# Lighter, Better, Faster Multi-Source Domain Adaptation with Gaussian Mixture Models and Optimal Transport

arXiv: https://arxiv.org/abs/2404.10261 · HTML: https://mlsanity.com/paper/2404.10261/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 34 references that are in the map.
- First posted on arXiv 16 Apr 2024.

## Builds on (most cited first, 16 of 16)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Moment Matching for Multi-Source Domain Adaptation](https://mlsanity.com/paper/1812.01754/) (2018)
- [Deep Hashing Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1706.07522/) (2017)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [Fast Computation of Wasserstein Barycenters](https://mlsanity.com/paper/1310.4375/) (2013)
- [A Wasserstein-type distance in the space of Gaussian Mixture Models](https://mlsanity.com/paper/1907.05254/) (2019)
- [Recent Advances in Optimal Transport for Machine Learning](https://mlsanity.com/paper/2306.16156/) (2023)
- [Learning to Combine: Knowledge Aggregation for Multi-Source Domain Adaptation](https://mlsanity.com/paper/2007.08801/) (2020)
- [KD3A: Unsupervised Multi-Source Decentralized Domain Adaptation via Knowledge Distillation](https://mlsanity.com/paper/2011.09757/) (2020)
- [Wasserstein Dictionary Learning: Optimal Transport-based unsupervised non-linear dictionary learning](https://mlsanity.com/paper/1708.01955/) (2017)
- [Multi-source Domain Adaptation via Weighted Joint Distributions Optimal Transport](https://mlsanity.com/paper/2006.12938/) (2020)
- [Multi-Source Domain Adaptation through Dataset Dictionary Learning in Wasserstein Space](https://mlsanity.com/paper/2307.14953/) (2023)
- [Multi-Source Domain Adaptation meets Dataset Distillation through Dataset Dictionary Learning](https://mlsanity.com/paper/2309.07666/) (2023)
- [Federated Dataset Dictionary Learning for Multi-Source Domain Adaptation](https://mlsanity.com/paper/2309.07670/) (2023)
- [Optimal Transport for Domain Adaptation through Gaussian Mixture Models](https://mlsanity.com/paper/2403.13847/) (2024)

## Built on by (most cited first, 5 of 5)

- [Slicing the Gaussian Mixture Wasserstein Distance](https://mlsanity.com/paper/2504.08544/) (2025)
- [Wasserstein Gradient Flows for Scalable and Regularized Barycenter Computation](https://mlsanity.com/paper/2510.04602/) (2025)
- [Online Multi-Source Domain Adaptation through Gaussian Mixtures and Dataset Dictionary Learning](https://mlsanity.com/paper/2407.19853/) (2024)
- [Differentiable Expectation-Maximisation and Applications to Gaussian Mixture Model Optimal Transport](https://mlsanity.com/paper/2509.02109/) (2025)
- [DeFed-GMM-DaDiL: A Decentralized Federated Framework for Domain Adaptation](https://mlsanity.com/paper/2605.04324/) (2026)

## Abstract (arXiv)

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-Wasserstein Barycenter Transport (WBT) and GMM-Dataset Dictionary Learning (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. Our code is publicly available at https://github.com/eddardd/gmm_msda