Your copula is a classifier in disguise: classification-based copula density estimation

David Huk, Mark Steel, Ritabrata Dutta
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:3790-3798, 2025.

Abstract

We propose reinterpreting copula density estimation as a discriminative task. Under this novel estimation scheme, we train a classifier to distinguish samples from the joint density from those of the product of independent marginals, recovering the copula density in the process. We derive equivalences between well-known copula classes and classification problems naturally arising in our interpretation. Furthermore, we show our estimator achieves theoretical guarantees akin to maximum likelihood estimation. By identifying a connection with density ratio estimation, we benefit from the rich literature and models available for such problems. Empirically, we demonstrate the applicability of our approach by estimating copulas of real and high-dimensional datasets, outperforming competing copula estimators in density evaluation as well as sampling.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-huk25a, title = {Your copula is a classifier in disguise: classification-based copula density estimation}, author = {Huk, David and Steel, Mark and Dutta, Ritabrata}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {3790--3798}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/huk25a/huk25a.pdf}, url = {https://proceedings.mlr.press/v258/huk25a.html}, abstract = {We propose reinterpreting copula density estimation as a discriminative task. Under this novel estimation scheme, we train a classifier to distinguish samples from the joint density from those of the product of independent marginals, recovering the copula density in the process. We derive equivalences between well-known copula classes and classification problems naturally arising in our interpretation. Furthermore, we show our estimator achieves theoretical guarantees akin to maximum likelihood estimation. By identifying a connection with density ratio estimation, we benefit from the rich literature and models available for such problems. Empirically, we demonstrate the applicability of our approach by estimating copulas of real and high-dimensional datasets, outperforming competing copula estimators in density evaluation as well as sampling.} }
Endnote
%0 Conference Paper %T Your copula is a classifier in disguise: classification-based copula density estimation %A David Huk %A Mark Steel %A Ritabrata Dutta %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-huk25a %I PMLR %P 3790--3798 %U https://proceedings.mlr.press/v258/huk25a.html %V 258 %X We propose reinterpreting copula density estimation as a discriminative task. Under this novel estimation scheme, we train a classifier to distinguish samples from the joint density from those of the product of independent marginals, recovering the copula density in the process. We derive equivalences between well-known copula classes and classification problems naturally arising in our interpretation. Furthermore, we show our estimator achieves theoretical guarantees akin to maximum likelihood estimation. By identifying a connection with density ratio estimation, we benefit from the rich literature and models available for such problems. Empirically, we demonstrate the applicability of our approach by estimating copulas of real and high-dimensional datasets, outperforming competing copula estimators in density evaluation as well as sampling.
APA
Huk, D., Steel, M. & Dutta, R.. (2025). Your copula is a classifier in disguise: classification-based copula density estimation. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:3790-3798 Available from https://proceedings.mlr.press/v258/huk25a.html.

Related Material