
- [Self-supervised Autoregressive Domain Adaptation for Time Series Data](https://mlsanity.com/paper/2111.14834/) (2021)
- [Generation, augmentation, and alignment: A pseudo-source domain based method for source-free domain adaptation](https://mlsanity.com/paper/2109.04015/) (2021)
- [Revisiting Domain-Adaptive 3D Object Detection by Reliable, Diverse and Class-balanced Pseudo-Labeling](https://mlsanity.com/paper/2307.07944/) (2023)
- [Domain Adaptation for Time-Series Classification to Mitigate Covariate Shift](https://mlsanity.com/paper/2204.03342/) (2022)
- [Sim-to-Real Domain Adaptation for Lane Detection and Classification in Autonomous Driving](https://mlsanity.com/paper/2202.07133/) (2022)
- [Compositional Semantic Mix for Domain Adaptation in Point Cloud Segmentation](https://mlsanity.com/paper/2308.14619/) (2023)
- [Generative Range Imaging for Learning Scene Priors of 3D LiDAR Data](https://mlsanity.com/paper/2210.11750/) (2022)
- [Contrastive Domain Adaptation for Time-Series via Temporal Mixup](https://mlsanity.com/paper/2212.01555/) (2022)
- [Domain-Specificity Inducing Transformers for Source-Free Domain Adaptation](https://mlsanity.com/paper/2308.14023/) (2023)
- [Source-Free Domain Adaptation with Temporal Imputation for Time Series Data](https://mlsanity.com/paper/2307.07542/) (2023)
- [Maximum Mean Discrepancy for Generalization in the Presence of Distribution and Missingness Shift](https://mlsanity.com/paper/2111.10344/) (2021)
- [Reducing the Covariate Shift by Mirror Samples in Cross Domain Alignment](https://mlsanity.com/paper/2110.06448/) (2021)
- [An Unsupervised Domain Adaptation Model based on Dual-module Adversarial Training](https://mlsanity.com/paper/2112.15555/) (2021)
- [SCoDA: Domain Adaptive Shape Completion for Real Scans](https://mlsanity.com/paper/2304.10179/) (2023)
- [A Survey on AI Sustainability: Emerging Trends on Learning Algorithms and Research Challenges](https://mlsanity.com/paper/2205.03824/) (2022)
- [Unsupervised Domain Adaptation for Point Cloud Semantic Segmentation via Graph Matching](https://mlsanity.com/paper/2208.04510/) (2022)
- [Spatial Distillation based Distribution Alignment (SDDA) for Cross-Headset EEG Classification](https://mlsanity.com/paper/2503.05349/) (2025)
- [SIMSHIFT: A Benchmark for Adapting Neural Surrogates to Distribution Shifts](https://mlsanity.com/paper/2506.12007/) (2025)

## Abstract (arXiv)

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 urlhttps://github.com/chenchao666/HoMM-Master