Inference-less Density Estimation using Copula Networks

Gal Elidan
Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence, PMLR R8:167-175, 2010.

Abstract

We consider learning continuous probabilistic graphical models in the face of missing data. For non-Gaussian models, learning the parameters and structure of such models depends on our abil- ity to perform efficient inference, and can be pro- hibitive even for relatively modest domains. Re- cently, we introduced the Copula Bayesian Net- work (CBN) density model - a flexible frame- work that captures complex high-dimensional dependency structures while offering direct con- trol over the univariate marginals, leading to im- proved generalization. In this work we show that the CBN model also offers significant computa- tional advantages when training data is partially observed. Concretely, we leverage on the spe- cialized form of the model to derive a compu- tationally amenable learning objective that is a lower bound on the log-likelihood function. Im- portantly, our energy-like bound circumvents the need for costly inference of an auxiliary distribu- tion, thus facilitating practical learning of high- dimensional densities. We demonstrate the effec- tiveness of our approach for learning the struc- ture and parameters of a CBN model for two real- life continuous domains.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR8-elidan10a, title = {Inference-less Density Estimation using Copula Networks}, author = {Elidan, Gal}, booktitle = {Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence}, pages = {167--175}, year = {2010}, editor = {Grünwald, Peter and Spirtes, Peter}, volume = {R8}, series = {Proceedings of Machine Learning Research}, month = {08--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r8/main/assets/elidan10a/elidan10a.pdf}, url = {https://proceedings.mlr.press/r8/elidan10a.html}, abstract = {We consider learning continuous probabilistic graphical models in the face of missing data. For non-Gaussian models, learning the parameters and structure of such models depends on our abil- ity to perform efficient inference, and can be pro- hibitive even for relatively modest domains. Re- cently, we introduced the Copula Bayesian Net- work (CBN) density model - a flexible frame- work that captures complex high-dimensional dependency structures while offering direct con- trol over the univariate marginals, leading to im- proved generalization. In this work we show that the CBN model also offers significant computa- tional advantages when training data is partially observed. Concretely, we leverage on the spe- cialized form of the model to derive a compu- tationally amenable learning objective that is a lower bound on the log-likelihood function. Im- portantly, our energy-like bound circumvents the need for costly inference of an auxiliary distribu- tion, thus facilitating practical learning of high- dimensional densities. We demonstrate the effec- tiveness of our approach for learning the struc- ture and parameters of a CBN model for two real- life continuous domains.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Inference-less Density Estimation using Copula Networks %A Gal Elidan %B Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2010 %E Peter Grünwald %E Peter Spirtes %F pmlr-vR8-elidan10a %I PMLR %P 167--175 %U https://proceedings.mlr.press/r8/elidan10a.html %V R8 %X We consider learning continuous probabilistic graphical models in the face of missing data. For non-Gaussian models, learning the parameters and structure of such models depends on our abil- ity to perform efficient inference, and can be pro- hibitive even for relatively modest domains. Re- cently, we introduced the Copula Bayesian Net- work (CBN) density model - a flexible frame- work that captures complex high-dimensional dependency structures while offering direct con- trol over the univariate marginals, leading to im- proved generalization. In this work we show that the CBN model also offers significant computa- tional advantages when training data is partially observed. Concretely, we leverage on the spe- cialized form of the model to derive a compu- tationally amenable learning objective that is a lower bound on the log-likelihood function. Im- portantly, our energy-like bound circumvents the need for costly inference of an auxiliary distribu- tion, thus facilitating practical learning of high- dimensional densities. We demonstrate the effec- tiveness of our approach for learning the struc- ture and parameters of a CBN model for two real- life continuous domains. %Z Reissued by PMLR on 04 October 2026.
APA
Elidan, G.. (2010). Inference-less Density Estimation using Copula Networks. Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R8:167-175 Available from https://proceedings.mlr.press/r8/elidan10a.html. Reissued by PMLR on 04 October 2026.

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