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 ability to perform efficient inference, and can be prohibitive even for relatively modest domains. Recently, we introduced the Copula Bayesian Network (CBN) density model - a flexible framework that captures complex high-dimensional dependency structures while offering direct control over the univariate marginals, leading to improved generalization. In this work we show that the CBN model also offers significant computational advantages when training data is partially observed. Concretely, we leverage on the specialized form of the model to derive a computationally amenable learning objective that is a lower bound on the log-likelihood function. Importantly, our energy-like bound circumvents the need for costly inference of an auxiliary distribution, thus facilitating practical learning of high-dimensional densities. We demonstrate the effectiveness of our approach for learning the structure 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 ability to perform efficient inference, and can be prohibitive even for relatively modest domains. Recently, we introduced the Copula Bayesian Network (CBN) density model - a flexible framework that captures complex high-dimensional dependency structures while offering direct control over the univariate marginals, leading to improved generalization. In this work we show that the CBN model also offers significant computational advantages when training data is partially observed. Concretely, we leverage on the specialized form of the model to derive a computationally amenable learning objective that is a lower bound on the log-likelihood function. Importantly, our energy-like bound circumvents the need for costly inference of an auxiliary distribution, thus facilitating practical learning of high-dimensional densities. We demonstrate the effectiveness of our approach for learning the structure 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 ability to perform efficient inference, and can be prohibitive even for relatively modest domains. Recently, we introduced the Copula Bayesian Network (CBN) density model - a flexible framework that captures complex high-dimensional dependency structures while offering direct control over the univariate marginals, leading to improved generalization. In this work we show that the CBN model also offers significant computational advantages when training data is partially observed. Concretely, we leverage on the specialized form of the model to derive a computationally amenable learning objective that is a lower bound on the log-likelihood function. Importantly, our energy-like bound circumvents the need for costly inference of an auxiliary distribution, thus facilitating practical learning of high-dimensional densities. We demonstrate the effectiveness of our approach for learning the structure 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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