Learning the Causal Structure of Copula Models with Latent Variables

Ruifei Cui, Perry Groot, Moritz Schauer, Tom Heskes
Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence, PMLR R16:187-196, 2018.

Abstract

A common goal in psychometrics, sociology, and econometrics is to uncover causal relations among latent variables representing hypothetical constructs that cannot be measured directly, such as attitude, intelligence, and motivation. Through measurement models, these constructs are typically linked to measurable indicators, e.g., responses to questionnaire items. This paper addresses the problem of causal structure learning among such latent variables and other observed variables. We propose the ‘Copula Factor PC’ algorithm as a novel two-step approach. It first draws samples of the underlying correlation matrix in a Gaussian copula factor model via a Gibbs sampler on rank-based data. These are then translated into an average correlation matrix and an effective sample size, which are taken as input to the standard PC algorithm for causal discovery in the second step. We prove the consistency of our ‘Copula Factor PC’ algorithm, and demonstrate that it outperforms the PC-MIMBuild algorithm and a greedy step-wise approach. We illustrate our method on a real-world data set about children with Attention Deficit Hyperactivity Disorder.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR16-cui18a, title = {Learning the Causal Structure of Copula Models with Latent Variables}, author = {Cui, Ruifei and Groot, Perry and Schauer, Moritz and Heskes, Tom}, booktitle = {Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence}, pages = {187--196}, year = {2018}, editor = {Globerson, Amir and Silva, Ricardo}, volume = {R16}, series = {Proceedings of Machine Learning Research}, month = {06--10 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r16/main/assets/cui18a/cui18a.pdf}, url = {https://proceedings.mlr.press/r16/cui18a.html}, abstract = {A common goal in psychometrics, sociology, and econometrics is to uncover causal relations among latent variables representing hypothetical constructs that cannot be measured directly, such as attitude, intelligence, and motivation. Through measurement models, these constructs are typically linked to measurable indicators, e.g., responses to questionnaire items. This paper addresses the problem of causal structure learning among such latent variables and other observed variables. We propose the ‘Copula Factor PC’ algorithm as a novel two-step approach. It first draws samples of the underlying correlation matrix in a Gaussian copula factor model via a Gibbs sampler on rank-based data. These are then translated into an average correlation matrix and an effective sample size, which are taken as input to the standard PC algorithm for causal discovery in the second step. We prove the consistency of our ‘Copula Factor PC’ algorithm, and demonstrate that it outperforms the PC-MIMBuild algorithm and a greedy step-wise approach. We illustrate our method on a real-world data set about children with Attention Deficit Hyperactivity Disorder.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Learning the Causal Structure of Copula Models with Latent Variables %A Ruifei Cui %A Perry Groot %A Moritz Schauer %A Tom Heskes %B Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2018 %E Amir Globerson %E Ricardo Silva %F pmlr-vR16-cui18a %I PMLR %P 187--196 %U https://proceedings.mlr.press/r16/cui18a.html %V R16 %X A common goal in psychometrics, sociology, and econometrics is to uncover causal relations among latent variables representing hypothetical constructs that cannot be measured directly, such as attitude, intelligence, and motivation. Through measurement models, these constructs are typically linked to measurable indicators, e.g., responses to questionnaire items. This paper addresses the problem of causal structure learning among such latent variables and other observed variables. We propose the ‘Copula Factor PC’ algorithm as a novel two-step approach. It first draws samples of the underlying correlation matrix in a Gaussian copula factor model via a Gibbs sampler on rank-based data. These are then translated into an average correlation matrix and an effective sample size, which are taken as input to the standard PC algorithm for causal discovery in the second step. We prove the consistency of our ‘Copula Factor PC’ algorithm, and demonstrate that it outperforms the PC-MIMBuild algorithm and a greedy step-wise approach. We illustrate our method on a real-world data set about children with Attention Deficit Hyperactivity Disorder. %Z Reissued by PMLR on 04 October 2026.
APA
Cui, R., Groot, P., Schauer, M. & Heskes, T.. (2018). Learning the Causal Structure of Copula Models with Latent Variables. Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R16:187-196 Available from https://proceedings.mlr.press/r16/cui18a.html. Reissued by PMLR on 04 October 2026.

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