[Paper Review] Optimal Transport for Multi-source Domain Adaptation under Target Shift

Ievgen Redko, Courty, Nicolas+2 more|Socio-Environmental Systems Modeling|Mar 13, 2018

Domain Adaptation and Few-Shot Learning26 references15 citations

TL;DR

This paper proposes JCPOT, a novel optimal transport-based method for multi-source domain adaptation under target shift, jointly estimating class proportions in the unlabeled target domain and learning domain alignments. It outperforms state-of-the-art methods on synthetic and real-world satellite image classification tasks, achieving up to 10% accuracy gain over baseline models.

ABSTRACT

In this paper, we propose to tackle the problem of reducing discrepancies between multiple domains referred to as multi-source domain adaptation and consider it under the target shift assumption: in all domains we aim to solve a classification problem with the same output classes, but with labels' proportions differing across them. This problem, generally ignored in the vast majority papers on domain adaptation papers, is nevertheless critical in real-world applications, and we theoretically show its impact on the adaptation success. To address this issue, we design a method based on optimal transport, a theory that has been successfully used to tackle adaptation problems in machine learning. Our method performs multi-source adaptation and target shift correction simultaneously by learning the class probabilities of the unlabeled target sample and the coupling allowing to align two (or more) probability distributions. Experiments on both synthetic and real-world data related to satellite image segmentation task show the superiority of the proposed method over the state-of-the-art.

Motivation & Objective

• To address the critical yet often overlooked problem of target shift in multi-source domain adaptation, where source and target domains have mismatched class proportions.
• To develop a method that simultaneously estimates unknown target class proportions and aligns source and target domain distributions using optimal transport.
• To improve adaptation performance in real-world applications—especially remote sensing—where class imbalance across spatial domains is common.
• To extend optimal transport frameworks to handle multi-source settings under unsupervised target shift, avoiding reliance on prior knowledge of class proportions.

Proposed method

• JCPOT jointly optimizes for the class proportions of the unlabeled target domain and the optimal transport coupling between source and target distributions.
• It formulates the adaptation problem as a Wasserstein barycenter computation, enabling alignment across multiple source domains and a single target domain.
• The method uses label propagation to refine predictions and improve generalization, especially in low-resource target settings.
• It leverages the computational efficiency of entropic regularization in optimal transport to scale to high-dimensional data like satellite image superpixels.
• The framework is trained end-to-end using a differentiable objective that balances domain alignment and proportion estimation.
• It avoids assumptions about prior knowledge of target class distributions, making it suitable for real-world unsupervised adaptation.

Experimental results

Research questions

• RQ1 How does target shift—specifically mismatched class proportions between source and target domains—affect the performance of standard domain adaptation methods?
• RQ2 Can optimal transport be effectively extended to jointly estimate target class proportions and align multi-source domains under target shift?
• RQ3 To what extent does joint estimation of proportions and domain alignment improve classification accuracy compared to separate or sequential approaches?
• RQ4 How does JCPOT perform relative to state-of-the-art methods in both synthetic and real-world remote sensing applications?
• RQ5 Can the method scale effectively to high-dimensional data such as superpixel features from very high-resolution satellite images?

Key findings

• On the Zurich Summer satellite image dataset, JCPOT-LP achieved a 10% improvement in classification accuracy over the 'No adaptation' baseline.
• JCPOT-LP outperformed the 'Target only' baseline, demonstrating the benefit of leveraging multiple source domains after proper adaptation.
• In multi-source synthetic experiments, JCPOT achieved the best F1-score of 0.673 on the 14th configuration, outperforming all baselines.
• The method showed consistent performance gains as the number of source domains increased, confirming its scalability and robustness.
• JCPOT’s performance closely matched that of a method with a priori knowledge of class proportions, indicating accurate and reliable estimation of unknown target distributions.
• The method achieved state-of-the-art results across all evaluated configurations, with the highest F1-scores consistently reported for JCPOT-LP.