Beyond Mean-Field: Tree-Copula Variational Autoencoders for Structured Latent Dependencies

Yarden Rachamim, Shai Fine
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:5601-5622, 2026.

Abstract

Variational Autoencoders (VAEs) typically assume a factorized {Gaussian} posterior and isotropic normal prior, implicitly imposing mean-field independence in the latent space. Rewriting the {ELBO} in copula form, we isolate a dependence-mismatch term that contributes to approximation and amortization gaps. We propose a Tree-Copula VAE that replaces the mean-field posterior with a tree-structured copula while retaining flexible learned marginals. The tree is inferred per datapoint via a Chow–Liu maximum-weight spanning tree, exploiting the monotonic relationship between mutual information and copula parameters. We further study an Average-of-Trees (AoT) copula prior for prior–posterior alignment and a rank-1 {Gaussian}-copula likelihood for low-rank observation correlations. Experiments on correlated dSprites and Fashion-{MNIST} show tighter importance-weighted bounds than mean-field VAEs when latent dependence is present, and highlight the role of prior alignment and likelihood modeling beyond mean-field inference.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-rachamim26a, title = {Beyond Mean-Field: Tree-Copula Variational Autoencoders for Structured Latent Dependencies}, author = {Rachamim, Yarden and Fine, Shai}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {5601--5622}, year = {2026}, editor = {Perković, Emilija and Malinsky, Daniel}, volume = {337}, series = {Proceedings of Machine Learning Research}, month = {17--21 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v337/main/assets/rachamim26a/rachamim26a.pdf}, url = {https://proceedings.mlr.press/v337/rachamim26a.html}, abstract = {Variational Autoencoders (VAEs) typically assume a factorized {Gaussian} posterior and isotropic normal prior, implicitly imposing mean-field independence in the latent space. Rewriting the {ELBO} in copula form, we isolate a dependence-mismatch term that contributes to approximation and amortization gaps. We propose a Tree-Copula VAE that replaces the mean-field posterior with a tree-structured copula while retaining flexible learned marginals. The tree is inferred per datapoint via a Chow–Liu maximum-weight spanning tree, exploiting the monotonic relationship between mutual information and copula parameters. We further study an Average-of-Trees (AoT) copula prior for prior–posterior alignment and a rank-1 {Gaussian}-copula likelihood for low-rank observation correlations. Experiments on correlated dSprites and Fashion-{MNIST} show tighter importance-weighted bounds than mean-field VAEs when latent dependence is present, and highlight the role of prior alignment and likelihood modeling beyond mean-field inference.} }
Endnote
%0 Conference Paper %T Beyond Mean-Field: Tree-Copula Variational Autoencoders for Structured Latent Dependencies %A Yarden Rachamim %A Shai Fine %B Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Emilija Perković %E Daniel Malinsky %F pmlr-v337-rachamim26a %I PMLR %P 5601--5622 %U https://proceedings.mlr.press/v337/rachamim26a.html %V 337 %X Variational Autoencoders (VAEs) typically assume a factorized {Gaussian} posterior and isotropic normal prior, implicitly imposing mean-field independence in the latent space. Rewriting the {ELBO} in copula form, we isolate a dependence-mismatch term that contributes to approximation and amortization gaps. We propose a Tree-Copula VAE that replaces the mean-field posterior with a tree-structured copula while retaining flexible learned marginals. The tree is inferred per datapoint via a Chow–Liu maximum-weight spanning tree, exploiting the monotonic relationship between mutual information and copula parameters. We further study an Average-of-Trees (AoT) copula prior for prior–posterior alignment and a rank-1 {Gaussian}-copula likelihood for low-rank observation correlations. Experiments on correlated dSprites and Fashion-{MNIST} show tighter importance-weighted bounds than mean-field VAEs when latent dependence is present, and highlight the role of prior alignment and likelihood modeling beyond mean-field inference.
APA
Rachamim, Y. & Fine, S.. (2026). Beyond Mean-Field: Tree-Copula Variational Autoencoders for Structured Latent Dependencies. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:5601-5622 Available from https://proceedings.mlr.press/v337/rachamim26a.html.

Related Material