Learning to Match Unpaired Data with Minimum Entropy Coupling

Mustapha Bounoua, Giulio Franzese, Pietro Michiardi
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:5218-5240, 2025.

Abstract

Multimodal data is a precious asset enabling a variety of downstream tasks in machine learning. However, real-world data collected across different modalities is often not paired, which is a significant challenge to learn a joint distribution. A prominent approach to address the modality coupling problem is Minimum Entropy Coupling (MEC), which seeks to minimize the joint Entropy, while satisfying constraints on the marginals. Existing approaches to the MEC problem focus on finite, discrete distributions, limiting their application for cases involving continuous data. In this work, we propose a novel method to solve the continuous MEC problem, using well-known generative diffusion models that learn to approximate and minimize the joint Entropy through a cooperative scheme, while satisfying a relaxed version of the marginal constraints. We empirically demonstrate that our method, DDMEC, is general and can be easily used to address challenging tasks, including unsupervised single-cell multi-omics data alignment and unpaired image translation, outperforming specialized methods.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-bounoua25a, title = {Learning to Match Unpaired Data with Minimum Entropy Coupling}, author = {Bounoua, Mustapha and Franzese, Giulio and Michiardi, Pietro}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {5218--5240}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/bounoua25a/bounoua25a.pdf}, url = {https://proceedings.mlr.press/v267/bounoua25a.html}, abstract = {Multimodal data is a precious asset enabling a variety of downstream tasks in machine learning. However, real-world data collected across different modalities is often not paired, which is a significant challenge to learn a joint distribution. A prominent approach to address the modality coupling problem is Minimum Entropy Coupling (MEC), which seeks to minimize the joint Entropy, while satisfying constraints on the marginals. Existing approaches to the MEC problem focus on finite, discrete distributions, limiting their application for cases involving continuous data. In this work, we propose a novel method to solve the continuous MEC problem, using well-known generative diffusion models that learn to approximate and minimize the joint Entropy through a cooperative scheme, while satisfying a relaxed version of the marginal constraints. We empirically demonstrate that our method, DDMEC, is general and can be easily used to address challenging tasks, including unsupervised single-cell multi-omics data alignment and unpaired image translation, outperforming specialized methods.} }
Endnote
%0 Conference Paper %T Learning to Match Unpaired Data with Minimum Entropy Coupling %A Mustapha Bounoua %A Giulio Franzese %A Pietro Michiardi %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-bounoua25a %I PMLR %P 5218--5240 %U https://proceedings.mlr.press/v267/bounoua25a.html %V 267 %X Multimodal data is a precious asset enabling a variety of downstream tasks in machine learning. However, real-world data collected across different modalities is often not paired, which is a significant challenge to learn a joint distribution. A prominent approach to address the modality coupling problem is Minimum Entropy Coupling (MEC), which seeks to minimize the joint Entropy, while satisfying constraints on the marginals. Existing approaches to the MEC problem focus on finite, discrete distributions, limiting their application for cases involving continuous data. In this work, we propose a novel method to solve the continuous MEC problem, using well-known generative diffusion models that learn to approximate and minimize the joint Entropy through a cooperative scheme, while satisfying a relaxed version of the marginal constraints. We empirically demonstrate that our method, DDMEC, is general and can be easily used to address challenging tasks, including unsupervised single-cell multi-omics data alignment and unpaired image translation, outperforming specialized methods.
APA
Bounoua, M., Franzese, G. & Michiardi, P.. (2025). Learning to Match Unpaired Data with Minimum Entropy Coupling. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:5218-5240 Available from https://proceedings.mlr.press/v267/bounoua25a.html.

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