Multi-Component VAE with Gaussian Markov Random Field

Fouad Oubari, Mohamed El Baha, Raphaël Meunier, Rodrigue Décatoire, Mathilde MOUGEOT
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:154-162, 2026.

Abstract

Multi-component datasets with intricate dependencies challenge current generative modeling techniques. Existing Multi-component Variational AutoEncoders rely on simplified aggregation strategies that compromise structural coherence across generated components. We introduce the Gaussian Markov Random Field Multi-Component Variational AutoEncoder, embedding Gaussian Markov Random Fields into both prior and posterior distributions to explicitly model cross-component relationships. This enables richer representation and faithful reproduction of complex interactions. Empirically, our model achieves state-of-the-art performance on a synthetic Copula dataset designed for intricate component relationships, competitive results on PolyMNIST, and significantly enhanced structural coherence on the real-world BIKED dataset, demonstrating its suitability for applications demanding robust multi-component coherence.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-oubari26a, title = { Multi-Component VAE with Gaussian Markov Random Field }, author = {Oubari, Fouad and El Baha, Mohamed and Meunier, Rapha{\"e}l and D{\'e}catoire, Rodrigue and MOUGEOT, Mathilde}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {154--162}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/oubari26a/oubari26a.pdf}, url = {https://proceedings.mlr.press/v300/oubari26a.html}, abstract = { Multi-component datasets with intricate dependencies challenge current generative modeling techniques. Existing Multi-component Variational AutoEncoders rely on simplified aggregation strategies that compromise structural coherence across generated components. We introduce the Gaussian Markov Random Field Multi-Component Variational AutoEncoder, embedding Gaussian Markov Random Fields into both prior and posterior distributions to explicitly model cross-component relationships. This enables richer representation and faithful reproduction of complex interactions. Empirically, our model achieves state-of-the-art performance on a synthetic Copula dataset designed for intricate component relationships, competitive results on PolyMNIST, and significantly enhanced structural coherence on the real-world BIKED dataset, demonstrating its suitability for applications demanding robust multi-component coherence. } }
Endnote
%0 Conference Paper %T Multi-Component VAE with Gaussian Markov Random Field %A Fouad Oubari %A Mohamed El Baha %A Raphaël Meunier %A Rodrigue Décatoire %A Mathilde MOUGEOT %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-oubari26a %I PMLR %P 154--162 %U https://proceedings.mlr.press/v300/oubari26a.html %V 300 %X Multi-component datasets with intricate dependencies challenge current generative modeling techniques. Existing Multi-component Variational AutoEncoders rely on simplified aggregation strategies that compromise structural coherence across generated components. We introduce the Gaussian Markov Random Field Multi-Component Variational AutoEncoder, embedding Gaussian Markov Random Fields into both prior and posterior distributions to explicitly model cross-component relationships. This enables richer representation and faithful reproduction of complex interactions. Empirically, our model achieves state-of-the-art performance on a synthetic Copula dataset designed for intricate component relationships, competitive results on PolyMNIST, and significantly enhanced structural coherence on the real-world BIKED dataset, demonstrating its suitability for applications demanding robust multi-component coherence.
APA
Oubari, F., El Baha, M., Meunier, R., Décatoire, R. & MOUGEOT, M.. (2026). Multi-Component VAE with Gaussian Markov Random Field . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:154-162 Available from https://proceedings.mlr.press/v300/oubari26a.html.

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